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Maybe this chapter I'm going to spend about two lectures in order to cover these objectives. 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A scatter plot can be used to show the relationship between two variables. For example, imagine that we have a random sample of 10 children. 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The second, we have to know the direction of the relationship. This direction might be positive or negative relationship. 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Also, we can determine the direction of the relationship. We can say there exists positive or negative based on the scatter plot. Also, we can know the strength of the relationship, either strong, moderate or weak. 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Here we can know the direction. 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And it's easy to make scatter plots for Y versus X. In Chapter 3, we talked about correlation, so correlation was first presented in Chapter 3. But here I will give just a review for computation about", "tokens": [2747, 1161, 28609, 645, 700, 8212, 294, 18874, 568, 11, 293, 321, 30193, 11, 498, 291, 1604, 11, 18874, 568, 13, 400, 309, 311, 1858, 281, 652, 34951, 28609, 337, 398, 5717, 1783, 13, 682, 18874, 805, 11, 321, 2825, 466, 20009, 11, 370, 20009, 390, 700, 8212, 294, 18874, 805, 13, 583, 510, 286, 486, 976, 445, 257, 3131, 337, 24903, 466], "avg_logprob": -0.2110595719423145, "compression_ratio": 1.6153846153846154, "no_speech_prob": 0.0, "words": [{"start": 518.38, "end": 518.94, "word": " Scatter", "probability": 0.7314453125}, {"start": 518.94, "end": 519.2, "word": " plots", "probability": 0.86572265625}, {"start": 519.2, "end": 519.58, "word": " were", "probability": 0.86376953125}, {"start": 519.58, "end": 520.1, "word": " first", "probability": 0.87890625}, {"start": 520.1, "end": 520.74, "word": " presented", "probability": 0.75439453125}, {"start": 520.74, "end": 521.06, "word": " in", "probability": 0.94091796875}, {"start": 521.06, "end": 521.4, "word": " Chapter", "probability": 0.3232421875}, {"start": 521.4, "end": 521.8, "word": " 2,", "probability": 0.5947265625}, {"start": 522.12, "end": 522.36, "word": " and", "probability": 0.9111328125}, {"start": 522.36, "end": 522.76, "word": " we", "probability": 0.95556640625}, {"start": 522.76, "end": 523.48, "word": " skipped,", "probability": 0.83544921875}, {"start": 523.6, "end": 523.72, "word": " if", "probability": 0.93603515625}, {"start": 523.72, "end": 523.78, "word": " you", "probability": 0.96435546875}, {"start": 523.78, "end": 524.0, "word": " remember,", "probability": 0.880859375}, {"start": 524.14, "end": 524.3, "word": " Chapter", "probability": 0.87841796875}, {"start": 524.3, "end": 524.58, "word": " 2.", "probability": 0.99609375}, {"start": 525.72, "end": 526.12, "word": " And", "probability": 0.75830078125}, {"start": 526.12, "end": 526.48, "word": " it's", "probability": 0.9541015625}, {"start": 526.48, "end": 526.78, "word": " easy", "probability": 0.8720703125}, {"start": 526.78, "end": 527.4, "word": " to", "probability": 0.9697265625}, {"start": 527.4, "end": 528.48, "word": " make", "probability": 0.8466796875}, {"start": 528.48, "end": 528.86, "word": " scatter", "probability": 0.9306640625}, {"start": 528.86, "end": 529.14, "word": " plots", "probability": 0.81591796875}, {"start": 529.14, "end": 529.36, "word": " for", "probability": 0.94482421875}, {"start": 529.36, "end": 529.56, "word": " Y", "probability": 0.62890625}, {"start": 529.56, "end": 529.88, "word": " versus", "probability": 0.8740234375}, {"start": 529.88, "end": 530.28, "word": " X.", "probability": 0.9951171875}, {"start": 531.1, "end": 531.26, "word": " In", "probability": 0.8427734375}, {"start": 531.26, "end": 531.48, "word": " Chapter", "probability": 0.88818359375}, {"start": 531.48, "end": 531.86, "word": " 3,", "probability": 0.98681640625}, {"start": 532.24, "end": 532.62, "word": " we", "probability": 0.9609375}, {"start": 532.62, "end": 533.74, "word": " talked", "probability": 0.87548828125}, {"start": 533.74, "end": 534.1, "word": " about", "probability": 0.90673828125}, {"start": 534.1, "end": 534.6, "word": " correlation,", "probability": 0.572265625}, {"start": 534.76, "end": 534.88, "word": " so", "probability": 0.9521484375}, {"start": 534.88, "end": 535.36, "word": " correlation", "probability": 0.9296875}, {"start": 535.36, "end": 536.14, "word": " was", "probability": 0.94970703125}, {"start": 536.14, "end": 536.44, "word": " first", "probability": 0.8603515625}, {"start": 536.44, "end": 536.9, "word": " presented", "probability": 0.775390625}, {"start": 536.9, "end": 537.12, "word": " in", "probability": 0.93359375}, {"start": 537.12, "end": 537.3, "word": " Chapter", "probability": 0.91357421875}, {"start": 537.3, "end": 537.66, "word": " 3.", "probability": 0.99609375}, {"start": 538.42, "end": 538.62, "word": " But", "probability": 0.9501953125}, {"start": 538.62, "end": 538.76, "word": " here", "probability": 0.82421875}, {"start": 538.76, "end": 538.88, "word": " I", "probability": 0.572265625}, {"start": 538.88, "end": 538.96, "word": " will", "probability": 0.853515625}, {"start": 538.96, "end": 539.2, "word": " give", "probability": 0.7666015625}, {"start": 539.2, "end": 540.06, "word": " just", "probability": 0.8798828125}, {"start": 540.06, "end": 542.6, "word": " a", "probability": 0.50244140625}, {"start": 542.6, "end": 543.48, "word": " review", "probability": 0.83642578125}, {"start": 543.48, "end": 544.08, "word": " for", "probability": 0.9453125}, {"start": 544.08, "end": 545.44, "word": " computation", "probability": 0.73486328125}, {"start": 545.44, "end": 545.94, "word": " about", "probability": 0.9033203125}], "temperature": 1.0}, {"id": 22, "seek": 56998, "start": 546.46, "end": 569.98, "text": " correlation coefficient or coefficient of correlation. First, coefficient of correlation measures the relative strength of the linear relationship between two numerical variables. So here, we are talking about numerical variables. Sample correlation coefficient is given by this equation.", "tokens": [20009, 17619, 420, 17619, 295, 20009, 13, 2386, 11, 17619, 295, 20009, 8000, 264, 4972, 3800, 295, 264, 8213, 2480, 1296, 732, 29054, 9102, 13, 407, 510, 11, 321, 366, 1417, 466, 29054, 9102, 13, 4832, 781, 20009, 17619, 307, 2212, 538, 341, 5367, 13], "avg_logprob": -0.16601561852123425, "compression_ratio": 1.9266666666666667, "no_speech_prob": 0.0, "words": [{"start": 546.46, "end": 547.24, "word": " correlation", "probability": 0.61328125}, {"start": 547.24, "end": 548.12, "word": " coefficient", "probability": 0.75439453125}, {"start": 548.12, "end": 548.46, "word": " or", "probability": 0.71484375}, {"start": 548.46, "end": 548.96, "word": " coefficient", "probability": 0.91259765625}, {"start": 548.96, "end": 549.18, "word": " of", "probability": 0.93017578125}, {"start": 549.18, "end": 549.64, "word": " correlation.", "probability": 0.912109375}, {"start": 550.82, "end": 551.46, "word": " First,", "probability": 0.70703125}, {"start": 552.8, "end": 553.48, "word": " coefficient", "probability": 0.8310546875}, {"start": 553.48, "end": 553.7, "word": " of", "probability": 0.461669921875}, {"start": 553.7, "end": 554.1, "word": " correlation", "probability": 0.91650390625}, {"start": 554.1, "end": 554.52, "word": " measures", "probability": 0.810546875}, {"start": 554.52, "end": 555.24, "word": " the", "probability": 0.88623046875}, {"start": 555.24, "end": 555.68, "word": " relative", "probability": 0.78466796875}, {"start": 555.68, "end": 556.24, "word": " strength", "probability": 0.849609375}, {"start": 556.24, "end": 557.68, "word": " of", "probability": 0.90869140625}, {"start": 557.68, "end": 558.04, "word": " the", "probability": 0.89306640625}, {"start": 558.04, "end": 558.58, "word": " linear", "probability": 0.89599609375}, {"start": 558.58, "end": 559.32, "word": " relationship", "probability": 0.9150390625}, {"start": 559.32, "end": 559.68, "word": " between", "probability": 0.8759765625}, {"start": 559.68, "end": 559.92, "word": " two", "probability": 0.90625}, {"start": 559.92, "end": 560.34, "word": " numerical", "probability": 0.9541015625}, {"start": 560.34, "end": 560.82, "word": " variables.", "probability": 0.9384765625}, {"start": 561.0, "end": 561.12, "word": " So", "probability": 0.919921875}, {"start": 561.12, "end": 561.34, "word": " here,", "probability": 0.68310546875}, {"start": 562.3, "end": 562.66, "word": " we", "probability": 0.95166015625}, {"start": 562.66, "end": 562.86, "word": " are", "probability": 0.93359375}, {"start": 562.86, "end": 563.26, "word": " talking", "probability": 0.84521484375}, {"start": 563.26, "end": 563.74, "word": " about", "probability": 0.8994140625}, {"start": 563.74, "end": 564.62, "word": " numerical", "probability": 0.7900390625}, {"start": 564.62, "end": 565.3, "word": " variables.", "probability": 0.92529296875}, {"start": 567.06, "end": 567.56, "word": " Sample", "probability": 0.92236328125}, {"start": 567.56, "end": 568.08, "word": " correlation", "probability": 0.9228515625}, {"start": 568.08, "end": 568.64, "word": " coefficient", "probability": 0.96630859375}, {"start": 568.64, "end": 568.94, "word": " is", "probability": 0.9482421875}, {"start": 568.94, "end": 569.12, "word": " given", "probability": 0.896484375}, {"start": 569.12, "end": 569.32, "word": " by", "probability": 0.9677734375}, {"start": 569.32, "end": 569.52, "word": " this", "probability": 0.94580078125}, {"start": 569.52, "end": 569.98, "word": " equation.", "probability": 0.97900390625}], "temperature": 1.0}, {"id": 23, "seek": 60072, "start": 571.08, "end": 600.72, "text": " which is sum of the product of xi minus x bar, yi minus y bar, divided by n minus 1 times standard deviation of x times standard deviation of y. We know that x bar and y bar are the means of x and y respectively. And Sx, Sy are the standard deviations of x and y values. And we know this equation before. 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And we know this equation from chapter three. Now again, x bar and y bar are the means. 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"start": 657.89, "end": 686.09, "text": " Some features about the coefficient of correlation. Here rho is the population coefficient of correlation, and R is the sample coefficient of correlation. Either rho or R have the following features. Number one, unity free. It means R has no units. 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And for example, suppose the correlation between these two variables is 0.8. It's unity free, so it's just 0.8. So there is no unit. You cannot say 0.8 kilogram per year or whatever it is. So just 0.8.", "tokens": [400, 3364, 294, 30690, 11, 12357, 294, 924, 13, 400, 337, 1365, 11, 7297, 264, 20009, 1296, 613, 732, 9102, 307, 1958, 13, 23, 13, 467, 311, 18205, 1737, 11, 370, 309, 311, 445, 1958, 13, 23, 13, 407, 456, 307, 572, 4985, 13, 509, 2644, 584, 1958, 13, 23, 21741, 680, 1064, 420, 2035, 309, 307, 13, 407, 445, 1958, 13, 23, 13], "avg_logprob": -0.1860576923076923, "compression_ratio": 1.4846625766871167, "no_speech_prob": 0.0, "words": [{"start": 686.96, "end": 687.32, "word": " And", "probability": 0.457763671875}, {"start": 687.32, "end": 687.92, "word": " weight", "probability": 0.79248046875}, {"start": 687.92, "end": 688.32, "word": " in", "probability": 0.85205078125}, {"start": 688.32, "end": 688.82, "word": " kilograms,", "probability": 0.79443359375}, {"start": 689.3, "end": 689.74, "word": " ages", "probability": 0.56005859375}, {"start": 689.74, "end": 689.96, "word": " in", "probability": 0.45751953125}, {"start": 689.96, "end": 690.3, "word": " years.", "probability": 0.93798828125}, {"start": 692.0, "end": 692.28, "word": " And", "probability": 0.71826171875}, {"start": 692.28, "end": 692.48, "word": " for", "probability": 0.80615234375}, {"start": 692.48, "end": 692.86, "word": " example,", "probability": 0.97216796875}, {"start": 693.0, "end": 693.42, "word": " suppose", "probability": 0.83837890625}, {"start": 693.42, "end": 693.7, "word": " the", "probability": 0.81591796875}, {"start": 693.7, "end": 694.16, "word": " correlation", "probability": 0.91455078125}, {"start": 694.16, "end": 694.66, "word": " between", "probability": 0.88720703125}, {"start": 694.66, "end": 695.52, "word": " these", "probability": 0.8544921875}, {"start": 695.52, "end": 695.74, "word": " two", "probability": 0.89990234375}, {"start": 695.74, "end": 696.16, "word": " variables", "probability": 0.9267578125}, {"start": 696.16, "end": 696.44, "word": " is", "probability": 0.9443359375}, {"start": 696.44, "end": 696.7, "word": " 0", "probability": 0.70703125}, {"start": 696.7, "end": 697.08, "word": ".8.", "probability": 0.9931640625}, {"start": 698.62, "end": 699.12, "word": " It's", "probability": 0.91748046875}, {"start": 699.12, "end": 699.32, "word": " unity", "probability": 0.748046875}, {"start": 699.32, "end": 699.58, "word": " free,", "probability": 0.5390625}, {"start": 699.74, "end": 699.9, "word": " so", "probability": 0.93603515625}, {"start": 699.9, "end": 700.14, "word": " it's", "probability": 0.77490234375}, {"start": 700.14, "end": 700.38, "word": " just", "probability": 0.9189453125}, {"start": 700.38, "end": 700.68, "word": " 0", "probability": 0.951171875}, {"start": 700.68, "end": 701.04, "word": ".8.", "probability": 0.99853515625}, {"start": 701.14, "end": 701.28, "word": " So", "probability": 0.9423828125}, {"start": 701.28, "end": 701.44, "word": " there", "probability": 0.81103515625}, {"start": 701.44, "end": 701.58, "word": " is", "probability": 0.8759765625}, {"start": 701.58, "end": 701.76, "word": " no", "probability": 0.943359375}, {"start": 701.76, "end": 702.0, "word": " unit.", "probability": 0.80078125}, {"start": 702.32, "end": 702.46, "word": " You", "probability": 0.92138671875}, {"start": 702.46, "end": 702.72, "word": " cannot", "probability": 0.87255859375}, {"start": 702.72, "end": 703.18, "word": " say", "probability": 0.94775390625}, {"start": 703.18, "end": 704.18, "word": " 0", "probability": 0.80615234375}, {"start": 704.18, "end": 704.5, "word": ".8", "probability": 0.998779296875}, {"start": 704.5, "end": 704.98, "word": " kilogram", "probability": 0.60302734375}, {"start": 704.98, "end": 705.24, "word": " per", "probability": 0.8388671875}, {"start": 705.24, "end": 705.5, "word": " year", "probability": 0.92578125}, {"start": 705.5, "end": 705.64, "word": " or", "probability": 0.7392578125}, {"start": 705.64, "end": 705.92, "word": " whatever", "probability": 0.94580078125}, {"start": 705.92, "end": 706.18, "word": " it", "probability": 0.78271484375}, {"start": 706.18, "end": 706.32, "word": " is.", "probability": 0.9404296875}, {"start": 706.48, "end": 706.7, "word": " So", "probability": 0.86083984375}, {"start": 706.7, "end": 706.96, "word": " just", "probability": 0.814453125}, {"start": 706.96, "end": 707.3, "word": " 0", "probability": 0.95654296875}, {"start": 707.3, "end": 707.64, "word": ".8.", "probability": 0.9990234375}], "temperature": 1.0}, {"id": 28, "seek": 73552, "start": 709.42, "end": 735.52, "text": " So the first feature of the correlation coefficient is unity-free. Number two ranges between negative one and plus one. So R is always, or rho, is always between minus one and plus one. So minus one smaller than or equal to R smaller than or equal to plus one. So R is always in this range. 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So the same as we had discussed before. Now, some types of scatter plots for different types of relationship between the two variables is presented in this slide. For example, if you look carefully at figure one here, sharp one, this one, and the other one,", "tokens": [440, 8236, 2158, 2709, 264, 3800, 295, 264, 2480, 1296, 264, 732, 9102, 13, 407, 264, 912, 382, 321, 632, 7152, 949, 13, 823, 11, 512, 3467, 295, 34951, 28609, 337, 819, 3467, 295, 2480, 1296, 264, 732, 9102, 307, 8212, 294, 341, 4137, 13, 1171, 1365, 11, 498, 291, 574, 7500, 412, 2573, 472, 510, 11, 8199, 472, 11, 341, 472, 11, 293, 264, 661, 472, 11], "avg_logprob": -0.1651947515598242, "compression_ratio": 1.698019801980198, "no_speech_prob": 0.0, "words": [{"start": 876.72, "end": 876.96, "word": " The", "probability": 0.39453125}, {"start": 876.96, "end": 877.48, "word": " absolute", "probability": 0.88623046875}, {"start": 877.48, "end": 877.92, "word": " value", "probability": 0.970703125}, {"start": 877.92, "end": 878.26, "word": " gives", "probability": 0.9013671875}, {"start": 878.26, "end": 878.64, "word": " the", "probability": 0.88037109375}, {"start": 878.64, "end": 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So if all points fall exactly on the straight line, it means they exist perfect.", "tokens": [682, 1184, 472, 11, 439, 2793, 366, 322, 264, 2997, 1622, 11, 309, 1355, 436, 2514, 2176, 13, 407, 498, 439, 2793, 2100, 2293, 322, 264, 2997, 1622, 11, 309, 1355, 436, 2514, 2176, 13], "avg_logprob": -0.22786458333333334, "compression_ratio": 1.7391304347826086, "no_speech_prob": 0.0, "words": [{"start": 906.76, "end": 907.06, "word": " In", "probability": 0.47412109375}, {"start": 907.06, "end": 907.38, "word": " each", "probability": 0.94677734375}, {"start": 907.38, "end": 907.64, "word": " one,", "probability": 0.921875}, {"start": 908.98, "end": 909.3, "word": " all", "probability": 0.904296875}, {"start": 909.3, "end": 909.72, "word": " points", "probability": 0.94970703125}, {"start": 909.72, "end": 913.02, "word": " are", "probability": 0.9130859375}, {"start": 913.02, "end": 913.28, "word": " on", "probability": 0.927734375}, {"start": 913.28, "end": 913.5, "word": " the", "probability": 0.888671875}, {"start": 913.5, "end": 914.0, "word": " straight", "probability": 0.90234375}, {"start": 914.0, "end": 914.32, "word": " line,", "probability": 0.91650390625}, {"start": 914.44, "end": 914.56, "word": " it", "probability": 0.77294921875}, {"start": 914.56, "end": 914.76, "word": " means", "probability": 0.9287109375}, {"start": 914.76, "end": 914.96, "word": " they", "probability": 0.53564453125}, {"start": 914.96, "end": 915.34, "word": " exist", "probability": 0.9072265625}, {"start": 915.34, "end": 915.82, "word": " perfect.", "probability": 0.5576171875}, {"start": 916.84, "end": 917.16, "word": " So", "probability": 0.896484375}, {"start": 917.16, "end": 917.4, "word": " if", "probability": 0.716796875}, {"start": 917.4, "end": 919.02, "word": " all", "probability": 0.505859375}, {"start": 919.02, "end": 919.56, "word": " points", "probability": 0.908203125}, {"start": 919.56, "end": 920.62, "word": " fall", "probability": 0.297119140625}, {"start": 920.62, "end": 921.1, "word": " exactly", "probability": 0.89111328125}, {"start": 921.1, "end": 921.28, "word": " on", "probability": 0.9384765625}, {"start": 921.28, "end": 921.4, "word": " the", "probability": 0.837890625}, {"start": 921.4, "end": 921.72, "word": " straight", "probability": 0.91357421875}, {"start": 921.72, "end": 922.06, "word": " line,", "probability": 0.9345703125}, {"start": 922.54, "end": 922.74, "word": " it", "probability": 0.94189453125}, {"start": 922.74, "end": 923.02, "word": " means", "probability": 0.93115234375}, {"start": 923.02, "end": 923.2, "word": " they", "probability": 0.72607421875}, {"start": 923.2, "end": 923.62, "word": " exist", "probability": 0.955078125}, {"start": 923.62, "end": 924.22, "word": " perfect.", "probability": 0.8974609375}], "temperature": 1.0}, {"id": 36, "seek": 95092, "start": 931.4, "end": 950.92, "text": " Here there exists perfect negative. So this is perfect negative relationship. The other one perfect positive relationship. In reality you will never see something like perfect positive or perfect negative. Maybe in real situation.", "tokens": [1692, 456, 8198, 2176, 3671, 13, 407, 341, 307, 2176, 3671, 2480, 13, 440, 661, 472, 2176, 3353, 2480, 13, 682, 4103, 291, 486, 1128, 536, 746, 411, 2176, 3353, 420, 2176, 3671, 13, 2704, 294, 957, 2590, 13], "avg_logprob": -0.2535156235098839, "compression_ratio": 1.7769230769230768, "no_speech_prob": 0.0, "words": [{"start": 931.4, "end": 931.68, "word": " Here", "probability": 0.3642578125}, {"start": 931.68, "end": 931.86, "word": " there", "probability": 0.78271484375}, {"start": 931.86, "end": 932.36, "word": " exists", "probability": 0.6572265625}, {"start": 932.36, "end": 932.86, "word": " perfect", "probability": 0.79736328125}, {"start": 932.86, "end": 933.32, "word": " negative.", "probability": 0.533203125}, {"start": 934.4, "end": 934.72, "word": " So", "probability": 0.79541015625}, {"start": 934.72, "end": 935.02, "word": " this", "probability": 0.78662109375}, {"start": 935.02, "end": 935.16, "word": " is", "probability": 0.7001953125}, {"start": 935.16, "end": 935.44, "word": " perfect", "probability": 0.806640625}, {"start": 935.44, "end": 935.98, "word": " negative", "probability": 0.92431640625}, {"start": 935.98, "end": 936.7, "word": " relationship.", "probability": 0.92333984375}, {"start": 937.16, "end": 937.3, "word": " The", "probability": 0.84033203125}, {"start": 937.3, "end": 937.48, "word": " other", "probability": 0.8916015625}, {"start": 937.48, "end": 937.74, "word": " one", "probability": 0.91455078125}, {"start": 937.74, "end": 938.1, "word": " perfect", "probability": 0.430419921875}, {"start": 938.1, "end": 938.62, "word": " positive", "probability": 0.9326171875}, {"start": 938.62, "end": 939.4, "word": " relationship.", "probability": 0.89990234375}, {"start": 940.0, "end": 940.22, "word": " In", "probability": 0.79296875}, {"start": 940.22, "end": 940.68, "word": " reality", "probability": 0.9638671875}, {"start": 940.68, "end": 941.08, "word": " you", "probability": 0.68505859375}, {"start": 941.08, "end": 941.24, "word": " will", "probability": 0.85302734375}, {"start": 941.24, "end": 941.56, "word": " never", "probability": 0.9326171875}, {"start": 941.56, "end": 942.52, "word": " see", "probability": 0.93701171875}, {"start": 942.52, "end": 945.68, "word": " something", "probability": 0.7763671875}, {"start": 945.68, "end": 946.16, "word": " like", "probability": 0.93701171875}, {"start": 946.16, "end": 946.66, "word": " perfect", "probability": 0.91162109375}, {"start": 946.66, "end": 947.26, "word": " positive", "probability": 0.94140625}, {"start": 947.26, "end": 947.52, "word": " or", "probability": 0.95166015625}, {"start": 947.52, "end": 947.88, "word": " perfect", "probability": 0.92041015625}, {"start": 947.88, "end": 948.4, "word": " negative.", "probability": 0.95703125}, {"start": 949.12, "end": 949.38, "word": " Maybe", "probability": 0.52197265625}, {"start": 949.38, "end": 949.6, "word": " in", "probability": 0.83203125}, {"start": 949.6, "end": 950.28, "word": " real", "probability": 0.8193359375}, {"start": 950.28, "end": 950.92, "word": " situation.", "probability": 0.880859375}], "temperature": 1.0}, {"id": 37, "seek": 98121, "start": 951.53, "end": 981.21, "text": " In real situation, most of the time, R is close to 0.9 or 0.85 or something like that, but it's not exactly equal one. Because equal one, it means if you know the value of a child's age, then you can predict the exact weight. And that never happened. If the data looks like this table, for example. 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In this case there exists perfect relationship but that never happened in real life. So perfect means all points are lie on the straight line otherwise if the points are close", "tokens": [407, 1783, 420, 316, 307, 6505, 538, 732, 6815, 337, 1184, 2158, 337, 1184, 2609, 293, 611, 17443, 366, 6505, 538, 1045, 6815, 337, 1184, 954, 13, 682, 341, 1389, 456, 8198, 2176, 2480, 457, 300, 1128, 2011, 294, 957, 993, 13, 407, 2176, 1355, 439, 2793, 366, 4544, 322, 264, 2997, 1622, 5911, 498, 264, 2793, 366, 1998], "avg_logprob": -0.2638020724058151, "compression_ratio": 1.6756756756756757, "no_speech_prob": 0.0, "words": [{"start": 1008.72, "end": 1009.0, "word": " So", "probability": 0.495849609375}, {"start": 1009.0, "end": 1009.4, "word": " X", "probability": 0.43798828125}, {"start": 1009.4, "end": 1009.86, "word": " or", "probability": 0.80810546875}, {"start": 1009.86, "end": 1010.06, "word": " A", "probability": 0.363037109375}, {"start": 1010.06, "end": 1010.18, "word": " is", "probability": 0.62646484375}, {"start": 1010.18, "end": 1010.46, "word": " increased", 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Here I will give a simple example in order to determine the correlation coefficient. A real estate agent wishes to examine the relationship between selling the price of a home", "tokens": [362, 364, 1558, 466, 264, 2480, 1296, 264, 732, 9102, 13, 1692, 286, 486, 976, 257, 2199, 1365, 294, 1668, 281, 6997, 264, 20009, 17619, 13, 316, 957, 9749, 9461, 15065, 281, 17496, 264, 2480, 1296, 6511, 264, 3218, 295, 257, 1280], "avg_logprob": -0.14280522632044415, "compression_ratio": 1.5933333333333333, "no_speech_prob": 0.0, "words": [{"start": 1110.56, "end": 1110.94, "word": " have", "probability": 0.291259765625}, {"start": 1110.94, "end": 1111.18, "word": " an", "probability": 0.94775390625}, {"start": 1111.18, "end": 1111.52, "word": " idea", "probability": 0.92578125}, {"start": 1111.52, "end": 1112.0, "word": " about", "probability": 0.89892578125}, {"start": 1112.0, "end": 1112.5, "word": " the", "probability": 0.9130859375}, {"start": 1112.5, "end": 1113.24, "word": " relationship", "probability": 0.90380859375}, {"start": 1113.24, "end": 1113.8, "word": " between", "probability": 0.8701171875}, {"start": 1113.8, "end": 1114.9, "word": " the", "probability": 0.83251953125}, {"start": 1114.9, "end": 1115.66, "word": " two", "probability": 0.927734375}, {"start": 1115.66, "end": 1116.34, "word": " variables.", "probability": 0.935546875}, {"start": 1116.82, "end": 1117.02, "word": " Here", "probability": 0.798828125}, {"start": 1117.02, "end": 1117.1, "word": " I", "probability": 0.70068359375}, {"start": 1117.1, "end": 1117.22, "word": " will", "probability": 0.8662109375}, {"start": 1117.22, "end": 1117.48, "word": " give", "probability": 0.88134765625}, {"start": 1117.48, "end": 1117.8, "word": " a", "probability": 0.8974609375}, {"start": 1117.8, "end": 1118.04, "word": " simple", "probability": 0.94482421875}, {"start": 1118.04, "end": 1118.46, "word": " example", "probability": 0.97412109375}, {"start": 1118.46, "end": 1118.9, "word": " in", "probability": 0.79052734375}, {"start": 1118.9, "end": 1119.08, "word": " order", "probability": 0.92626953125}, {"start": 1119.08, "end": 1119.3, "word": " to", "probability": 0.96923828125}, {"start": 1119.3, "end": 1119.78, "word": " determine", "probability": 0.908203125}, {"start": 1119.78, "end": 1121.12, "word": " the", "probability": 0.8876953125}, {"start": 1121.12, "end": 1121.74, "word": " correlation", "probability": 0.935546875}, {"start": 1121.74, "end": 1122.2, "word": " coefficient.", "probability": 0.908203125}, {"start": 1123.58, "end": 1123.82, "word": " A", "probability": 0.93310546875}, {"start": 1123.82, "end": 1124.04, "word": " real", "probability": 0.962890625}, {"start": 1124.04, "end": 1124.48, "word": " estate", "probability": 0.89794921875}, {"start": 1124.48, "end": 1125.16, "word": " agent", "probability": 0.8837890625}, {"start": 1125.16, "end": 1126.0, "word": " wishes", "probability": 0.833984375}, {"start": 1126.0, "end": 1126.36, "word": " to", "probability": 0.970703125}, {"start": 1126.36, "end": 1126.88, "word": " examine", "probability": 0.95458984375}, {"start": 1126.88, "end": 1128.78, "word": " the", "probability": 0.89306640625}, {"start": 1128.78, "end": 1129.5, "word": " relationship", "probability": 0.8984375}, {"start": 1129.5, "end": 1130.02, "word": " between", "probability": 0.8857421875}, {"start": 1130.02, "end": 1130.38, "word": " selling", "probability": 0.841796875}, {"start": 1130.38, "end": 1130.56, "word": " the", "probability": 0.6865234375}, {"start": 1130.56, "end": 1130.96, "word": " price", "probability": 0.9296875}, {"start": 1130.96, "end": 1131.2, "word": " of", "probability": 0.97021484375}, {"start": 1131.2, "end": 1131.32, "word": " a", "probability": 0.98876953125}, {"start": 1131.32, "end": 1131.6, "word": " home", "probability": 0.87744140625}], "temperature": 1.0}, {"id": 44, "seek": 115802, "start": 1132.48, "end": 1158.02, "text": " and its size measured in square feet. So in this case, there are two variables of interest. One is called selling price of a home. So here, selling price of a home and its size. Now, selling price in $1,000.", "tokens": [293, 1080, 2744, 12690, 294, 3732, 3521, 13, 407, 294, 341, 1389, 11, 456, 366, 732, 9102, 295, 1179, 13, 1485, 307, 1219, 6511, 3218, 295, 257, 1280, 13, 407, 510, 11, 6511, 3218, 295, 257, 1280, 293, 1080, 2744, 13, 823, 11, 6511, 3218, 294, 1848, 16, 11, 1360, 13], "avg_logprob": -0.2223557669382829, "compression_ratio": 1.5757575757575757, "no_speech_prob": 0.0, "words": [{"start": 1132.48, "end": 1132.88, "word": " and", "probability": 0.461669921875}, {"start": 1132.88, "end": 1133.24, "word": " its", "probability": 0.68017578125}, {"start": 1133.24, "end": 1133.72, "word": " size", "probability": 0.81201171875}, {"start": 1133.72, "end": 1134.28, "word": " measured", "probability": 0.70361328125}, {"start": 1134.28, "end": 1134.58, "word": " in", "probability": 0.93994140625}, {"start": 1134.58, "end": 1134.96, "word": " square", "probability": 0.880859375}, {"start": 1134.96, "end": 1135.28, "word": " feet.", "probability": 0.95361328125}, {"start": 1135.8, "end": 1136.02, "word": " So", "probability": 0.88134765625}, {"start": 1136.02, "end": 1136.24, "word": " in", "probability": 0.76416015625}, {"start": 1136.24, "end": 1136.44, "word": " this", "probability": 0.947265625}, {"start": 1136.44, "end": 1136.66, "word": " case,", "probability": 0.92138671875}, {"start": 1136.74, "end": 1136.82, "word": " there", "probability": 0.908203125}, {"start": 1136.82, "end": 1136.98, "word": " are", "probability": 0.939453125}, {"start": 1136.98, "end": 1137.14, "word": " two", "probability": 0.92626953125}, {"start": 1137.14, "end": 1137.62, "word": " variables", "probability": 0.92041015625}, {"start": 1137.62, "end": 1137.98, "word": " of", "probability": 0.94287109375}, {"start": 1137.98, "end": 1138.46, "word": " interest.", "probability": 0.900390625}, {"start": 1138.88, "end": 1139.6, "word": " One", "probability": 0.88916015625}, {"start": 1139.6, "end": 1139.82, "word": " is", "probability": 0.896484375}, {"start": 1139.82, "end": 1140.22, "word": " called", "probability": 0.83837890625}, {"start": 1140.22, "end": 1141.82, "word": " selling", "probability": 0.77734375}, {"start": 1141.82, "end": 1142.4, "word": " price", "probability": 0.9326171875}, {"start": 1142.4, "end": 1143.76, "word": " of", "probability": 0.95654296875}, {"start": 1143.76, "end": 1143.88, "word": " a", "probability": 0.9931640625}, {"start": 1143.88, "end": 1144.14, "word": " home.", "probability": 0.892578125}, {"start": 1144.92, "end": 1145.32, "word": " So", "probability": 0.9326171875}, {"start": 1145.32, "end": 1145.6, "word": " here,", "probability": 0.486572265625}, {"start": 1146.0, "end": 1146.46, "word": " selling", "probability": 0.87060546875}, {"start": 1146.46, "end": 1149.14, "word": " price", "probability": 0.703125}, {"start": 1149.14, "end": 1151.74, "word": " of", "probability": 0.9609375}, {"start": 1151.74, "end": 1151.88, "word": " a", "probability": 0.98779296875}, {"start": 1151.88, "end": 1152.18, "word": " home", "probability": 0.89306640625}, {"start": 1152.18, "end": 1153.72, "word": " and", "probability": 0.4921875}, {"start": 1153.72, "end": 1154.84, "word": " its", "probability": 0.84716796875}, {"start": 1154.84, "end": 1155.32, "word": " size.", "probability": 0.85546875}, {"start": 1156.44, "end": 1156.7, "word": " Now,", "probability": 0.91748046875}, {"start": 1156.76, "end": 1157.0, "word": " selling", "probability": 0.876953125}, {"start": 1157.0, "end": 1157.44, "word": " price", "probability": 0.92138671875}, {"start": 1157.44, "end": 1157.64, "word": " in", "probability": 0.442138671875}, {"start": 1157.64, "end": 1157.88, "word": " $1", "probability": 0.5989990234375}, {"start": 1157.88, "end": 1158.02, "word": ",000.", "probability": 0.9990234375}], "temperature": 1.0}, {"id": 45, "seek": 118161, "start": 1165.36, "end": 1181.62, "text": " And size in feet squared. Here we have to distinguish between dependent and independent. So your dependent variable is house price, sometimes called response variable.", "tokens": [400, 2744, 294, 3521, 8889, 13, 1692, 321, 362, 281, 20206, 1296, 12334, 293, 6695, 13, 407, 428, 12334, 7006, 307, 1782, 3218, 11, 2171, 1219, 4134, 7006, 13], "avg_logprob": -0.21041666070620219, "compression_ratio": 1.3658536585365855, "no_speech_prob": 0.0, "words": [{"start": 1165.3600000000001, "end": 1166.2, "word": " And", "probability": 0.410888671875}, {"start": 1166.2, "end": 1166.7, "word": " size", "probability": 0.55908203125}, {"start": 1166.7, "end": 1167.0, "word": " in", "probability": 0.84228515625}, {"start": 1167.0, "end": 1167.2, "word": " feet", "probability": 0.94140625}, {"start": 1167.2, "end": 1167.6, "word": " squared.", "probability": 0.442138671875}, {"start": 1168.64, "end": 1169.02, "word": " Here", "probability": 0.82373046875}, {"start": 1169.02, "end": 1169.12, "word": " we", "probability": 0.736328125}, {"start": 1169.12, "end": 1169.28, "word": " have", "probability": 0.9189453125}, {"start": 1169.28, "end": 1169.38, "word": " to", "probability": 0.951171875}, {"start": 1169.38, "end": 1169.8, "word": " distinguish", "probability": 0.85888671875}, {"start": 1169.8, "end": 1171.08, "word": " between", "probability": 0.81640625}, {"start": 1171.08, "end": 1173.46, "word": " dependent", "probability": 0.544921875}, {"start": 1173.46, "end": 1173.94, "word": " and", "probability": 0.94775390625}, {"start": 1173.94, "end": 1174.4, "word": " independent.", "probability": 0.9052734375}, {"start": 1175.28, "end": 1175.64, "word": " So", "probability": 0.9296875}, {"start": 1175.64, "end": 1175.9, "word": " your", "probability": 0.7333984375}, {"start": 1175.9, "end": 1176.22, "word": " dependent", "probability": 0.87451171875}, {"start": 1176.22, "end": 1176.7, "word": " variable", "probability": 0.9169921875}, {"start": 1176.7, "end": 1176.98, "word": " is", "probability": 0.947265625}, {"start": 1176.98, "end": 1177.3, "word": " house", "probability": 0.82080078125}, {"start": 1177.3, "end": 1177.9, "word": " price,", "probability": 0.90185546875}, {"start": 1179.34, "end": 1179.74, "word": " sometimes", "probability": 0.939453125}, {"start": 1179.74, "end": 1180.32, "word": " called", "probability": 0.8828125}, {"start": 1180.32, "end": 1181.18, "word": " response", "probability": 0.92578125}, {"start": 1181.18, "end": 1181.62, "word": " variable.", "probability": 0.8994140625}], "temperature": 1.0}, {"id": 46, "seek": 121291, "start": 1185.75, "end": 1212.91, "text": " The independent variable is the size, which is in square feet, sometimes called sub-planetary variable. So my Y is ceiling rise, and size is square feet, or size of the house. In this case, there are 10.", "tokens": [440, 6695, 7006, 307, 264, 2744, 11, 597, 307, 294, 3732, 3521, 11, 2171, 1219, 1422, 12, 16554, 302, 822, 7006, 13, 407, 452, 398, 307, 13655, 6272, 11, 293, 2744, 307, 3732, 3521, 11, 420, 2744, 295, 264, 1782, 13, 682, 341, 1389, 11, 456, 366, 1266, 13], "avg_logprob": -0.2570312625169754, "compression_ratio": 1.4166666666666667, "no_speech_prob": 0.0, "words": [{"start": 1185.75, "end": 1186.07, "word": " The", "probability": 0.74951171875}, {"start": 1186.07, "end": 1186.55, "word": " independent", "probability": 0.80126953125}, {"start": 1186.55, "end": 1186.95, "word": " variable", "probability": 0.86474609375}, {"start": 1186.95, "end": 1187.51, "word": " is", "probability": 0.9326171875}, {"start": 1187.51, "end": 1187.85, "word": " the", "probability": 0.51708984375}, {"start": 1187.85, "end": 1188.87, "word": " size,", "probability": 0.81982421875}, {"start": 1189.01, "end": 1189.21, "word": " which", "probability": 0.939453125}, {"start": 1189.21, "end": 1189.37, "word": " is", "probability": 0.86474609375}, {"start": 1189.37, "end": 1189.49, "word": " in", "probability": 0.9140625}, {"start": 1189.49, "end": 1189.79, "word": " square", "probability": 0.88818359375}, {"start": 1189.79, "end": 1190.25, "word": " feet,", "probability": 0.95068359375}, {"start": 1190.87, "end": 1193.29, "word": " sometimes", "probability": 0.93359375}, {"start": 1193.29, "end": 1193.73, "word": " called", "probability": 0.88720703125}, {"start": 1193.73, "end": 1194.13, "word": " sub", "probability": 0.154541015625}, {"start": 1194.13, "end": 1194.57, "word": "-planetary", "probability": 0.7734375}, {"start": 1194.57, "end": 1194.85, "word": " variable.", "probability": 0.8369140625}, {"start": 1199.57, "end": 1200.37, "word": " So", "probability": 0.92724609375}, {"start": 1200.37, "end": 1200.63, "word": " my", "probability": 0.87548828125}, {"start": 1200.63, "end": 1200.95, "word": " Y", "probability": 0.626953125}, {"start": 1200.95, "end": 1201.35, "word": " is", "probability": 0.9375}, {"start": 1201.35, "end": 1201.67, "word": " ceiling", "probability": 0.634765625}, {"start": 1201.67, "end": 1202.15, "word": " rise,", "probability": 0.405517578125}, {"start": 1203.47, "end": 1203.91, "word": " and", "probability": 0.8974609375}, {"start": 1203.91, "end": 1204.43, "word": " size", "probability": 0.814453125}, {"start": 1204.43, "end": 1204.93, "word": " is", "probability": 0.94091796875}, {"start": 1204.93, "end": 1205.35, "word": " square", "probability": 0.8955078125}, {"start": 1205.35, "end": 1206.37, "word": " feet,", "probability": 0.96875}, {"start": 1207.53, "end": 1207.77, "word": " or", "probability": 0.7431640625}, {"start": 1207.77, "end": 1208.13, "word": " size", "probability": 0.70166015625}, {"start": 1208.13, "end": 1208.43, "word": " of", "probability": 0.96728515625}, {"start": 1208.43, "end": 1208.55, "word": " the", "probability": 0.91748046875}, {"start": 1208.55, "end": 1208.85, "word": " house.", "probability": 0.87109375}, {"start": 1211.33, "end": 1211.85, "word": " In", "probability": 0.87841796875}, {"start": 1211.85, "end": 1212.07, "word": " this", "probability": 0.94921875}, {"start": 1212.07, "end": 1212.27, "word": " case,", "probability": 0.92138671875}, {"start": 1212.31, "end": 1212.43, "word": " there", "probability": 0.90380859375}, {"start": 1212.43, "end": 1212.61, "word": " are", "probability": 0.94482421875}, {"start": 1212.61, "end": 1212.91, "word": " 10.", "probability": 0.7177734375}], "temperature": 1.0}, {"id": 47, "seek": 124213, "start": 1214.29, "end": 1242.13, "text": " It's sample size is 10. So the first house with size 1,400 square feet, it's selling price is 245 multiplied by 1,000. Because these values are in $1,000. Now based on this data, you can first plot the scatterplot of house price", "tokens": [467, 311, 6889, 2744, 307, 1266, 13, 407, 264, 700, 1782, 365, 2744, 502, 11, 13741, 3732, 3521, 11, 309, 311, 6511, 3218, 307, 4022, 20, 17207, 538, 502, 11, 1360, 13, 1436, 613, 4190, 366, 294, 1848, 16, 11, 1360, 13, 823, 2361, 322, 341, 1412, 11, 291, 393, 700, 7542, 264, 34951, 564, 310, 295, 1782, 3218], "avg_logprob": -0.21406249850988388, "compression_ratio": 1.396341463414634, "no_speech_prob": 0.0, "words": [{"start": 1214.29, "end": 1214.61, "word": " It's", "probability": 0.6973876953125}, {"start": 1214.61, "end": 1214.79, "word": " sample", "probability": 0.33642578125}, {"start": 1214.79, "end": 1215.11, "word": " size", "probability": 0.84521484375}, {"start": 1215.11, "end": 1215.29, "word": " is", "probability": 0.703125}, {"start": 1215.29, "end": 1215.49, "word": " 10.", "probability": 0.830078125}, {"start": 1216.15, "end": 1216.65, "word": " So", "probability": 0.96240234375}, {"start": 1216.65, "end": 1216.83, "word": " the", "probability": 0.8798828125}, {"start": 1216.83, "end": 1217.15, "word": " first", "probability": 0.88427734375}, {"start": 1217.15, "end": 1217.57, "word": " house", "probability": 0.869140625}, {"start": 1217.57, "end": 1217.89, "word": " with", "probability": 0.79150390625}, {"start": 1217.89, "end": 1218.41, "word": " size", "probability": 0.8349609375}, {"start": 1218.41, "end": 1219.39, "word": " 1", "probability": 0.6328125}, {"start": 1219.39, "end": 1219.71, "word": ",400", "probability": 0.949951171875}, {"start": 1219.71, "end": 1220.35, "word": " square", "probability": 0.89208984375}, {"start": 1220.35, "end": 1220.87, "word": " feet,", "probability": 0.96337890625}, {"start": 1222.35, "end": 1222.83, "word": " it's", "probability": 0.74169921875}, {"start": 1222.83, "end": 1223.07, "word": " selling", "probability": 0.845703125}, {"start": 1223.07, "end": 1223.67, "word": " price", "probability": 0.8203125}, {"start": 1223.67, "end": 1225.03, "word": " is", "probability": 0.86962890625}, {"start": 1225.03, "end": 1226.85, "word": " 245", "probability": 0.7257080078125}, {"start": 1226.85, "end": 1227.69, "word": " multiplied", "probability": 0.62060546875}, {"start": 1227.69, "end": 1228.01, "word": " by", "probability": 0.97509765625}, {"start": 1228.01, "end": 1228.31, "word": " 1", "probability": 0.84326171875}, {"start": 1228.31, "end": 1228.43, "word": ",000.", "probability": 0.999267578125}, {"start": 1230.11, "end": 1230.55, "word": " Because", "probability": 0.86083984375}, {"start": 1230.55, "end": 1230.83, "word": " these", "probability": 0.8623046875}, {"start": 1230.83, "end": 1231.29, "word": " values", "probability": 0.951171875}, {"start": 1231.29, "end": 1231.55, "word": " are", "probability": 0.8955078125}, {"start": 1231.55, "end": 1231.67, "word": " in", "probability": 0.74560546875}, {"start": 1231.67, "end": 1231.91, "word": " $1", "probability": 0.654541015625}, {"start": 1231.91, "end": 1232.05, "word": ",000.", "probability": 0.998779296875}, {"start": 1233.71, "end": 1234.43, "word": " Now", "probability": 0.95751953125}, {"start": 1234.43, "end": 1234.75, "word": " based", "probability": 0.5263671875}, {"start": 1234.75, "end": 1234.91, "word": " on", "probability": 0.94482421875}, {"start": 1234.91, "end": 1235.11, "word": " this", "probability": 0.943359375}, {"start": 1235.11, "end": 1235.47, "word": " data,", "probability": 0.9306640625}, {"start": 1235.69, "end": 1235.83, "word": " you", "probability": 0.90966796875}, {"start": 1235.83, "end": 1236.13, "word": " can", "probability": 0.94482421875}, {"start": 1236.13, "end": 1237.55, "word": " first", "probability": 0.6591796875}, {"start": 1237.55, "end": 1237.95, "word": " plot", "probability": 0.86279296875}, {"start": 1237.95, "end": 1238.31, "word": " the", "probability": 0.884765625}, {"start": 1238.31, "end": 1239.01, "word": " scatterplot", "probability": 0.7880859375}, {"start": 1239.01, "end": 1239.77, "word": " of", "probability": 0.96728515625}, {"start": 1239.77, "end": 1241.57, "word": " house", "probability": 0.8662109375}, {"start": 1241.57, "end": 1242.13, "word": " price", "probability": 0.91162109375}], "temperature": 1.0}, {"id": 48, "seek": 126993, "start": 1244.55, "end": 1269.93, "text": " In Y direction, the vertical direction. So here is house. And rise. And size in the X axis. You will get this scatter plot. Now, the data here is just 10 points, so sometimes it's hard to tell.", "tokens": [682, 398, 3513, 11, 264, 9429, 3513, 13, 407, 510, 307, 1782, 13, 400, 6272, 13, 400, 2744, 294, 264, 1783, 10298, 13, 509, 486, 483, 341, 34951, 7542, 13, 823, 11, 264, 1412, 510, 307, 445, 1266, 2793, 11, 370, 2171, 309, 311, 1152, 281, 980, 13], "avg_logprob": -0.33290816326530615, "compression_ratio": 1.375886524822695, "no_speech_prob": 0.0, "words": [{"start": 1244.55, "end": 1244.83, "word": " In", "probability": 0.301513671875}, {"start": 1244.83, "end": 1245.15, "word": " Y", "probability": 0.517578125}, {"start": 1245.15, "end": 1245.83, "word": " direction,", "probability": 0.74658203125}, {"start": 1246.47, "end": 1246.59, "word": " the", "probability": 0.55859375}, {"start": 1246.59, "end": 1246.93, "word": " vertical", "probability": 0.83837890625}, {"start": 1246.93, "end": 1247.55, "word": " direction.", "probability": 0.9619140625}, {"start": 1247.97, "end": 1248.03, "word": " So", "probability": 0.7490234375}, {"start": 1248.03, "end": 1248.25, "word": " here", "probability": 0.75634765625}, {"start": 1248.25, "end": 1248.49, "word": " is", "probability": 0.7978515625}, {"start": 1248.49, "end": 1248.95, "word": " house.", "probability": 0.6865234375}, {"start": 1250.85, "end": 1251.57, "word": " And", "probability": 0.293701171875}, {"start": 1251.57, "end": 1251.87, "word": " rise.", "probability": 0.2568359375}, {"start": 1254.23, "end": 1255.03, "word": " And", "probability": 0.93701171875}, {"start": 1255.03, "end": 1255.59, "word": " size", "probability": 0.85546875}, {"start": 1255.59, "end": 1256.75, "word": " in", "probability": 0.552734375}, {"start": 1256.75, "end": 1256.91, "word": " the", "probability": 0.90966796875}, {"start": 1256.91, "end": 1257.09, "word": " X", "probability": 0.7734375}, {"start": 1257.09, "end": 1257.49, "word": " axis.", "probability": 0.638671875}, {"start": 1260.05, "end": 1260.29, "word": " You", "probability": 0.8740234375}, {"start": 1260.29, "end": 1260.47, "word": " will", "probability": 0.86767578125}, {"start": 1260.47, "end": 1260.65, "word": " get", "probability": 0.94140625}, {"start": 1260.65, "end": 1261.01, "word": " this", "probability": 0.90673828125}, {"start": 1261.01, "end": 1261.47, "word": " scatter", "probability": 0.8017578125}, {"start": 1261.47, "end": 1261.71, "word": " plot.", "probability": 0.89990234375}, {"start": 1262.97, "end": 1263.41, "word": " Now,", "probability": 0.9423828125}, {"start": 1263.83, "end": 1264.27, "word": " the", "probability": 0.67578125}, {"start": 1264.27, "end": 1265.33, "word": " data", "probability": 0.8583984375}, {"start": 1265.33, "end": 1265.69, "word": " here", "probability": 0.84765625}, {"start": 1265.69, "end": 1265.85, "word": " is", "probability": 0.91357421875}, {"start": 1265.85, "end": 1266.15, "word": " just", "probability": 0.916015625}, {"start": 1266.15, "end": 1266.65, "word": " 10", "probability": 0.623046875}, {"start": 1266.65, "end": 1267.07, "word": " points,", "probability": 0.92724609375}, {"start": 1267.23, "end": 1267.37, "word": " so", "probability": 0.94384765625}, {"start": 1267.37, "end": 1268.07, "word": " sometimes", "probability": 0.65234375}, {"start": 1268.07, "end": 1268.99, "word": " it's", "probability": 0.937744140625}, {"start": 1268.99, "end": 1269.33, "word": " hard", "probability": 0.8994140625}, {"start": 1269.33, "end": 1269.65, "word": " to", "probability": 0.966796875}, {"start": 1269.65, "end": 1269.93, "word": " tell.", "probability": 0.900390625}], "temperature": 1.0}, {"id": 49, "seek": 130010, "start": 1271.51, "end": 1300.11, "text": " the relationship between the two variables if your data is small. But just this example for illustration. But at least you can determine that there exists linear relationship between the two variables. It is positive. So the form is linear. Direction is positive. Weak or strong or moderate.", "tokens": [264, 2480, 1296, 264, 732, 9102, 498, 428, 1412, 307, 1359, 13, 583, 445, 341, 1365, 337, 22645, 13, 583, 412, 1935, 291, 393, 6997, 300, 456, 8198, 8213, 2480, 1296, 264, 732, 9102, 13, 467, 307, 3353, 13, 407, 264, 1254, 307, 8213, 13, 5822, 882, 307, 3353, 13, 492, 514, 420, 2068, 420, 18174, 13], "avg_logprob": -0.17941810730202445, "compression_ratio": 1.7076023391812865, "no_speech_prob": 0.0, "words": [{"start": 1271.51, "end": 1271.93, "word": " the", "probability": 0.266357421875}, {"start": 1271.93, "end": 1272.59, "word": " relationship", "probability": 0.90478515625}, {"start": 1272.59, "end": 1273.01, "word": " between", "probability": 0.86865234375}, {"start": 1273.01, "end": 1273.23, "word": " the", "probability": 0.85693359375}, {"start": 1273.23, "end": 1273.37, "word": " two", "probability": 0.90966796875}, {"start": 1273.37, "end": 1273.75, "word": " variables", "probability": 0.9296875}, {"start": 1273.75, "end": 1274.09, "word": " if", "probability": 0.6435546875}, {"start": 1274.09, "end": 1274.47, "word": " your", "probability": 0.85302734375}, {"start": 1274.47, "end": 1274.81, "word": " data", "probability": 0.9619140625}, {"start": 1274.81, "end": 1275.03, "word": " is", "probability": 0.9501953125}, {"start": 1275.03, "end": 1275.51, "word": " small.", "probability": 0.880859375}, {"start": 1276.51, "end": 1276.83, "word": " But", "probability": 0.69580078125}, {"start": 1276.83, "end": 1277.13, "word": " just", "probability": 0.5205078125}, {"start": 1277.13, "end": 1278.27, "word": " this", "probability": 0.6376953125}, {"start": 1278.27, "end": 1278.61, "word": " example", "probability": 0.943359375}, {"start": 1278.61, "end": 1279.01, "word": " for", "probability": 0.91796875}, {"start": 1279.01, "end": 1279.73, "word": " illustration.", "probability": 0.93798828125}, {"start": 1280.69, "end": 1280.99, "word": " But", "probability": 0.93994140625}, {"start": 1280.99, "end": 1281.17, "word": " at", "probability": 0.927734375}, {"start": 1281.17, "end": 1281.39, "word": " least", "probability": 0.95556640625}, {"start": 1281.39, "end": 1281.57, "word": " you", "probability": 0.8310546875}, {"start": 1281.57, "end": 1281.75, "word": " can", "probability": 0.9462890625}, {"start": 1281.75, "end": 1282.33, "word": " determine", "probability": 0.91015625}, {"start": 1282.33, "end": 1283.21, "word": " that", "probability": 0.9267578125}, {"start": 1283.21, "end": 1284.29, "word": " there", "probability": 0.87353515625}, {"start": 1284.29, "end": 1284.79, "word": " exists", "probability": 0.78759765625}, {"start": 1284.79, "end": 1285.37, "word": " linear", "probability": 0.87158203125}, {"start": 1285.37, "end": 1286.59, "word": " relationship", "probability": 0.9248046875}, {"start": 1286.59, "end": 1287.03, "word": " between", "probability": 0.86962890625}, {"start": 1287.03, "end": 1287.17, "word": " the", "probability": 0.8544921875}, {"start": 1287.17, "end": 1287.31, "word": " two", "probability": 0.9375}, {"start": 1287.31, "end": 1287.81, "word": " variables.", "probability": 0.931640625}, {"start": 1288.39, "end": 1288.65, "word": " It", "probability": 0.91796875}, {"start": 1288.65, "end": 1288.81, "word": " is", "probability": 0.94287109375}, {"start": 1288.81, "end": 1289.19, "word": " positive.", "probability": 0.92236328125}, {"start": 1290.71, "end": 1291.01, "word": " So", "probability": 0.94580078125}, {"start": 1291.01, "end": 1291.53, "word": " the", "probability": 0.63232421875}, {"start": 1291.53, "end": 1291.89, "word": " form", "probability": 0.9150390625}, {"start": 1291.89, "end": 1292.13, "word": " is", "probability": 0.9501953125}, {"start": 1292.13, "end": 1292.47, "word": " linear.", "probability": 0.89501953125}, {"start": 1294.35, "end": 1295.11, "word": " Direction", "probability": 0.941650390625}, {"start": 1295.11, "end": 1295.49, "word": " is", "probability": 0.94677734375}, {"start": 1295.49, "end": 1295.87, "word": " positive.", "probability": 0.92578125}, {"start": 1298.05, "end": 1298.81, "word": " Weak", "probability": 0.96142578125}, {"start": 1298.81, "end": 1299.01, "word": " or", "probability": 0.89453125}, {"start": 1299.01, "end": 1299.45, "word": " strong", "probability": 0.8701171875}, {"start": 1299.45, "end": 1299.75, "word": " or", "probability": 0.93310546875}, {"start": 1299.75, "end": 1300.11, "word": " moderate.", "probability": 0.94482421875}], "temperature": 1.0}, {"id": 50, "seek": 132272, "start": 1301.26, "end": 1322.72, "text": " Sometimes it's not easy to tell if it is strong or moderate. Now if you look at these points, some of them are close to the straight line and others are away from the straight line. So maybe there exists moderate for example, but you cannot say strong.", "tokens": [4803, 309, 311, 406, 1858, 281, 980, 498, 309, 307, 2068, 420, 18174, 13, 823, 498, 291, 574, 412, 613, 2793, 11, 512, 295, 552, 366, 1998, 281, 264, 2997, 1622, 293, 2357, 366, 1314, 490, 264, 2997, 1622, 13, 407, 1310, 456, 8198, 18174, 337, 1365, 11, 457, 291, 2644, 584, 2068, 13], "avg_logprob": -0.16022727597843517, "compression_ratio": 1.5617283950617284, "no_speech_prob": 0.0, "words": [{"start": 1301.26, "end": 1301.88, "word": " Sometimes", "probability": 0.56201171875}, {"start": 1301.88, "end": 1302.12, "word": " it's", "probability": 0.72314453125}, {"start": 1302.12, "end": 1302.32, "word": " not", "probability": 0.94873046875}, {"start": 1302.32, "end": 1302.62, "word": " easy", "probability": 0.908203125}, {"start": 1302.62, "end": 1302.96, "word": " to", "probability": 0.97314453125}, {"start": 1302.96, "end": 1303.38, "word": " tell", "probability": 0.87841796875}, {"start": 1303.38, "end": 1304.16, "word": " if", "probability": 0.9208984375}, {"start": 1304.16, "end": 1304.28, "word": " it", "probability": 0.9404296875}, {"start": 1304.28, "end": 1304.4, "word": " is", "probability": 0.73388671875}, {"start": 1304.4, "end": 1304.84, "word": " strong", "probability": 0.7822265625}, {"start": 1304.84, "end": 1305.24, "word": " or", "probability": 0.96142578125}, {"start": 1305.24, "end": 1305.62, "word": " moderate.", "probability": 0.9228515625}, {"start": 1307.72, "end": 1308.06, "word": " Now", "probability": 0.859375}, {"start": 1308.06, "end": 1308.22, "word": " if", "probability": 0.60888671875}, {"start": 1308.22, "end": 1308.26, "word": " you", "probability": 0.90771484375}, {"start": 1308.26, "end": 1308.4, "word": " look", "probability": 0.96630859375}, {"start": 1308.4, "end": 1308.52, "word": " at", "probability": 0.96630859375}, {"start": 1308.52, "end": 1308.74, "word": " these", "probability": 0.81005859375}, {"start": 1308.74, "end": 1309.06, "word": " points,", "probability": 0.94677734375}, {"start": 1309.24, "end": 1309.44, "word": " some", "probability": 0.8994140625}, {"start": 1309.44, "end": 1309.6, "word": " of", "probability": 0.9619140625}, {"start": 1309.6, "end": 1309.82, "word": " them", "probability": 0.896484375}, {"start": 1309.82, "end": 1310.12, "word": " are", "probability": 0.943359375}, {"start": 1310.12, "end": 1310.56, "word": " close", "probability": 0.84912109375}, {"start": 1310.56, "end": 1310.7, "word": " to", "probability": 0.96630859375}, {"start": 1310.7, "end": 1310.84, "word": " the", "probability": 0.90673828125}, {"start": 1310.84, "end": 1311.06, "word": " straight", "probability": 0.92578125}, {"start": 1311.06, "end": 1311.4, "word": " line", "probability": 0.9091796875}, {"start": 1311.4, "end": 1311.96, "word": " and", "probability": 0.66357421875}, {"start": 1311.96, "end": 1312.38, "word": " others", "probability": 0.86865234375}, {"start": 1312.38, "end": 1312.96, "word": " are", "probability": 0.93798828125}, {"start": 1312.96, "end": 1313.7, "word": " away", "probability": 0.87158203125}, {"start": 1313.7, "end": 1313.98, "word": " from", "probability": 0.8828125}, {"start": 1313.98, "end": 1314.26, "word": " the", "probability": 0.869140625}, {"start": 1314.26, "end": 1314.54, "word": " straight", "probability": 0.90869140625}, {"start": 1314.54, "end": 1314.86, "word": " line.", "probability": 0.9423828125}, {"start": 1315.32, "end": 1315.52, "word": " So", "probability": 0.912109375}, {"start": 1315.52, "end": 1315.92, "word": " maybe", "probability": 0.833984375}, {"start": 1315.92, "end": 1316.18, "word": " there", "probability": 0.74560546875}, {"start": 1316.18, "end": 1316.7, "word": " exists", "probability": 0.76904296875}, {"start": 1316.7, "end": 1317.94, "word": " moderate", "probability": 0.904296875}, {"start": 1317.94, "end": 1318.22, "word": " for", "probability": 0.6708984375}, {"start": 1318.22, "end": 1318.64, "word": " example,", "probability": 0.97509765625}, {"start": 1319.4, "end": 1319.64, "word": " but", "probability": 0.9189453125}, {"start": 1319.64, "end": 1320.0, "word": " you", "probability": 0.9287109375}, {"start": 1320.0, "end": 1320.36, "word": " cannot", "probability": 0.84033203125}, {"start": 1320.36, "end": 1320.78, "word": " say", "probability": 0.93359375}, {"start": 1320.78, "end": 1322.72, "word": " strong.", "probability": 0.7734375}], "temperature": 1.0}, {"id": 51, "seek": 135143, "start": 1323.93, "end": 1351.43, "text": " Here, strong it means the points are close to the straight line. Sometimes it's hard to tell the strength of the relationship, but you can know the form or the direction. But to measure the exact strength, you have to measure the correlation coefficient, R. 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Now plug these values into the formula we have for the shortcut formula. 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So that means if the size increases, the selling price also increases. 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But fields is not strong relationship, you can say it's moderate relationship. Because it's close if now if you just compare this value and other data gives 9%.", "tokens": [22792, 309, 1355, 1998, 281, 502, 11, 1958, 13, 23, 11, 1958, 13, 19287, 11, 1958, 13, 24, 11, 291, 393, 584, 456, 8198, 2068, 13, 583, 7909, 307, 406, 2068, 2480, 11, 291, 393, 584, 309, 311, 18174, 2480, 13, 1436, 309, 311, 1998, 498, 586, 498, 291, 445, 6794, 341, 2158, 293, 661, 1412, 2709, 1722, 6856], "avg_logprob": -0.28828125943740207, "compression_ratio": 1.4875, "no_speech_prob": 0.0, "words": [{"start": 1415.8, "end": 1416.44, "word": " Strong", "probability": 0.1849365234375}, {"start": 1416.44, "end": 1416.66, "word": " it", "probability": 0.272705078125}, {"start": 1416.66, "end": 1416.88, "word": " means", "probability": 0.91357421875}, {"start": 1416.88, "end": 1417.24, "word": " close", "probability": 0.76123046875}, {"start": 1417.24, "end": 1417.44, "word": " to", "probability": 0.95849609375}, {"start": 1417.44, "end": 1417.66, "word": " 1,", "probability": 0.490478515625}, {"start": 1417.78, "end": 1417.96, "word": " 0", "probability": 0.62890625}, {"start": 1417.96, "end": 1418.38, "word": ".8,", "probability": 0.9482421875}, {"start": 1418.48, "end": 1418.66, "word": " 0", "probability": 0.9794921875}, {"start": 1418.66, "end": 1419.32, "word": ".85,", "probability": 0.985107421875}, {"start": 1419.48, "end": 1419.56, "word": " 0", "probability": 0.974609375}, {"start": 1419.56, "end": 1419.96, "word": ".9,", "probability": 0.98828125}, {"start": 1420.1, "end": 1420.3, "word": " you", "probability": 0.8779296875}, {"start": 1420.3, "end": 1420.54, "word": " can", "probability": 0.9453125}, {"start": 1420.54, "end": 1420.74, "word": " say", "probability": 0.57958984375}, {"start": 1420.74, "end": 1420.92, "word": " there", "probability": 0.6494140625}, {"start": 1420.92, "end": 1421.16, "word": " exists", "probability": 0.47265625}, {"start": 1421.16, "end": 1421.64, "word": " strong.", "probability": 0.84033203125}, {"start": 1422.18, "end": 1422.48, "word": " But", "probability": 0.93994140625}, {"start": 1422.48, "end": 1422.84, "word": " fields", "probability": 0.312255859375}, {"start": 1422.84, "end": 1424.08, "word": " is", "probability": 0.75341796875}, {"start": 1424.08, "end": 1424.4, "word": " not", "probability": 0.9482421875}, {"start": 1424.4, "end": 1425.42, "word": " strong", "probability": 0.69775390625}, {"start": 1425.42, "end": 1426.02, "word": " relationship,", "probability": 0.91455078125}, {"start": 1426.24, "end": 1426.34, "word": " you", "probability": 0.94091796875}, {"start": 1426.34, "end": 1426.54, "word": " can", "probability": 0.94580078125}, {"start": 1426.54, "end": 1426.76, "word": " say", "probability": 0.90673828125}, {"start": 1426.76, "end": 1427.56, "word": " it's", "probability": 0.840087890625}, {"start": 1427.56, "end": 1427.96, "word": " moderate", "probability": 0.91748046875}, {"start": 1427.96, "end": 1428.62, "word": " relationship.", "probability": 0.9052734375}, {"start": 1430.16, "end": 1430.6, "word": " Because", "probability": 0.89990234375}, {"start": 1430.6, "end": 1430.84, "word": " it's", "probability": 0.93212890625}, {"start": 1430.84, "end": 1431.28, "word": " close", "probability": 0.873046875}, {"start": 1431.28, "end": 1432.5, "word": " if", "probability": 0.546875}, {"start": 1432.5, "end": 1433.12, "word": " now", "probability": 0.4326171875}, {"start": 1433.12, "end": 1433.34, "word": " if", "probability": 0.79638671875}, {"start": 1433.34, "end": 1433.44, "word": " you", "probability": 0.958984375}, {"start": 1433.44, "end": 1433.72, "word": " just", "probability": 0.8662109375}, {"start": 1433.72, "end": 1434.06, "word": " compare", "probability": 0.94482421875}, {"start": 1434.06, "end": 1434.28, "word": " this", "probability": 0.9453125}, {"start": 1434.28, "end": 1434.7, "word": " value", "probability": 0.97509765625}, {"start": 1434.7, "end": 1435.3, "word": " and", "probability": 0.685546875}, {"start": 1435.3, "end": 1435.62, "word": " other", "probability": 0.88232421875}, {"start": 1435.62, "end": 1435.98, "word": " data", "probability": 0.94482421875}, {"start": 1435.98, "end": 1436.3, "word": " gives", "probability": 0.78076171875}, {"start": 1436.3, "end": 1437.08, "word": " 9%.", "probability": 0.621337890625}], "temperature": 1.0}, {"id": 55, "seek": 146339, "start": 1438.83, "end": 1463.39, "text": " Other one gives 85%. So these values are much closer to 1 than 0.7, but still this value is considered to be high. Any question? Next, I will give some introduction to regression analysis.", "tokens": [5358, 472, 2709, 14695, 6856, 407, 613, 4190, 366, 709, 4966, 281, 502, 813, 1958, 13, 22, 11, 457, 920, 341, 2158, 307, 4888, 281, 312, 1090, 13, 2639, 1168, 30, 3087, 11, 286, 486, 976, 512, 9339, 281, 24590, 5215, 13], "avg_logprob": -0.24781975358031516, "compression_ratio": 1.2857142857142858, "no_speech_prob": 0.0, "words": [{"start": 1438.83, "end": 1439.21, "word": " Other", "probability": 0.2149658203125}, {"start": 1439.21, "end": 1439.47, "word": " one", "probability": 0.90478515625}, {"start": 1439.47, "end": 1439.85, "word": " gives", "probability": 0.83837890625}, {"start": 1439.85, "end": 1441.39, "word": " 85%.", "probability": 0.5093994140625}, {"start": 1441.39, "end": 1442.17, "word": " So", "probability": 0.89892578125}, {"start": 1442.17, "end": 1442.43, "word": " these", "probability": 0.67822265625}, {"start": 1442.43, "end": 1442.93, "word": " values", "probability": 0.9619140625}, {"start": 1442.93, "end": 1443.47, "word": " are", "probability": 0.9423828125}, {"start": 1443.47, "end": 1443.79, "word": " much", "probability": 0.9140625}, {"start": 1443.79, "end": 1444.33, "word": " closer", "probability": 0.919921875}, {"start": 1444.33, "end": 1445.57, "word": " to", "probability": 0.92138671875}, {"start": 1445.57, "end": 1445.85, "word": " 1", "probability": 0.69384765625}, {"start": 1445.85, "end": 1446.57, "word": " than", "probability": 0.8037109375}, {"start": 1446.57, "end": 1446.83, "word": " 0", "probability": 0.384521484375}, {"start": 1446.83, "end": 1447.09, "word": ".7,", "probability": 0.991455078125}, {"start": 1447.19, "end": 1447.35, "word": " but", "probability": 0.923828125}, {"start": 1447.35, "end": 1447.75, "word": " still", "probability": 0.94873046875}, {"start": 1447.75, "end": 1448.03, "word": " this", "probability": 0.64453125}, {"start": 1448.03, "end": 1448.31, "word": " value", "probability": 0.9150390625}, {"start": 1448.31, "end": 1448.55, "word": " is", "probability": 0.90478515625}, {"start": 1448.55, "end": 1448.91, "word": " considered", "probability": 0.771484375}, {"start": 1448.91, "end": 1449.13, "word": " to", "probability": 0.96533203125}, {"start": 1449.13, "end": 1449.25, "word": " be", "probability": 0.951171875}, {"start": 1449.25, "end": 1449.57, "word": " high.", "probability": 0.8974609375}, {"start": 1455.71, "end": 1456.43, "word": " Any", "probability": 0.8564453125}, {"start": 1456.43, "end": 1456.81, "word": " question?", "probability": 0.587890625}, {"start": 1459.85, "end": 1460.57, "word": " Next,", "probability": 0.8916015625}, {"start": 1460.73, "end": 1460.87, "word": " I", "probability": 0.99853515625}, {"start": 1460.87, "end": 1460.97, "word": " will", "probability": 0.8701171875}, {"start": 1460.97, "end": 1461.13, "word": " give", "probability": 0.86865234375}, {"start": 1461.13, "end": 1461.47, "word": " some", "probability": 0.88818359375}, {"start": 1461.47, "end": 1462.09, "word": " introduction", "probability": 0.8984375}, {"start": 1462.09, "end": 1462.45, "word": " to", "probability": 0.96630859375}, {"start": 1462.45, "end": 1462.81, "word": " regression", "probability": 0.95263671875}, {"start": 1462.81, "end": 1463.39, "word": " analysis.", "probability": 0.85888671875}], "temperature": 1.0}, {"id": 56, "seek": 149189, "start": 1466.97, "end": 1491.89, "text": " regression analysis used to number one, predict the value of a dependent variable based on the value of at least one independent variable. So by using the data we have for selling price of a home and size, you can predict the selling price by knowing the value of its size. So suppose for example,", "tokens": [24590, 5215, 1143, 281, 1230, 472, 11, 6069, 264, 2158, 295, 257, 12334, 7006, 2361, 322, 264, 2158, 295, 412, 1935, 472, 6695, 7006, 13, 407, 538, 1228, 264, 1412, 321, 362, 337, 6511, 3218, 295, 257, 1280, 293, 2744, 11, 291, 393, 6069, 264, 6511, 3218, 538, 5276, 264, 2158, 295, 1080, 2744, 13, 407, 7297, 337, 1365, 11], "avg_logprob": -0.18173667739649288, "compression_ratio": 1.7633136094674555, "no_speech_prob": 0.0, "words": [{"start": 1466.9699999999998, "end": 1467.6699999999998, "word": " regression", "probability": 0.31201171875}, {"start": 1467.6699999999998, "end": 1468.37, "word": " analysis", "probability": 0.76708984375}, {"start": 1468.37, "end": 1468.75, "word": " used", "probability": 0.67724609375}, {"start": 1468.75, "end": 1469.01, "word": " to", "probability": 0.87158203125}, {"start": 1469.01, "end": 1469.29, "word": " number", "probability": 0.6767578125}, {"start": 1469.29, "end": 1469.77, "word": " one,", "probability": 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What do you predict its size, its sale or price? So by using this value, we can predict the selling price. Next, explain the impact of changes in independent variable on the dependent variable.", "tokens": [509, 458, 300, 264, 2744, 295, 257, 1782, 307, 3499, 2803, 11, 3499, 2803, 3732, 3521, 13, 708, 360, 291, 6069, 1080, 2744, 11, 1080, 8680, 420, 3218, 30, 407, 538, 1228, 341, 2158, 11, 321, 393, 6069, 264, 6511, 3218, 13, 3087, 11, 2903, 264, 2712, 295, 2962, 294, 6695, 7006, 322, 264, 12334, 7006, 13], "avg_logprob": -0.2163254258961513, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 1492.59, "end": 1492.83, "word": " You", "probability": 0.51904296875}, {"start": 1492.83, "end": 1492.97, "word": " know", "probability": 0.88427734375}, {"start": 1492.97, "end": 1493.31, "word": " that", "probability": 0.90087890625}, {"start": 1493.31, "end": 1493.69, "word": " the", "probability": 0.802734375}, {"start": 1493.69, "end": 1494.01, "word": " size", "probability": 0.83837890625}, {"start": 1494.01, "end": 1494.13, "word": " of", "probability": 0.96533203125}, {"start": 1494.13, "end": 1494.25, "word": " a", "probability": 0.60205078125}, {"start": 1494.25, "end": 1494.53, "word": " house", "probability": 0.87548828125}, {"start": 1494.53, "end": 1494.87, "word": " is", "probability": 0.9482421875}, {"start": 1494.87, "end": 1496.35, "word": " 1450,", "probability": 0.796630859375}, {"start": 1496.85, "end": 1498.13, "word": " 1450", "probability": 0.93115234375}, {"start": 1498.13, "end": 1498.65, "word": " square", "probability": 0.79052734375}, {"start": 1498.65, "end": 1499.11, "word": " feet.", "probability": 0.953125}, {"start": 1499.97, "end": 1500.33, "word": " What", "probability": 0.88037109375}, {"start": 1500.33, "end": 1500.73, "word": " do", "probability": 0.86572265625}, {"start": 1500.73, "end": 1500.91, "word": " you", "probability": 0.95751953125}, {"start": 1500.91, "end": 1501.49, "word": " predict", "probability": 0.93505859375}, {"start": 1501.49, "end": 1503.51, "word": " its", "probability": 0.50634765625}, {"start": 1503.51, "end": 1504.07, "word": " size,", "probability": 0.86181640625}, {"start": 1504.27, "end": 1504.77, "word": " its", "probability": 0.84228515625}, {"start": 1504.77, "end": 1507.17, "word": " sale", "probability": 0.155029296875}, {"start": 1507.17, "end": 1507.37, "word": " or", "probability": 0.486328125}, {"start": 1507.37, "end": 1507.69, "word": " price?", "probability": 0.94482421875}, {"start": 1508.63, "end": 1509.11, "word": " So", "probability": 0.869140625}, {"start": 1509.11, "end": 1509.31, "word": " by", "probability": 0.82421875}, {"start": 1509.31, "end": 1509.53, "word": " using", "probability": 0.92529296875}, {"start": 1509.53, "end": 1509.81, "word": " this", "probability": 0.9453125}, {"start": 1509.81, "end": 1510.19, "word": " value,", "probability": 0.966796875}, {"start": 1510.31, "end": 1510.57, "word": " we", "probability": 0.95458984375}, {"start": 1510.57, "end": 1510.83, "word": " can", "probability": 0.935546875}, {"start": 1510.83, "end": 1511.33, "word": " predict", "probability": 0.93359375}, {"start": 1511.33, "end": 1512.29, "word": " the", "probability": 0.9140625}, {"start": 1512.29, "end": 1512.79, "word": " selling", "probability": 0.88134765625}, {"start": 1512.79, "end": 1513.25, "word": " price.", "probability": 0.67236328125}, {"start": 1514.99, "end": 1515.75, "word": " Next,", "probability": 0.90869140625}, {"start": 1516.03, "end": 1516.51, "word": " explain", "probability": 0.8916015625}, {"start": 1516.51, "end": 1516.81, "word": " the", "probability": 0.91455078125}, {"start": 1516.81, "end": 1517.29, "word": " impact", "probability": 0.94677734375}, {"start": 1517.29, "end": 1517.99, "word": " of", "probability": 0.9521484375}, {"start": 1517.99, "end": 1518.47, "word": " changes", "probability": 0.837890625}, {"start": 1518.47, "end": 1518.71, "word": " in", "probability": 0.9326171875}, {"start": 1518.71, "end": 1519.13, "word": " independent", "probability": 0.56494140625}, {"start": 1519.13, "end": 1519.59, "word": " variable", "probability": 0.85498046875}, {"start": 1519.59, "end": 1519.89, "word": " on", "probability": 0.904296875}, {"start": 1519.89, "end": 1520.01, "word": " the", "probability": 0.66650390625}, {"start": 1520.01, "end": 1520.31, "word": " dependent", "probability": 0.8935546875}, {"start": 1520.31, "end": 1520.75, "word": " variable.", "probability": 0.89599609375}], "temperature": 1.0}, {"id": 58, "seek": 154955, "start": 1521.89, "end": 1549.55, "text": " You can say, for example, 90% of the variability in the dependent variable in selling price is explained by its size. So we can predict the value of dependent variable based on a value of one independent variable at least. 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For example, maybe there are more than one variable that affects a price, a selling price. 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So in this case there are two variables. If there exists more than one variable, in this case we have something called multiple linear regression.", "tokens": [2704, 4914, 307, 611, 1071, 5952, 300, 11807, 264, 6511, 3218, 13, 407, 294, 341, 1389, 456, 366, 732, 9102, 13, 759, 456, 8198, 544, 813, 472, 7006, 11, 294, 341, 1389, 321, 362, 746, 1219, 3866, 8213, 24590, 13], "avg_logprob": -0.19721798780487804, "compression_ratio": 1.4466666666666668, "no_speech_prob": 0.0, "words": [{"start": 1579.48, "end": 1579.76, "word": " Maybe", "probability": 0.229736328125}, {"start": 1579.76, "end": 1580.18, "word": " location", "probability": 0.9345703125}, {"start": 1580.18, "end": 1580.46, "word": " is", "probability": 0.93701171875}, {"start": 1580.46, "end": 1580.78, "word": " also", "probability": 0.66650390625}, {"start": 1580.78, "end": 1581.1, "word": " another", "probability": 0.93115234375}, {"start": 1581.1, "end": 1581.66, "word": " factor", "probability": 0.87109375}, {"start": 1581.66, "end": 1582.86, "word": " that", "probability": 0.8896484375}, {"start": 1582.86, "end": 1583.58, "word": " affects", "probability": 0.72802734375}, {"start": 1583.58, "end": 1584.7, "word": " the", "probability": 0.5234375}, {"start": 1584.7, "end": 1584.88, "word": " selling", "probability": 0.89990234375}, {"start": 1584.88, "end": 1585.26, "word": " price.", "probability": 0.84033203125}, {"start": 1585.42, "end": 1585.48, "word": " So", "probability": 0.78125}, {"start": 1585.48, "end": 1585.58, "word": " in", "probability": 0.65234375}, {"start": 1585.58, "end": 1585.72, "word": " this", "probability": 0.9462890625}, {"start": 1585.72, "end": 1585.92, "word": " case", "probability": 0.91552734375}, {"start": 1585.92, "end": 1586.1, "word": " there", "probability": 0.5673828125}, {"start": 1586.1, "end": 1586.36, "word": " are", "probability": 0.94140625}, {"start": 1586.36, "end": 1587.36, "word": " two", "probability": 0.86474609375}, {"start": 1587.36, "end": 1587.82, "word": " variables.", "probability": 0.97509765625}, {"start": 1589.8, "end": 1590.44, "word": " If", "probability": 0.943359375}, {"start": 1590.44, "end": 1590.68, "word": " there", "probability": 0.90380859375}, {"start": 1590.68, "end": 1591.02, "word": " exists", "probability": 0.787109375}, {"start": 1591.02, "end": 1591.4, "word": " more", "probability": 0.943359375}, {"start": 1591.4, "end": 1591.64, "word": " than", "probability": 0.93505859375}, {"start": 1591.64, "end": 1591.86, "word": " one", "probability": 0.92822265625}, {"start": 1591.86, "end": 1592.24, "word": " variable,", "probability": 0.94775390625}, {"start": 1592.64, "end": 1592.8, "word": " in", "probability": 0.873046875}, {"start": 1592.8, "end": 1593.02, "word": " this", "probability": 0.9462890625}, {"start": 1593.02, "end": 1593.28, "word": " case", "probability": 0.9111328125}, {"start": 1593.28, "end": 1593.48, "word": " we", "probability": 0.8603515625}, {"start": 1593.48, "end": 1593.8, "word": " have", "probability": 0.94482421875}, {"start": 1593.8, "end": 1594.24, "word": " something", "probability": 0.87939453125}, {"start": 1594.24, "end": 1594.76, "word": " called", "probability": 0.89208984375}, {"start": 1594.76, "end": 1596.08, "word": " multiple", "probability": 0.7255859375}, {"start": 1596.08, "end": 1598.06, "word": " linear", "probability": 0.92626953125}, {"start": 1598.06, "end": 1598.68, "word": " regression.", "probability": 0.98583984375}], "temperature": 1.0}, {"id": 61, "seek": 162677, "start": 1602.03, "end": 1626.77, "text": " Here, we just talk about one independent variable. There is only, in this chapter, there is only one x. So it's called simple linear regression. The calculations for multiple takes time.", "tokens": [1692, 11, 321, 445, 751, 466, 472, 6695, 7006, 13, 821, 307, 787, 11, 294, 341, 7187, 11, 456, 307, 787, 472, 2031, 13, 407, 309, 311, 1219, 2199, 8213, 24590, 13, 440, 20448, 337, 3866, 2516, 565, 13], "avg_logprob": -0.20605469383299352, "compression_ratio": 1.375, "no_speech_prob": 0.0, "words": [{"start": 1602.03, "end": 1602.43, "word": " Here,", "probability": 0.67529296875}, {"start": 1602.95, "end": 1603.63, "word": " we", "probability": 0.935546875}, {"start": 1603.63, "end": 1603.95, "word": " just", "probability": 0.82275390625}, {"start": 1603.95, "end": 1604.25, "word": " talk", "probability": 0.6884765625}, {"start": 1604.25, "end": 1604.75, "word": " about", "probability": 0.90966796875}, {"start": 1604.75, "end": 1605.81, "word": " one", "probability": 0.904296875}, {"start": 1605.81, "end": 1606.25, "word": " independent", "probability": 0.84033203125}, {"start": 1606.25, "end": 1606.71, "word": " variable.", "probability": 0.9248046875}, {"start": 1607.03, "end": 1607.29, "word": " There", "probability": 0.494384765625}, {"start": 1607.29, "end": 1607.45, "word": " is", "probability": 0.89013671875}, {"start": 1607.45, "end": 1607.87, "word": " only,", "probability": 0.931640625}, {"start": 1608.05, "end": 1608.41, "word": " in", "probability": 0.93505859375}, {"start": 1608.41, "end": 1608.73, "word": " this", "probability": 0.943359375}, {"start": 1608.73, "end": 1609.01, "word": " chapter,", "probability": 0.75830078125}, {"start": 1609.81, "end": 1610.45, "word": " there", "probability": 0.85693359375}, {"start": 1610.45, "end": 1610.63, "word": " is", "probability": 0.9248046875}, {"start": 1610.63, "end": 1611.05, "word": " only", "probability": 0.923828125}, {"start": 1611.05, "end": 1611.61, "word": " one", "probability": 0.8837890625}, {"start": 1611.61, "end": 1612.01, "word": " x.", "probability": 0.64013671875}, {"start": 1612.85, "end": 1613.25, "word": " So", "probability": 0.9453125}, {"start": 1613.25, "end": 1613.45, "word": " it's", "probability": 0.8662109375}, {"start": 1613.45, "end": 1613.79, "word": " called", "probability": 0.8935546875}, {"start": 1613.79, "end": 1614.37, "word": " simple", "probability": 0.869140625}, {"start": 1614.37, "end": 1618.33, "word": " linear", "probability": 0.900390625}, {"start": 1618.33, "end": 1619.33, "word": " regression.", "probability": 0.935546875}, {"start": 1622.19, "end": 1622.47, "word": " The", "probability": 0.82568359375}, {"start": 1622.47, "end": 1623.15, "word": " calculations", "probability": 0.91552734375}, {"start": 1623.15, "end": 1623.61, "word": " for", "probability": 0.953125}, {"start": 1623.61, "end": 1624.27, "word": " multiple", "probability": 0.912109375}, {"start": 1624.27, "end": 1626.41, "word": " takes", "probability": 0.57958984375}, {"start": 1626.41, "end": 1626.77, "word": " time.", "probability": 0.89453125}], "temperature": 1.0}, {"id": 62, "seek": 165523, "start": 1627.05, "end": 1655.23, "text": " So we are going just to cover one independent variable. 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Again, the dependent variable is the variable we wish to predict or explain, the same as weight. Independent variable, the variable used to predict or explain the dependent variable. 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Suppose we are talking about your scores. Scores is the dependent variable can be affected by number of hours. Hour of study. 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In this case, if there is only one X, one independent variable, it's called simple linear regression. Maybe another variable, number of missing classes or attendance.", "tokens": [2704, 382, 1230, 295, 7601, 1773, 8637, 11, 428, 13444, 611, 3488, 13, 682, 341, 1389, 11, 498, 456, 307, 787, 472, 1783, 11, 472, 6695, 7006, 11, 309, 311, 1219, 2199, 8213, 24590, 13, 2704, 1071, 7006, 11, 1230, 295, 5361, 5359, 420, 24337, 13], "avg_logprob": -0.20246010004205905, "compression_ratio": 1.5256410256410255, "no_speech_prob": 0.0, "words": [{"start": 1716.91, "end": 1717.31, "word": " Maybe", "probability": 0.6728515625}, {"start": 1717.31, "end": 1717.67, "word": " as", "probability": 0.8251953125}, {"start": 1717.67, "end": 1718.01, "word": " number", "probability": 0.7314453125}, {"start": 1718.01, "end": 1718.21, "word": " of", "probability": 0.94091796875}, {"start": 1718.21, "end": 1718.43, "word": " studying", "probability": 0.83154296875}, {"start": 1718.43, "end": 1718.63, "word": " hour", "probability": 0.6298828125}, {"start": 1718.63, "end": 1719.09, "word": " increases,", "probability": 0.91943359375}, {"start": 1719.63, "end": 1719.81, "word": " your", "probability": 0.8837890625}, {"start": 1719.81, "end": 1720.21, "word": " scores", "probability": 0.6904296875}, {"start": 1720.21, "end": 1720.59, "word": " also", "probability": 0.83154296875}, {"start": 1720.59, "end": 1721.11, "word": " increase.", "probability": 0.81494140625}, {"start": 1722.27, "end": 1722.53, "word": " In", "probability": 0.93603515625}, {"start": 1722.53, "end": 1722.75, "word": " this", "probability": 0.94580078125}, {"start": 1722.75, "end": 1722.99, "word": " case,", "probability": 0.91259765625}, {"start": 1723.05, "end": 1723.13, "word": " if", "probability": 0.931640625}, {"start": 1723.13, "end": 1723.25, "word": " there", "probability": 0.91357421875}, {"start": 1723.25, "end": 1723.39, "word": " is", "probability": 0.8896484375}, {"start": 1723.39, "end": 1723.69, "word": " only", "probability": 0.92236328125}, {"start": 1723.69, "end": 1723.97, "word": " one", "probability": 0.8974609375}, {"start": 1723.97, "end": 1724.31, "word": " X,", "probability": 0.60888671875}, {"start": 1724.71, "end": 1724.93, "word": " one", "probability": 0.91064453125}, {"start": 1724.93, "end": 1725.35, "word": " independent", "probability": 0.86328125}, {"start": 1725.35, "end": 1725.79, "word": " variable,", "probability": 0.89013671875}, {"start": 1726.01, "end": 1726.03, "word": " it's", "probability": 0.78759765625}, {"start": 1726.03, "end": 1726.33, "word": " called", "probability": 0.91259765625}, {"start": 1726.33, "end": 1726.93, "word": " simple", "probability": 0.77685546875}, {"start": 1726.93, "end": 1728.17, "word": " linear", "probability": 0.859375}, {"start": 1728.17, "end": 1728.65, "word": " regression.", "probability": 0.8486328125}, {"start": 1729.45, "end": 1730.05, "word": " Maybe", "probability": 0.93896484375}, {"start": 1730.05, "end": 1730.53, "word": " another", "probability": 0.9296875}, {"start": 1730.53, "end": 1731.11, "word": " variable,", "probability": 0.9150390625}, {"start": 1732.27, "end": 1732.73, "word": " number", "probability": 0.92724609375}, {"start": 1732.73, "end": 1733.39, "word": " of", "probability": 0.9716796875}, {"start": 1733.39, "end": 1735.39, "word": " missing", "probability": 0.78076171875}, {"start": 1735.39, "end": 1736.05, "word": " classes", "probability": 0.89208984375}, {"start": 1736.05, "end": 1739.73, "word": " or", "probability": 0.412109375}, {"start": 1739.73, "end": 1740.13, "word": " attendance.", "probability": 0.77294921875}], "temperature": 1.0}, {"id": 66, "seek": 177088, "start": 1742.04, "end": 1770.88, "text": " As number of missing classes increases, your score goes down. That means there exists negative relationship between missing classes and your score. So sometimes, maybe there exists positive or negative. It depends on the variable itself. In this case, if there are more than one variable, then we are talking about multiple linear regression model. But here, we have only one independent variable.", "tokens": [1018, 1230, 295, 5361, 5359, 8637, 11, 428, 6175, 1709, 760, 13, 663, 1355, 456, 8198, 3671, 2480, 1296, 5361, 5359, 293, 428, 6175, 13, 407, 2171, 11, 1310, 456, 8198, 3353, 420, 3671, 13, 467, 5946, 322, 264, 7006, 2564, 13, 682, 341, 1389, 11, 498, 456, 366, 544, 813, 472, 7006, 11, 550, 321, 366, 1417, 466, 3866, 8213, 24590, 2316, 13, 583, 510, 11, 321, 362, 787, 472, 6695, 7006, 13], "avg_logprob": -0.15208334008852642, "compression_ratio": 1.7155172413793103, "no_speech_prob": 0.0, "words": [{"start": 1742.04, "end": 1742.38, "word": " As", "probability": 0.68798828125}, {"start": 1742.38, "end": 1742.64, "word": " number", "probability": 0.81298828125}, {"start": 1742.64, "end": 1742.78, "word": " of", "probability": 0.9580078125}, {"start": 1742.78, "end": 1742.94, "word": " missing", "probability": 0.76171875}, {"start": 1742.94, "end": 1743.16, "word": " classes", "probability": 0.916015625}, {"start": 1743.16, 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The form, the strength. Here, the form we are talking about is just linear. Now, another type of relationship, the strength of the relationship. 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So it depends on the direction. 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It depends on the direction of the relationship between the two variables. 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If the points are scattered away from the regression line, I mean you cannot determine if it is positive or negative, then there is no relationship between the two variables, the same as this one. 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We know the regression is the straight line equation is given by this one. Y equals beta 0 plus beta 1x plus epsilon.", "tokens": [1610, 577, 393, 321, 915, 264, 1151, 24590, 1622, 300, 9001, 264, 1412, 291, 362, 30, 492, 458, 264, 24590, 307, 264, 2997, 1622, 5367, 307, 2212, 538, 341, 472, 13, 398, 6915, 9861, 1958, 1804, 9861, 502, 87, 1804, 17889, 13], "avg_logprob": -0.20367005259491677, "compression_ratio": 1.4360902255639099, "no_speech_prob": 0.0, "words": [{"start": 1971.25, "end": 1971.53, "word": " Or", "probability": 0.85888671875}, {"start": 1971.53, "end": 1971.77, "word": " how", "probability": 0.8544921875}, {"start": 1971.77, "end": 1971.99, "word": " can", "probability": 0.93359375}, {"start": 1971.99, "end": 1972.17, "word": " we", "probability": 0.9423828125}, {"start": 1972.17, "end": 1972.55, "word": " find", "probability": 0.892578125}, {"start": 1972.55, "end": 1972.81, "word": " the", "probability": 0.916015625}, {"start": 1972.81, "end": 1973.17, "word": " best", "probability": 0.91650390625}, {"start": 1973.17, "end": 1973.71, "word": " regression", "probability": 0.93798828125}, {"start": 1973.71, "end": 1974.17, "word": " line", "probability": 0.93408203125}, {"start": 1974.17, "end": 1975.29, "word": " that", "probability": 0.87939453125}, {"start": 1975.29, "end": 1975.73, "word": " fits", "probability": 0.8623046875}, {"start": 1975.73, "end": 1975.97, "word": " the", "probability": 0.9150390625}, {"start": 1975.97, "end": 1976.21, "word": " data", "probability": 0.9267578125}, {"start": 1976.21, "end": 1976.45, "word": " you", "probability": 0.73583984375}, {"start": 1976.45, "end": 1976.67, "word": " have?", "probability": 0.91845703125}, {"start": 1978.21, "end": 1978.57, "word": " We", "probability": 0.92822265625}, {"start": 1978.57, "end": 1978.71, "word": " know", "probability": 0.8779296875}, {"start": 1978.71, "end": 1978.87, "word": " the", "probability": 0.78076171875}, {"start": 1978.87, "end": 1979.19, "word": " regression", "probability": 0.94873046875}, {"start": 1979.19, "end": 1979.57, "word": " is", "probability": 0.54443359375}, {"start": 1979.57, "end": 1979.93, "word": " the", "probability": 0.6630859375}, {"start": 1979.93, "end": 1982.49, "word": " straight", "probability": 0.6396484375}, {"start": 1982.49, "end": 1982.79, "word": " line", "probability": 0.873046875}, {"start": 1982.79, "end": 1983.25, "word": " equation", "probability": 0.94775390625}, {"start": 1983.25, "end": 1983.65, "word": " is", "probability": 0.395263671875}, {"start": 1983.65, "end": 1983.83, "word": " given", "probability": 0.904296875}, {"start": 1983.83, "end": 1984.07, "word": " by", "probability": 0.9677734375}, {"start": 1984.07, "end": 1984.35, "word": " this", "probability": 0.95166015625}, {"start": 1984.35, "end": 1984.71, "word": " one.", "probability": 0.9326171875}, {"start": 1985.51, "end": 1986.27, "word": " Y", "probability": 0.9248046875}, {"start": 1986.27, "end": 1989.17, "word": " equals", "probability": 0.802734375}, {"start": 1989.17, "end": 1990.93, "word": " beta", "probability": 0.83740234375}, {"start": 1990.93, "end": 1991.35, "word": " 0", "probability": 0.521484375}, {"start": 1991.35, "end": 1993.03, "word": " plus", "probability": 0.90478515625}, {"start": 1993.03, "end": 1995.59, "word": " beta", "probability": 0.88037109375}, {"start": 1995.59, "end": 1996.21, "word": " 1x", "probability": 0.6492919921875}, {"start": 1996.21, "end": 1997.61, "word": " plus", "probability": 0.94482421875}, {"start": 1997.61, "end": 1998.45, "word": " epsilon.", "probability": 0.88623046875}], "temperature": 1.0}, {"id": 76, "seek": 202697, "start": 1999.35, "end": 2026.97, "text": " This can be pronounced as epsilon. It's a great letter, the same as alpha, beta, mu, sigma, and so on. So it's epsilon. I, it means observation number I. I 1, 2, 3, up to 10, for example, is the same for selling price of a home. So I 1, 2, 3, all the way up to the sample size.", "tokens": [639, 393, 312, 23155, 382, 17889, 13, 467, 311, 257, 869, 5063, 11, 264, 912, 382, 8961, 11, 9861, 11, 2992, 11, 12771, 11, 293, 370, 322, 13, 407, 309, 311, 17889, 13, 286, 11, 309, 1355, 14816, 1230, 286, 13, 286, 502, 11, 568, 11, 805, 11, 493, 281, 1266, 11, 337, 1365, 11, 307, 264, 912, 337, 6511, 3218, 295, 257, 1280, 13, 407, 286, 502, 11, 568, 11, 805, 11, 439, 264, 636, 493, 281, 264, 6889, 2744, 13], "avg_logprob": -0.17884036754987326, "compression_ratio": 1.5108695652173914, "no_speech_prob": 0.0, "words": [{"start": 1999.35, "end": 1999.77, "word": " This", "probability": 0.71923828125}, {"start": 1999.77, "end": 2000.13, "word": " can", "probability": 0.134033203125}, {"start": 2000.13, "end": 2000.49, "word": " be", "probability": 0.58740234375}, {"start": 2000.49, "end": 2000.93, "word": " pronounced", "probability": 0.83203125}, {"start": 2000.93, "end": 2001.25, "word": " as", "probability": 0.96875}, 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Beta 0 is population Y intercept. For example, if we have this scatter plot. Now, beta 0 is this one. So this is your beta 0. 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So in this case, beta zero equals zero. So it could be positive and negative or equal zero, but still we have positive relationship. 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X is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is your independent variable, Y is 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Maybe you select a random sample, that sample is small. Maybe there is a random, I'm sorry, there is sampling error. 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So all of them are in this term. So epsilon I means something you don't include in your regression modeling. For example, you don't include all the independent variables that affect Y, or your sample size is not large enough. So all of these measured in random error term. 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Now, the data you have, the blue circles represent the observed value. So these blue circles are the observed values. 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Now, the predicted value can be determined by using the regression line. So this line is the predicted value of Y for XR. Again, beta zero is the intercept. As we mentioned before, it could be positive or negative or even equal zero. 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The relationship may be positive or negative. It could be negative. Now, for negative relationship,", "tokens": [2639, 1168, 30, 440, 2480, 815, 312, 3353, 420, 3671, 13, 467, 727, 312, 3671, 13, 823, 11, 337, 3671, 2480, 11], "avg_logprob": -0.3536005305207294, "compression_ratio": 1.3103448275862069, "no_speech_prob": 0.0, "words": [{"start": 2365.01, "end": 2365.27, "word": " Any", "probability": 0.3095703125}, {"start": 2365.27, "end": 2365.65, "word": " question?", "probability": 0.57958984375}, {"start": 2371.75, "end": 2372.57, "word": " The", "probability": 0.65625}, {"start": 2372.57, "end": 2373.01, "word": " relationship", "probability": 0.38427734375}, {"start": 2373.01, "end": 2373.47, "word": " may", "probability": 0.54248046875}, {"start": 2373.47, "end": 2373.59, "word": " be", "probability": 0.9482421875}, {"start": 2373.59, "end": 2373.89, "word": " positive", "probability": 0.87451171875}, {"start": 2373.89, "end": 2374.79, "word": " or", "probability": 0.91650390625}, {"start": 2374.79, "end": 2375.33, "word": " negative.", "probability": 0.92529296875}, {"start": 2376.57, "end": 2376.61, "word": " It", "probability": 0.6796875}, {"start": 2376.61, "end": 2376.73, "word": " could", "probability": 0.8740234375}, {"start": 2376.73, "end": 2376.87, "word": " be", "probability": 0.95361328125}, {"start": 2376.87, "end": 2377.19, "word": " negative.", "probability": 0.88232421875}, {"start": 2380.95, "end": 2381.41, "word": " Now,", "probability": 0.67724609375}, {"start": 2381.49, "end": 2381.73, "word": " for", "probability": 0.9189453125}, {"start": 2381.73, "end": 2382.05, "word": " negative", "probability": 0.7119140625}, {"start": 2382.05, "end": 2382.71, "word": " relationship,", "probability": 0.865234375}], "temperature": 1.0}, {"id": 91, "seek": 242206, "start": 2397.0, "end": 2422.06, "text": " Or negative, where beta zero is negative. Or beta zero equals zero. So here there exists negative relationship, but beta zero may be positive.", "tokens": [1610, 3671, 11, 689, 9861, 4018, 307, 3671, 13, 1610, 9861, 4018, 6915, 4018, 13, 407, 510, 456, 8198, 3671, 2480, 11, 457, 9861, 4018, 815, 312, 3353, 13], "avg_logprob": -0.30286457339922584, "compression_ratio": 1.4895833333333333, "no_speech_prob": 0.0, "words": [{"start": 2397.0, "end": 2397.76, "word": " Or", "probability": 0.29931640625}, {"start": 2397.76, "end": 2398.16, "word": " negative,", "probability": 0.59375}, {"start": 2399.54, "end": 2400.3, "word": " where", "probability": 0.73291015625}, {"start": 2400.3, "end": 2400.56, "word": " beta", "probability": 0.67236328125}, {"start": 2400.56, "end": 2400.9, "word": " zero", "probability": 0.439208984375}, {"start": 2400.9, "end": 2401.5, "word": " is", "probability": 0.9248046875}, {"start": 2401.5, "end": 2404.46, "word": " negative.", "probability": 0.92724609375}, {"start": 2404.52, "end": 2405.24, "word": " Or", "probability": 0.92236328125}, {"start": 2405.24, "end": 2408.7, "word": " beta", "probability": 0.60498046875}, {"start": 2408.7, "end": 2409.08, "word": " zero", "probability": 0.88720703125}, {"start": 2409.08, "end": 2409.38, "word": " equals", "probability": 0.841796875}, {"start": 2409.38, "end": 2409.74, "word": " zero.", "probability": 0.8515625}, {"start": 2416.68, "end": 2417.44, "word": " So", "probability": 0.89599609375}, {"start": 2417.44, "end": 2417.7, "word": " here", "probability": 0.75732421875}, {"start": 2417.7, "end": 2418.0, "word": " there", "probability": 0.56640625}, {"start": 2418.0, "end": 2418.32, "word": " exists", "probability": 0.75927734375}, {"start": 2418.32, "end": 2418.72, "word": " negative", "probability": 0.8203125}, {"start": 2418.72, "end": 2419.32, "word": " relationship,", "probability": 0.916015625}, {"start": 2420.16, "end": 2420.62, "word": " but", "probability": 0.90283203125}, {"start": 2420.62, "end": 2420.96, "word": " beta", "probability": 0.91796875}, {"start": 2420.96, "end": 2421.34, "word": " zero", "probability": 0.89599609375}, {"start": 2421.34, "end": 2421.56, "word": " may", "probability": 0.7802734375}, {"start": 2421.56, "end": 2421.68, "word": " be", "probability": 0.9541015625}, {"start": 2421.68, "end": 2422.06, "word": " positive.", "probability": 0.9365234375}], "temperature": 1.0}, {"id": 92, "seek": 245231, "start": 2425.87, "end": 2452.31, "text": " So again, the sign of beta 0 also does not affect the relationship between the two variables. Now, we don't actually know the values of beta 0 and beta 1. We are going to estimate these values from the sample we have. So the simple linear regression equation provides an estimate of the population regression line.", "tokens": [407, 797, 11, 264, 1465, 295, 9861, 1958, 611, 775, 406, 3345, 264, 2480, 1296, 264, 732, 9102, 13, 823, 11, 321, 500, 380, 767, 458, 264, 4190, 295, 9861, 1958, 293, 9861, 502, 13, 492, 366, 516, 281, 12539, 613, 4190, 490, 264, 6889, 321, 362, 13, 407, 264, 2199, 8213, 24590, 5367, 6417, 364, 12539, 295, 264, 4415, 24590, 1622, 13], "avg_logprob": -0.17431640136055648, "compression_ratio": 1.6153846153846154, "no_speech_prob": 0.0, "words": [{"start": 2425.8700000000003, "end": 2426.51, "word": " So", "probability": 0.13330078125}, {"start": 2426.51, "end": 2427.15, "word": " again,", "probability": 0.6865234375}, {"start": 2427.45, "end": 2427.45, "word": " the", "probability": 0.78857421875}, {"start": 2427.45, "end": 2427.73, "word": " sign", "probability": 0.49169921875}, {"start": 2427.73, "end": 2427.89, "word": " of", "probability": 0.92822265625}, {"start": 2427.89, 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1.", "probability": 0.9765625}, {"start": 2441.57, "end": 2441.87, "word": " We", "probability": 0.9443359375}, {"start": 2441.87, "end": 2442.03, "word": " are", "probability": 0.92041015625}, {"start": 2442.03, "end": 2442.27, "word": " going", "probability": 0.94384765625}, {"start": 2442.27, "end": 2442.47, "word": " to", "probability": 0.966796875}, {"start": 2442.47, "end": 2442.91, "word": " estimate", "probability": 0.91748046875}, {"start": 2442.91, "end": 2444.03, "word": " these", "probability": 0.85498046875}, {"start": 2444.03, "end": 2444.51, "word": " values", "probability": 0.9638671875}, {"start": 2444.51, "end": 2444.93, "word": " from", "probability": 0.8837890625}, {"start": 2444.93, "end": 2445.39, "word": " the", "probability": 0.9130859375}, {"start": 2445.39, "end": 2445.65, "word": " sample", "probability": 0.5322265625}, {"start": 2445.65, "end": 2445.85, "word": " we", "probability": 0.9267578125}, {"start": 2445.85, "end": 2446.13, "word": " have.", "probability": 0.93701171875}, {"start": 2446.97, "end": 2447.19, "word": " So", "probability": 0.8642578125}, {"start": 2447.19, "end": 2447.35, "word": " the", "probability": 0.68798828125}, {"start": 2447.35, "end": 2447.67, "word": " simple", "probability": 0.630859375}, {"start": 2447.67, "end": 2448.11, "word": " linear", "probability": 0.9169921875}, {"start": 2448.11, "end": 2448.45, "word": " regression", "probability": 0.9736328125}, {"start": 2448.45, "end": 2448.89, "word": " equation", "probability": 0.96484375}, {"start": 2448.89, "end": 2449.61, "word": " provides", "probability": 0.89111328125}, {"start": 2449.61, "end": 2449.93, "word": " an", "probability": 0.9443359375}, {"start": 2449.93, "end": 2450.45, "word": " estimate", "probability": 0.91552734375}, {"start": 2450.45, "end": 2450.85, "word": " of", "probability": 0.96533203125}, {"start": 2450.85, "end": 2450.97, "word": " the", "probability": 0.9111328125}, {"start": 2450.97, "end": 2451.37, "word": " population", "probability": 0.94287109375}, {"start": 2451.37, "end": 2451.81, "word": " regression", "probability": 0.91357421875}, {"start": 2451.81, "end": 2452.31, "word": " line.", "probability": 0.94287109375}], "temperature": 1.0}, {"id": 93, "seek": 246681, "start": 2453.45, "end": 2466.81, "text": " So here we have Yi hat is the estimated or predicted Y value for observation I. The estimate of the regression intercept P0.", "tokens": [407, 510, 321, 362, 16747, 2385, 307, 264, 14109, 420, 19147, 398, 2158, 337, 14816, 286, 13, 440, 12539, 295, 264, 24590, 24700, 430, 15, 13], "avg_logprob": -0.22410301036304897, "compression_ratio": 1.2135922330097086, "no_speech_prob": 0.0, "words": [{"start": 2453.45, "end": 2453.71, "word": " So", "probability": 0.86572265625}, {"start": 2453.71, "end": 2453.89, "word": " here", "probability": 0.759765625}, {"start": 2453.89, "end": 2454.05, "word": " we", "probability": 0.8466796875}, {"start": 2454.05, "end": 2454.31, "word": " have", "probability": 0.9423828125}, {"start": 2454.31, "end": 2454.75, "word": " Yi", "probability": 0.364013671875}, {"start": 2454.75, "end": 2455.27, "word": " hat", "probability": 0.80078125}, {"start": 2455.27, "end": 2457.11, "word": " is", "probability": 0.74072265625}, {"start": 2457.11, "end": 2457.43, "word": " the", "probability": 0.9140625}, {"start": 2457.43, "end": 2458.13, "word": " estimated", "probability": 0.900390625}, {"start": 2458.13, "end": 2458.57, "word": " or", "probability": 0.9130859375}, {"start": 2458.57, "end": 2459.09, "word": " predicted", "probability": 0.85888671875}, {"start": 2459.09, "end": 2459.43, "word": " Y", "probability": 0.8515625}, {"start": 2459.43, "end": 2459.79, "word": " value", "probability": 0.85400390625}, {"start": 2459.79, "end": 2460.01, "word": " for", "probability": 0.93212890625}, {"start": 2460.01, "end": 2460.47, "word": " observation", "probability": 0.88330078125}, {"start": 2460.47, "end": 2460.85, "word": " I.", "probability": 0.65576171875}, {"start": 2463.53, "end": 2464.41, "word": " The", "probability": 0.84716796875}, {"start": 2464.41, "end": 2464.93, "word": " estimate", "probability": 0.921875}, {"start": 2464.93, "end": 2465.19, "word": " of", "probability": 0.96044921875}, {"start": 2465.19, "end": 2465.31, "word": " the", "probability": 0.888671875}, {"start": 2465.31, "end": 2465.59, "word": " regression", "probability": 0.94140625}, {"start": 2465.59, "end": 2466.15, "word": " intercept", "probability": 0.9501953125}, {"start": 2466.15, "end": 2466.81, "word": " P0.", "probability": 0.745849609375}], "temperature": 1.0}, {"id": 94, "seek": 249596, "start": 2468.0, "end": 2495.96, "text": " The estimate of the regression slope is b1, and this is your x, all independent variable. So here is the regression equation. Simple linear regression equation is given by y hat, the predicted value of y equals b0 plus b1 times x1. Now these coefficients, b0 and b1 can be computed", "tokens": [440, 12539, 295, 264, 24590, 13525, 307, 272, 16, 11, 293, 341, 307, 428, 2031, 11, 439, 6695, 7006, 13, 407, 510, 307, 264, 24590, 5367, 13, 21532, 8213, 24590, 5367, 307, 2212, 538, 288, 2385, 11, 264, 19147, 2158, 295, 288, 6915, 272, 15, 1804, 272, 16, 1413, 2031, 16, 13, 823, 613, 31994, 11, 272, 15, 293, 272, 16, 393, 312, 40610], "avg_logprob": -0.18774038461538461, "compression_ratio": 1.5932203389830508, "no_speech_prob": 0.0, "words": [{"start": 2468.0, "end": 2468.22, "word": " The", "probability": 0.7294921875}, {"start": 2468.22, "end": 2468.74, "word": " estimate", "probability": 0.92431640625}, {"start": 2468.74, "end": 2469.02, "word": " of", "probability": 0.9599609375}, {"start": 2469.02, "end": 2469.16, "word": " the", "probability": 0.88232421875}, {"start": 2469.16, "end": 2469.46, "word": " regression", "probability": 0.9208984375}, {"start": 2469.46, "end": 2469.84, "word": " slope", "probability": 0.80419921875}, {"start": 2469.84, "end": 2470.02, "word": " is", "probability": 0.93603515625}, {"start": 2470.02, "end": 2470.42, "word": " b1,", "probability": 0.6295166015625}, {"start": 2470.8, "end": 2471.18, "word": " and", "probability": 0.93310546875}, {"start": 2471.18, "end": 2471.36, "word": " this", "probability": 0.93896484375}, {"start": 2471.36, "end": 2471.52, "word": " is", "probability": 0.93701171875}, {"start": 2471.52, "end": 2471.86, "word": " your", "probability": 0.89697265625}, {"start": 2471.86, "end": 2473.36, "word": " x,", "probability": 0.77294921875}, {"start": 2473.72, "end": 2474.1, "word": " all", "probability": 0.7255859375}, {"start": 2474.1, "end": 2474.5, "word": " independent", "probability": 0.84423828125}, {"start": 2474.5, "end": 2474.96, "word": " variable.", "probability": 0.75341796875}, {"start": 2475.68, "end": 2476.1, "word": " So", "probability": 0.9560546875}, {"start": 2476.1, "end": 2476.42, "word": " here", "probability": 0.75341796875}, {"start": 2476.42, "end": 2476.68, "word": " is", "probability": 0.93994140625}, {"start": 2476.68, "end": 2476.82, "word": " the", "probability": 0.91259765625}, {"start": 2476.82, "end": 2477.18, "word": " regression", "probability": 0.9638671875}, {"start": 2477.18, "end": 2478.02, "word": " equation.", "probability": 0.97705078125}, {"start": 2479.0, "end": 2479.52, "word": " Simple", "probability": 0.88330078125}, {"start": 2479.52, "end": 2479.94, "word": " linear", "probability": 0.72998046875}, {"start": 2479.94, "end": 2480.34, "word": " regression", "probability": 0.9677734375}, {"start": 2480.34, "end": 2480.74, "word": " equation", "probability": 0.91748046875}, {"start": 2480.74, "end": 2480.92, "word": " is", "probability": 0.853515625}, {"start": 2480.92, "end": 2481.12, "word": " given", "probability": 0.8974609375}, {"start": 2481.12, "end": 2481.54, "word": " by", "probability": 0.974609375}, {"start": 2481.54, "end": 2482.72, "word": " y", "probability": 0.72021484375}, {"start": 2482.72, "end": 2483.08, "word": " hat,", "probability": 0.83642578125}, {"start": 2483.34, "end": 2483.52, "word": " the", "probability": 0.908203125}, {"start": 2483.52, "end": 2483.88, "word": " predicted", "probability": 0.42822265625}, {"start": 2483.88, "end": 2484.22, "word": " value", "probability": 0.9677734375}, {"start": 2484.22, "end": 2484.4, "word": " of", "probability": 0.96630859375}, {"start": 2484.4, "end": 2484.7, "word": " y", "probability": 0.94921875}, {"start": 2484.7, "end": 2485.76, "word": " equals", "probability": 0.50537109375}, {"start": 2485.76, "end": 2486.46, "word": " b0", "probability": 0.902587890625}, {"start": 2486.46, "end": 2486.72, "word": " plus", "probability": 0.92919921875}, {"start": 2486.72, "end": 2487.12, "word": " b1", "probability": 0.98681640625}, {"start": 2487.12, "end": 2487.66, "word": " times", "probability": 0.921875}, {"start": 2487.66, "end": 2489.38, "word": " x1.", "probability": 0.97998046875}, {"start": 2491.24, "end": 2491.74, "word": " Now", "probability": 0.95849609375}, {"start": 2491.74, "end": 2492.1, "word": " these", "probability": 0.50390625}, {"start": 2492.1, "end": 2492.84, "word": " coefficients,", "probability": 0.89111328125}, {"start": 2493.08, "end": 2493.46, "word": " b0", "probability": 0.968505859375}, {"start": 2493.46, "end": 2493.62, "word": " and", "probability": 0.9423828125}, {"start": 2493.62, "end": 2494.02, "word": " b1", "probability": 0.99755859375}, {"start": 2494.02, "end": 2494.26, "word": " can", "probability": 0.5810546875}, {"start": 2494.26, "end": 2495.28, "word": " be", "probability": 0.95458984375}, {"start": 2495.28, "end": 2495.96, "word": " computed", "probability": 0.8828125}], "temperature": 1.0}, {"id": 95, "seek": 252667, "start": 2497.9, "end": 2526.68, "text": " by the following equations. So the regression equation is given by y hat equals b0 plus b1x. Now the slope, b1, is r times standard deviation of y", "tokens": [538, 264, 3480, 11787, 13, 407, 264, 24590, 5367, 307, 2212, 538, 288, 2385, 6915, 272, 15, 1804, 272, 16, 87, 13, 823, 264, 13525, 11, 272, 16, 11, 307, 367, 1413, 3832, 25163, 295, 288], "avg_logprob": -0.23205237130861026, "compression_ratio": 1.2894736842105263, "no_speech_prob": 0.0, "words": [{"start": 2497.9, "end": 2498.4, "word": " by", "probability": 0.368896484375}, {"start": 2498.4, "end": 2499.22, "word": " the", "probability": 0.89892578125}, {"start": 2499.22, "end": 2499.48, "word": " following", "probability": 0.859375}, {"start": 2499.48, "end": 2500.04, "word": " equations.", "probability": 0.89013671875}, {"start": 2501.68, "end": 2502.54, "word": " So", "probability": 0.95068359375}, {"start": 2502.54, "end": 2502.72, "word": " the", "probability": 0.7294921875}, {"start": 2502.72, "end": 2503.04, "word": " regression", "probability": 0.95947265625}, {"start": 2503.04, "end": 2503.64, "word": " equation", "probability": 0.9775390625}, {"start": 2503.64, "end": 2512.92, "word": " is", "probability": 0.76318359375}, {"start": 2512.92, "end": 2513.16, "word": " given", "probability": 0.90625}, {"start": 2513.16, "end": 2513.54, "word": " by", "probability": 0.96435546875}, {"start": 2513.54, "end": 2515.12, "word": " y", "probability": 0.6318359375}, {"start": 2515.12, "end": 2515.38, "word": " hat", "probability": 0.89453125}, {"start": 2515.38, "end": 2515.7, "word": " equals", "probability": 0.603515625}, {"start": 2515.7, "end": 2516.18, "word": " b0", "probability": 0.615234375}, {"start": 2516.18, "end": 2516.52, "word": " plus", "probability": 0.9423828125}, {"start": 2516.52, "end": 2517.26, "word": " b1x.", "probability": 0.82470703125}, {"start": 2519.94, "end": 2520.4, "word": " Now", "probability": 0.90576171875}, {"start": 2520.4, "end": 2520.58, "word": " the", "probability": 0.4697265625}, {"start": 2520.58, "end": 2520.94, "word": " slope,", "probability": 0.94970703125}, {"start": 2521.24, "end": 2521.68, "word": " b1,", "probability": 0.983154296875}, {"start": 2523.2, "end": 2523.66, "word": " is", "probability": 0.93701171875}, {"start": 2523.66, "end": 2524.08, "word": " r", "probability": 0.64599609375}, {"start": 2524.08, "end": 2525.46, "word": " times", "probability": 0.92822265625}, {"start": 2525.46, "end": 2525.82, "word": " standard", "probability": 0.666015625}, {"start": 2525.82, "end": 2526.14, "word": " deviation", "probability": 0.89990234375}, {"start": 2526.14, "end": 2526.36, "word": " of", "probability": 0.9677734375}, {"start": 2526.36, "end": 2526.68, "word": " y", "probability": 0.9873046875}], "temperature": 1.0}, {"id": 96, "seek": 255362, "start": 2527.5, "end": 2553.62, "text": " Times standard deviation of x. This is the simplest equation to determine the value of the star. B1r, r is the correlation coefficient. Sy is xr, the standard deviations of y and x. Where b0, which is y intercept, is y bar minus b x bar, or b1 x bar.", "tokens": [11366, 3832, 25163, 295, 2031, 13, 639, 307, 264, 22811, 5367, 281, 6997, 264, 2158, 295, 264, 3543, 13, 363, 16, 81, 11, 367, 307, 264, 20009, 17619, 13, 3902, 307, 2031, 81, 11, 264, 3832, 31219, 763, 295, 288, 293, 2031, 13, 2305, 272, 15, 11, 597, 307, 288, 24700, 11, 307, 288, 2159, 3175, 272, 2031, 2159, 11, 420, 272, 16, 2031, 2159, 13], "avg_logprob": -0.24277051838476266, "compression_ratio": 1.5493827160493827, "no_speech_prob": 0.0, "words": [{"start": 2527.5, "end": 2527.92, "word": " Times", "probability": 0.19921875}, {"start": 2527.92, "end": 2528.18, "word": " standard", "probability": 0.578125}, {"start": 2528.18, "end": 2528.42, "word": " deviation", "probability": 0.85546875}, {"start": 2528.42, "end": 2528.56, "word": " of", "probability": 0.833984375}, {"start": 2528.56, "end": 2528.74, "word": " x.", "probability": 0.6171875}, {"start": 2529.58, "end": 2530.26, "word": " This", "probability": 0.89111328125}, {"start": 2530.26, "end": 2530.38, "word": " is", "probability": 0.95068359375}, {"start": 2530.38, "end": 2530.54, "word": " the", "probability": 0.91552734375}, {"start": 2530.54, "end": 2530.88, "word": " simplest", "probability": 0.8916015625}, {"start": 2530.88, "end": 2531.42, "word": " equation", "probability": 0.9755859375}, {"start": 2531.42, "end": 2531.96, "word": " to", "probability": 0.9541015625}, {"start": 2531.96, "end": 2532.52, "word": " determine", "probability": 0.92919921875}, {"start": 2532.52, "end": 2533.4, "word": " the", "probability": 0.89013671875}, {"start": 2533.4, "end": 2533.58, "word": " value", "probability": 0.84912109375}, {"start": 2533.58, "end": 2533.7, "word": " of", "probability": 0.96484375}, {"start": 2533.7, "end": 2533.82, "word": " the", "probability": 0.7822265625}, {"start": 2533.82, "end": 2534.06, "word": " star.", "probability": 0.66162109375}, {"start": 2534.58, "end": 2535.26, "word": " B1r,", "probability": 0.613037109375}, {"start": 2535.4, "end": 2535.64, "word": " r", "probability": 0.9697265625}, {"start": 2535.64, "end": 2535.8, "word": " is", "probability": 0.93310546875}, {"start": 2535.8, "end": 2535.92, "word": " the", "probability": 0.75}, {"start": 2535.92, "end": 2536.28, "word": " correlation", "probability": 0.919921875}, {"start": 2536.28, "end": 2536.86, "word": " coefficient.", "probability": 0.94091796875}, {"start": 2538.22, "end": 2538.74, "word": " Sy", "probability": 0.86962890625}, {"start": 2538.74, "end": 2538.98, "word": " is", "probability": 0.39794921875}, {"start": 2538.98, "end": 2539.7, "word": " xr,", "probability": 0.786376953125}, {"start": 2539.94, "end": 2540.2, "word": " the", "probability": 0.79443359375}, {"start": 2540.2, "end": 2540.5, "word": " standard", "probability": 0.95458984375}, {"start": 2540.5, "end": 2541.0, "word": " deviations", "probability": 0.918212890625}, {"start": 2541.0, "end": 2541.26, "word": " of", "probability": 0.96484375}, {"start": 2541.26, "end": 2541.54, "word": " y", "probability": 0.98828125}, {"start": 2541.54, "end": 2541.72, "word": " and", "probability": 0.943359375}, {"start": 2541.72, "end": 2542.06, "word": " x.", "probability": 0.99755859375}, {"start": 2543.64, "end": 2544.24, "word": " Where", "probability": 0.8427734375}, {"start": 2544.24, "end": 2545.08, "word": " b0,", "probability": 0.6103515625}, {"start": 2545.52, "end": 2545.88, "word": " which", "probability": 0.66357421875}, {"start": 2545.88, "end": 2545.96, "word": " is", "probability": 0.9541015625}, {"start": 2545.96, "end": 2546.22, "word": " y", "probability": 0.98388671875}, {"start": 2546.22, "end": 2546.58, "word": " intercept,", "probability": 0.876953125}, {"start": 2547.44, "end": 2547.9, "word": " is", "probability": 0.931640625}, {"start": 2547.9, "end": 2548.32, "word": " y", "probability": 0.98681640625}, {"start": 2548.32, "end": 2548.56, "word": " bar", "probability": 0.865234375}, {"start": 2548.56, "end": 2548.92, "word": " minus", "probability": 0.95751953125}, {"start": 2548.92, "end": 2549.14, "word": " b", "probability": 0.90283203125}, {"start": 2549.14, "end": 2549.36, "word": " x", "probability": 0.51904296875}, {"start": 2549.36, "end": 2549.68, "word": " bar,", "probability": 0.9404296875}, {"start": 2549.9, "end": 2550.88, "word": " or", "probability": 0.908203125}, {"start": 2550.88, "end": 2551.34, "word": " b1", "probability": 0.949951171875}, {"start": 2551.34, "end": 2553.2, "word": " x", "probability": 0.78173828125}, {"start": 2553.2, "end": 2553.62, "word": " bar.", "probability": 0.93896484375}], "temperature": 1.0}, {"id": 97, "seek": 257896, "start": 2555.12, "end": 2578.96, "text": " Sx, as we know, is the sum of x minus y squared divided by n minus 1 under square root, similarly for y values. So this, how can we, these formulas compute the values of b0 and b1. So we are going to use these equations in order to determine the values of b0 and b1.", "tokens": [318, 87, 11, 382, 321, 458, 11, 307, 264, 2408, 295, 2031, 3175, 288, 8889, 6666, 538, 297, 3175, 502, 833, 3732, 5593, 11, 14138, 337, 288, 4190, 13, 407, 341, 11, 577, 393, 321, 11, 613, 30546, 14722, 264, 4190, 295, 272, 15, 293, 272, 16, 13, 407, 321, 366, 516, 281, 764, 613, 11787, 294, 1668, 281, 6997, 264, 4190, 295, 272, 15, 293, 272, 16, 13], "avg_logprob": -0.2294642897588866, "compression_ratio": 1.6181818181818182, "no_speech_prob": 0.0, "words": [{"start": 2555.12, "end": 2555.66, "word": " Sx,", "probability": 0.55242919921875}, {"start": 2555.8, "end": 2555.98, "word": " as", "probability": 0.96533203125}, {"start": 2555.98, "end": 2556.12, "word": " we", "probability": 0.8916015625}, {"start": 2556.12, "end": 2556.34, "word": " know,", "probability": 0.88623046875}, {"start": 2556.48, "end": 2556.58, "word": " is", "probability": 0.65625}, {"start": 2556.58, "end": 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For example, suppose we are talking about your score Y and X number of missing classes. And suppose, for example, Y hat", "tokens": [823, 11, 437, 311, 428, 14174, 466, 264, 13525, 293, 264, 24700, 30, 1171, 1365, 11, 7297, 321, 366, 1417, 466, 428, 6175, 398, 293, 1783, 1230, 295, 5361, 5359, 13, 400, 7297, 11, 337, 1365, 11, 398, 2385], "avg_logprob": -0.2259765576571226, "compression_ratio": 1.385185185185185, "no_speech_prob": 0.0, "words": [{"start": 2584.67, "end": 2584.99, "word": " Now,", "probability": 0.7666015625}, {"start": 2585.17, "end": 2585.43, "word": " what's", "probability": 0.84326171875}, {"start": 2585.43, "end": 2585.57, "word": " your", "probability": 0.8935546875}, {"start": 2585.57, "end": 2586.41, "word": " interpretation", "probability": 0.85595703125}, {"start": 2586.41, "end": 2587.07, "word": " about", "probability": 0.8603515625}, {"start": 2587.07, "end": 2587.37, "word": " the", "probability": 0.83544921875}, {"start": 2587.37, "end": 2587.71, "word": " slope", "probability": 0.80810546875}, {"start": 2587.71, "end": 2588.29, "word": " and", "probability": 0.90771484375}, {"start": 2588.29, "end": 2589.43, "word": " the", "probability": 0.88427734375}, {"start": 2589.43, "end": 2589.77, "word": " intercept?", "probability": 0.5234375}, {"start": 2589.97, "end": 2590.13, "word": " For", "probability": 0.94091796875}, {"start": 2590.13, "end": 2590.51, "word": " example,", "probability": 0.97119140625}, {"start": 2590.65, "end": 2591.09, "word": " suppose", "probability": 0.88671875}, {"start": 2591.09, "end": 2592.89, "word": " we", "probability": 0.734375}, {"start": 2592.89, "end": 2593.13, "word": " are", "probability": 0.8896484375}, {"start": 2593.13, "end": 2593.63, "word": " talking", "probability": 0.830078125}, {"start": 2593.63, "end": 2594.07, "word": " about", "probability": 0.91748046875}, {"start": 2594.07, "end": 2594.33, "word": " your", "probability": 0.67578125}, {"start": 2594.33, "end": 2594.69, "word": " score", "probability": 0.79931640625}, {"start": 2594.69, "end": 2595.07, "word": " Y", "probability": 0.3974609375}, {"start": 2595.07, "end": 2598.61, "word": " and", "probability": 0.57763671875}, {"start": 2598.61, "end": 2599.57, "word": " X", "probability": 0.94482421875}, {"start": 2599.57, "end": 2600.99, "word": " number", "probability": 0.9140625}, {"start": 2600.99, "end": 2601.27, "word": " of", "probability": 0.96533203125}, {"start": 2601.27, "end": 2601.55, "word": " missing", "probability": 0.86279296875}, {"start": 2601.55, "end": 2602.11, "word": " classes.", "probability": 0.91845703125}, {"start": 2609.21, "end": 2609.95, "word": " And", "probability": 0.8857421875}, {"start": 2609.95, "end": 2610.25, "word": " suppose,", "probability": 0.88427734375}, {"start": 2610.39, "end": 2610.47, "word": " for", "probability": 0.95361328125}, {"start": 2610.47, "end": 2610.87, "word": " example,", "probability": 0.97265625}, {"start": 2611.09, "end": 2611.67, "word": " Y", "probability": 0.955078125}, {"start": 2611.67, "end": 2612.11, "word": " hat", "probability": 0.896484375}], "temperature": 1.0}, {"id": 99, "seek": 263920, "start": 2612.96, "end": 2639.2, "text": " Equal 95 minus 5x. Now let's see what's the interpretation of B0. This is B0. So B0 is 95. And B1 is 5. Now what's your interpretation about B0 and B1? B0 is the estimated mean value of Y when the value of X is 0.", "tokens": [15624, 304, 13420, 3175, 1025, 87, 13, 823, 718, 311, 536, 437, 311, 264, 14174, 295, 363, 15, 13, 639, 307, 363, 15, 13, 407, 363, 15, 307, 13420, 13, 400, 363, 16, 307, 1025, 13, 823, 437, 311, 428, 14174, 466, 363, 15, 293, 363, 16, 30, 363, 15, 307, 264, 14109, 914, 2158, 295, 398, 562, 264, 2158, 295, 1783, 307, 1958, 13], "avg_logprob": -0.18880208446220917, "compression_ratio": 1.445945945945946, "no_speech_prob": 0.0, "words": [{"start": 2612.96, "end": 2613.42, "word": " Equal", "probability": 0.4514312744140625}, {"start": 2613.42, "end": 2613.88, "word": " 95", "probability": 0.89208984375}, {"start": 2613.88, "end": 2614.58, "word": " minus", "probability": 0.83056640625}, {"start": 2614.58, "end": 2615.46, "word": " 5x.", "probability": 0.71337890625}, {"start": 2617.78, "end": 2618.5, "word": " Now", "probability": 0.86328125}, {"start": 2618.5, "end": 2618.74, "word": " let's", "probability": 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So as one unit increase in x, y is our, his weight is expected to increase by four units. So again, sometimes we can interpret the y intercept, but in some cases it has no meaning.", "tokens": [1396, 321, 2066, 702, 3364, 281, 3488, 538, 1451, 30690, 13, 407, 382, 472, 4985, 3488, 294, 2031, 11, 288, 307, 527, 11, 702, 3364, 307, 5176, 281, 3488, 538, 1451, 6815, 13, 407, 797, 11, 2171, 321, 393, 7302, 264, 288, 24700, 11, 457, 294, 512, 3331, 309, 575, 572, 3620, 13], "avg_logprob": -0.22077547013759613, "compression_ratio": 1.63013698630137, "no_speech_prob": 0.0, "words": [{"start": 2813.63, "end": 2813.93, "word": " Then", "probability": 0.40673828125}, {"start": 2813.93, "end": 2814.17, "word": " we", "probability": 0.81298828125}, {"start": 2814.17, "end": 2814.79, "word": " expect", "probability": 0.92822265625}, {"start": 2814.79, "end": 2815.55, "word": " his", "probability": 0.89599609375}, {"start": 2815.55, "end": 2815.95, "word": " weight", "probability": 0.890625}, {"start": 2815.95, "end": 2816.57, "word": " to", "probability": 0.92041015625}, {"start": 2816.57, "end": 2816.93, "word": " increase", "probability": 0.63134765625}, {"start": 2816.93, "end": 2817.21, "word": " by", "probability": 0.96923828125}, {"start": 2817.21, "end": 2817.71, "word": " four", "probability": 0.386474609375}, {"start": 2817.71, "end": 2818.43, "word": " kilograms.", "probability": 0.48828125}, {"start": 2819.75, "end": 2820.01, "word": " So", "probability": 0.86572265625}, {"start": 2820.01, "end": 2820.23, "word": " as", "probability": 0.77880859375}, {"start": 2820.23, "end": 2820.47, "word": " one", "probability": 0.74755859375}, {"start": 2820.47, "end": 2820.69, "word": " unit", "probability": 0.87451171875}, {"start": 2820.69, "end": 2821.07, "word": " increase", "probability": 0.472900390625}, {"start": 2821.07, "end": 2821.29, "word": " in", "probability": 0.91748046875}, {"start": 2821.29, "end": 2821.61, "word": " x,", "probability": 0.54150390625}, {"start": 2822.59, "end": 2823.05, "word": " y", "probability": 0.74951171875}, {"start": 2823.05, "end": 2823.77, "word": " is", "probability": 0.884765625}, {"start": 2823.77, "end": 2824.19, "word": " our,", "probability": 0.77392578125}, {"start": 2824.39, "end": 2824.55, "word": " his", "probability": 0.95947265625}, {"start": 2824.55, "end": 2824.91, "word": " weight", "probability": 0.90380859375}, {"start": 2824.91, "end": 2825.13, "word": " is", "probability": 0.837890625}, {"start": 2825.13, "end": 2825.69, "word": " expected", "probability": 0.880859375}, {"start": 2825.69, "end": 2827.01, "word": " to", "probability": 0.939453125}, {"start": 2827.01, "end": 2827.43, "word": " increase", "probability": 0.83837890625}, {"start": 2827.43, "end": 2827.79, "word": " by", "probability": 0.97119140625}, {"start": 2827.79, "end": 2828.39, "word": " four", "probability": 0.802734375}, {"start": 2828.39, "end": 2828.79, "word": " units.", "probability": 0.90234375}, {"start": 2829.61, "end": 2829.87, "word": " So", "probability": 0.9560546875}, {"start": 2829.87, "end": 2830.15, "word": " again,", "probability": 0.89501953125}, {"start": 2830.37, "end": 2830.99, "word": " sometimes", "probability": 0.9560546875}, {"start": 2830.99, "end": 2831.77, "word": " we", "probability": 0.8857421875}, {"start": 2831.77, "end": 2832.25, "word": " can", "probability": 0.94287109375}, {"start": 2832.25, "end": 2833.23, "word": " interpret", "probability": 0.87255859375}, {"start": 2833.23, "end": 2833.91, "word": " the", "probability": 0.90966796875}, {"start": 2833.91, "end": 2834.31, "word": " y", "probability": 0.91552734375}, {"start": 2834.31, "end": 2834.77, "word": " intercept,", "probability": 0.6572265625}, {"start": 2836.11, "end": 2836.59, "word": " but", "probability": 0.84326171875}, {"start": 2836.59, "end": 2836.95, "word": " in", "probability": 0.92529296875}, {"start": 2836.95, "end": 2837.23, "word": " some", "probability": 0.89501953125}, {"start": 2837.23, "end": 2837.77, "word": " cases", "probability": 0.9267578125}, {"start": 2837.77, "end": 2838.05, "word": " it", "probability": 0.68115234375}, {"start": 2838.05, "end": 2838.27, "word": " has", "probability": 0.9462890625}, {"start": 2838.27, "end": 2838.45, "word": " no", "probability": 0.91357421875}, {"start": 2838.45, "end": 2838.67, "word": " meaning.", "probability": 0.89404296875}], "temperature": 1.0}, {"id": 107, "seek": 287067, "start": 2844.97, "end": 2870.67, "text": " Now for the previous example, for the selling price of a home and its size, B1rSy divided by Sx, r is computed, r is found to be 76%, 76%Sy divided by Sx, that will give 0.109. B0y bar minus B1x bar,", "tokens": [823, 337, 264, 3894, 1365, 11, 337, 264, 6511, 3218, 295, 257, 1280, 293, 1080, 2744, 11, 363, 16, 81, 50, 88, 6666, 538, 318, 87, 11, 367, 307, 40610, 11, 367, 307, 1352, 281, 312, 24733, 8923, 24733, 4, 50, 88, 6666, 538, 318, 87, 11, 300, 486, 976, 1958, 13, 3279, 24, 13, 363, 15, 88, 2159, 3175, 363, 16, 87, 2159, 11], "avg_logprob": -0.2923768939393939, "compression_ratio": 1.342281879194631, "no_speech_prob": 0.0, "words": [{"start": 2844.97, "end": 2845.23, "word": " Now", "probability": 0.6982421875}, {"start": 2845.23, "end": 2845.41, "word": " for", "probability": 0.71044921875}, {"start": 2845.41, "end": 2845.55, "word": " the", "probability": 0.9189453125}, {"start": 2845.55, "end": 2845.79, "word": " previous", "probability": 0.75}, {"start": 2845.79, "end": 2846.37, "word": " example,", "probability": 0.96630859375}, {"start": 2846.69, "end": 2846.83, "word": " for", "probability": 0.80029296875}, {"start": 2846.83, "end": 2846.99, "word": " the", "probability": 0.75048828125}, {"start": 2846.99, "end": 2847.19, "word": " selling", "probability": 0.814453125}, {"start": 2847.19, "end": 2847.69, "word": " price", "probability": 0.93359375}, {"start": 2847.69, "end": 2847.87, "word": " of", "probability": 0.465087890625}, {"start": 2847.87, "end": 2847.99, "word": " a", "probability": 0.875}, {"start": 2847.99, "end": 2848.17, "word": " home", "probability": 0.892578125}, {"start": 2848.17, "end": 2848.43, "word": " and", "probability": 0.81640625}, {"start": 2848.43, "end": 2848.71, "word": " its", "probability": 0.62548828125}, {"start": 2848.71, "end": 2849.13, "word": " size,", "probability": 0.81201171875}, {"start": 2850.09, "end": 2851.43, "word": " B1rSy", "probability": 0.582275390625}, {"start": 2851.43, "end": 2852.19, "word": " divided", "probability": 0.419921875}, {"start": 2852.19, "end": 2852.39, "word": " by", "probability": 0.97509765625}, {"start": 2852.39, "end": 2852.93, "word": " Sx,", "probability": 0.944580078125}, {"start": 2853.79, "end": 2854.15, "word": " r", "probability": 0.58349609375}, {"start": 2854.15, "end": 2854.33, "word": " is", "probability": 0.92626953125}, {"start": 2854.33, "end": 2855.31, "word": " computed,", "probability": 0.935546875}, {"start": 2856.81, "end": 2857.15, "word": " r", "probability": 0.76318359375}, {"start": 2857.15, "end": 2858.09, "word": " is", "probability": 0.9375}, {"start": 2858.09, "end": 2858.31, "word": " found", "probability": 0.873046875}, {"start": 2858.31, "end": 2858.49, "word": " to", "probability": 0.97119140625}, {"start": 2858.49, "end": 2858.63, "word": " be", "probability": 0.94970703125}, {"start": 2858.63, "end": 2859.83, "word": " 76%,", "probability": 0.609375}, {"start": 2859.83, "end": 2860.35, "word": " 76", "probability": 0.728515625}, {"start": 2860.35, "end": 2862.79, "word": "%Sy", "probability": 0.726806640625}, {"start": 2862.79, "end": 2863.55, "word": " divided", "probability": 0.74560546875}, {"start": 2863.55, "end": 2863.79, "word": " by", "probability": 0.97265625}, {"start": 2863.79, "end": 2864.33, "word": " Sx,", "probability": 0.99267578125}, {"start": 2864.91, "end": 2865.13, "word": " that", "probability": 0.9306640625}, {"start": 2865.13, "end": 2865.31, "word": " will", "probability": 0.86181640625}, {"start": 2865.31, "end": 2865.49, "word": " give", "probability": 0.79296875}, {"start": 2865.49, "end": 2865.67, "word": " 0", "probability": 0.75927734375}, {"start": 2865.67, "end": 2866.55, "word": ".109.", "probability": 0.9840494791666666}, {"start": 2868.11, "end": 2868.77, "word": " B0y", "probability": 0.9099934895833334}, {"start": 2868.77, "end": 2869.03, "word": " bar", "probability": 0.82275390625}, {"start": 2869.03, "end": 2869.33, "word": " minus", "probability": 0.9677734375}, {"start": 2869.33, "end": 2869.99, "word": " B1x", "probability": 0.9025065104166666}, {"start": 2869.99, "end": 2870.67, "word": " bar,", "probability": 0.9501953125}], "temperature": 1.0}, {"id": 108, "seek": 290299, "start": 2873.61, "end": 2902.99, "text": " Y bar for this data is 286 minus D1. So we have to compute first D1 because we use it in order to determine D0. And calculation gives 98. So that means based on these equations, Y hat equals 0.10977 plus 98.248.", "tokens": [398, 2159, 337, 341, 1412, 307, 7562, 21, 3175, 413, 16, 13, 407, 321, 362, 281, 14722, 700, 413, 16, 570, 321, 764, 309, 294, 1668, 281, 6997, 413, 15, 13, 400, 17108, 2709, 20860, 13, 407, 300, 1355, 2361, 322, 613, 11787, 11, 398, 2385, 6915, 1958, 13, 3279, 24, 17512, 1804, 20860, 13, 7911, 23, 13], "avg_logprob": -0.15426376765057193, "compression_ratio": 1.3333333333333333, "no_speech_prob": 0.0, "words": [{"start": 2873.61, "end": 2873.95, "word": " Y", "probability": 0.319580078125}, {"start": 2873.95, "end": 2874.31, "word": " bar", "probability": 0.9267578125}, {"start": 2874.31, "end": 2874.75, "word": " for", "probability": 0.763671875}, {"start": 2874.75, "end": 2875.07, "word": " this", "probability": 0.935546875}, {"start": 2875.07, "end": 2875.41, "word": " data", "probability": 0.80126953125}, {"start": 2875.41, "end": 2875.65, "word": " is", "probability": 0.931640625}, {"start": 2875.65, "end": 2876.61, "word": " 286", "probability": 0.93212890625}, {"start": 2876.61, "end": 2877.71, "word": " minus", "probability": 0.9150390625}, {"start": 2877.71, "end": 2878.37, "word": " D1.", "probability": 0.7080078125}, {"start": 2879.21, "end": 2879.55, "word": " So", "probability": 0.95166015625}, {"start": 2879.55, "end": 2879.71, "word": " we", "probability": 0.728515625}, {"start": 2879.71, "end": 2879.93, "word": " have", "probability": 0.9423828125}, {"start": 2879.93, "end": 2880.15, "word": " to", "probability": 0.96728515625}, {"start": 2880.15, "end": 2880.55, "word": " compute", "probability": 0.900390625}, {"start": 2880.55, "end": 2880.87, "word": " first", "probability": 0.7734375}, {"start": 2880.87, "end": 2881.23, "word": " D1", "probability": 0.9609375}, {"start": 2881.23, "end": 2881.55, "word": " because", "probability": 0.68017578125}, {"start": 2881.55, "end": 2881.73, "word": " we", "probability": 0.9482421875}, {"start": 2881.73, "end": 2881.93, "word": " use", "probability": 0.794921875}, {"start": 2881.93, "end": 2882.35, "word": " it", "probability": 0.94873046875}, {"start": 2882.35, "end": 2883.03, "word": " in", "probability": 0.88037109375}, {"start": 2883.03, "end": 2883.23, "word": " order", "probability": 0.9228515625}, {"start": 2883.23, "end": 2883.49, "word": " to", "probability": 0.95556640625}, {"start": 2883.49, "end": 2883.79, "word": " determine", "probability": 0.70556640625}, {"start": 2883.79, "end": 2884.37, "word": " D0.", "probability": 0.83740234375}, {"start": 2885.49, "end": 2886.21, "word": " And", "probability": 0.94091796875}, {"start": 2886.21, "end": 2886.73, "word": " calculation", "probability": 0.7890625}, {"start": 2886.73, "end": 2887.13, "word": " gives", "probability": 0.91357421875}, {"start": 2887.13, "end": 2887.71, "word": " 98.", "probability": 0.95263671875}, {"start": 2888.05, "end": 2888.31, "word": " So", "probability": 0.96533203125}, {"start": 2888.31, "end": 2888.59, "word": " that", "probability": 0.9091796875}, {"start": 2888.59, "end": 2889.01, "word": " means", "probability": 0.9326171875}, {"start": 2889.01, "end": 2891.21, "word": " based", "probability": 0.57958984375}, {"start": 2891.21, "end": 2891.53, "word": " on", "probability": 0.94921875}, {"start": 2891.53, "end": 2892.03, "word": " these", "probability": 0.8125}, {"start": 2892.03, "end": 2892.71, "word": " equations,", "probability": 0.9326171875}, {"start": 2893.57, "end": 2893.79, "word": " Y", "probability": 0.732421875}, {"start": 2893.79, "end": 2894.19, "word": " hat", "probability": 0.93603515625}, {"start": 2894.19, "end": 2896.13, "word": " equals", "probability": 0.91845703125}, {"start": 2896.13, "end": 2896.45, "word": " 0", "probability": 0.81884765625}, {"start": 2896.45, "end": 2898.37, "word": ".10977", "probability": 0.9501953125}, {"start": 2898.37, "end": 2899.57, "word": " plus", "probability": 0.91162109375}, {"start": 2899.57, "end": 2900.15, "word": " 98", "probability": 0.98095703125}, {"start": 2900.15, "end": 2902.99, "word": ".248.", "probability": 0.9601236979166666}], "temperature": 1.0}, {"id": 109, "seek": 293271, "start": 2904.79, "end": 2932.71, "text": " times X. X is the size. 0.1 B1 is 0.1, B0 is 98, so 98.248 plus B1.", "tokens": [1413, 1783, 13, 1783, 307, 264, 2744, 13, 1958, 13, 16, 363, 16, 307, 1958, 13, 16, 11, 363, 15, 307, 20860, 11, 370, 20860, 13, 7911, 23, 1804, 363, 16, 13], "avg_logprob": -0.37523674242424243, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 2904.79, "end": 2905.21, "word": " times", "probability": 0.1964111328125}, {"start": 2905.21, "end": 2905.61, "word": " X.", "probability": 0.4091796875}, {"start": 2906.19, "end": 2906.63, "word": " X", "probability": 0.966796875}, {"start": 2906.63, "end": 2906.97, "word": " is", "probability": 0.9326171875}, {"start": 2906.97, "end": 2907.69, "word": " the", "probability": 0.9248046875}, {"start": 2907.69, "end": 2909.37, "word": " size.", "probability": 0.73681640625}, {"start": 2912.89, "end": 2913.77, "word": " 0", "probability": 0.480224609375}, {"start": 2913.77, "end": 2914.19, "word": ".1", "probability": 0.967041015625}, {"start": 2914.19, "end": 2919.83, "word": " B1", "probability": 0.40185546875}, {"start": 2919.83, "end": 2925.31, "word": " is", "probability": 0.8837890625}, {"start": 2925.31, "end": 2925.55, "word": " 0", "probability": 0.8818359375}, {"start": 2925.55, "end": 2925.93, "word": ".1,", "probability": 0.9892578125}, {"start": 2926.17, "end": 2926.63, "word": " B0", "probability": 0.945556640625}, {"start": 2926.63, "end": 2926.77, "word": " is", "probability": 0.93408203125}, {"start": 2926.77, "end": 2927.15, "word": " 98,", "probability": 0.2257080078125}, {"start": 2927.35, "end": 2927.51, "word": " so", "probability": 0.814453125}, {"start": 2927.51, "end": 2928.03, "word": " 98", "probability": 0.90087890625}, {"start": 2928.03, "end": 2930.63, "word": ".248", "probability": 0.9153645833333334}, {"start": 2930.63, "end": 2932.17, "word": " plus", "probability": 0.72998046875}, {"start": 2932.17, "end": 2932.71, "word": " B1.", "probability": 0.979248046875}], "temperature": 1.0}, {"id": 110, "seek": 296127, "start": 2935.07, "end": 2961.27, "text": " So this is your regression equation. So again, the intercept is 98. So this amount, the segment is 98. Now the slope is 0.109. So house price, the expected value of house price equals B098 plus 0.109 square feet.", "tokens": [407, 341, 307, 428, 24590, 5367, 13, 407, 797, 11, 264, 24700, 307, 20860, 13, 407, 341, 2372, 11, 264, 9469, 307, 20860, 13, 823, 264, 13525, 307, 1958, 13, 3279, 24, 13, 407, 1782, 3218, 11, 264, 5176, 2158, 295, 1782, 3218, 6915, 363, 13811, 23, 1804, 1958, 13, 3279, 24, 3732, 3521, 13], "avg_logprob": -0.17340960114129952, "compression_ratio": 1.4689655172413794, "no_speech_prob": 0.0, "words": [{"start": 2935.0699999999997, "end": 2935.91, "word": " So", "probability": 0.35498046875}, {"start": 2935.91, "end": 2936.21, "word": " this", "probability": 0.79345703125}, {"start": 2936.21, "end": 2936.35, "word": " is", "probability": 0.9208984375}, {"start": 2936.35, "end": 2936.65, "word": " your", "probability": 0.888671875}, {"start": 2936.65, "end": 2937.89, "word": " regression", "probability": 0.818359375}, {"start": 2937.89, "end": 2938.39, "word": " equation.", "probability": 0.97900390625}, {"start": 2940.89, "end": 2941.73, "word": " So", "probability": 0.91455078125}, {"start": 2941.73, "end": 2942.39, "word": " again,", "probability": 0.8203125}, {"start": 2942.81, "end": 2942.99, "word": " the", "probability": 0.833984375}, {"start": 2942.99, "end": 2943.43, "word": " intercept", "probability": 0.9814453125}, {"start": 2943.43, "end": 2943.73, "word": " is", "probability": 0.9326171875}, {"start": 2943.73, "end": 2944.11, "word": " 98.", "probability": 0.95703125}, {"start": 2945.35, "end": 2946.19, "word": " So", "probability": 0.94921875}, {"start": 2946.19, "end": 2946.45, "word": " this", "probability": 0.9189453125}, {"start": 2946.45, "end": 2946.77, "word": " amount,", "probability": 0.79736328125}, {"start": 2946.93, "end": 2947.07, "word": " the", "probability": 0.4560546875}, {"start": 2947.07, "end": 2947.39, "word": " segment", "probability": 0.86572265625}, {"start": 2947.39, "end": 2947.93, "word": " is", "probability": 0.71923828125}, {"start": 2947.93, "end": 2948.33, "word": " 98.", "probability": 0.98583984375}, {"start": 2948.99, "end": 2949.45, "word": " Now", "probability": 0.95849609375}, {"start": 2949.45, "end": 2949.75, "word": " the", "probability": 0.6171875}, {"start": 2949.75, "end": 2950.09, "word": " slope", "probability": 0.81884765625}, {"start": 2950.09, "end": 2950.69, "word": " is", "probability": 0.93505859375}, {"start": 2950.69, "end": 2950.93, "word": " 0", "probability": 0.8984375}, {"start": 2950.93, "end": 2952.07, "word": ".109.", "probability": 0.9840494791666666}, {"start": 2952.67, "end": 2952.95, "word": " So", "probability": 0.9609375}, {"start": 2952.95, "end": 2953.29, "word": " house", "probability": 0.56884765625}, {"start": 2953.29, "end": 2953.63, "word": " price,", "probability": 0.9296875}, {"start": 2953.79, "end": 2953.85, "word": " the", "probability": 0.912109375}, {"start": 2953.85, "end": 2954.33, "word": " expected", "probability": 0.88818359375}, {"start": 2954.33, "end": 2954.79, "word": " value", "probability": 0.9638671875}, {"start": 2954.79, "end": 2954.97, "word": " of", "probability": 0.93017578125}, {"start": 2954.97, "end": 2955.25, "word": " house", "probability": 0.853515625}, {"start": 2955.25, "end": 2955.73, "word": " price", "probability": 0.92138671875}, {"start": 2955.73, "end": 2956.29, "word": " equals", "probability": 0.85888671875}, {"start": 2956.29, "end": 2958.23, "word": " B098", "probability": 0.6427408854166666}, {"start": 2958.23, "end": 2959.15, "word": " plus", "probability": 0.81787109375}, {"start": 2959.15, "end": 2959.43, "word": " 0", "probability": 0.97900390625}, {"start": 2959.43, "end": 2960.43, "word": ".109", "probability": 0.9850260416666666}, {"start": 2960.43, "end": 2960.97, "word": " square", "probability": 0.814453125}, {"start": 2960.97, "end": 2961.27, "word": " feet.", "probability": 0.94921875}], "temperature": 1.0}, {"id": 111, "seek": 298991, "start": 2963.15, "end": 2989.91, "text": " So that's the prediction line for the house price. So again, house price equal B0 98 plus 0.10977 times square root. Now, what's your interpretation about B0 and B1? B0 is the estimated mean value of Y when the value of X is 0. So if X is 0, this range of X observed X values and", "tokens": [407, 300, 311, 264, 17630, 1622, 337, 264, 1782, 3218, 13, 407, 797, 11, 1782, 3218, 2681, 363, 15, 20860, 1804, 1958, 13, 3279, 24, 17512, 1413, 3732, 5593, 13, 823, 11, 437, 311, 428, 14174, 466, 363, 15, 293, 363, 16, 30, 363, 15, 307, 264, 14109, 914, 2158, 295, 398, 562, 264, 2158, 295, 1783, 307, 1958, 13, 407, 498, 1783, 307, 1958, 11, 341, 3613, 295, 1783, 13095, 1783, 4190, 293], "avg_logprob": -0.23208333651224772, "compression_ratio": 1.5384615384615385, "no_speech_prob": 0.0, "words": [{"start": 2963.15, "end": 2963.41, "word": " So", "probability": 0.91064453125}, {"start": 2963.41, "end": 2963.75, "word": " that's", "probability": 0.9033203125}, {"start": 2963.75, "end": 2963.95, "word": " the", "probability": 0.91357421875}, {"start": 2963.95, "end": 2964.37, "word": " prediction", "probability": 0.912109375}, {"start": 2964.37, "end": 2964.83, "word": " line", "probability": 0.943359375}, {"start": 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So that means this value has no meaning. Because a house cannot have a square footage of zero. So B0 has no practical application in this case. So sometimes it makes sense, in other cases it doesn't have that. So for this specific example,", "tokens": [291, 362, 257, 1280, 420, 257, 1782, 295, 2744, 4018, 13, 407, 300, 1355, 341, 2158, 575, 572, 3620, 13, 1436, 257, 1782, 2644, 362, 257, 3732, 9556, 295, 4018, 13, 407, 363, 15, 575, 572, 8496, 3861, 294, 341, 1389, 13, 407, 2171, 309, 1669, 2020, 11, 294, 661, 3331, 309, 1177, 380, 362, 300, 13, 407, 337, 341, 2685, 1365, 11], "avg_logprob": -0.183715823572129, "compression_ratio": 1.6149425287356323, "no_speech_prob": 0.0, "words": [{"start": 2991.06, "end": 2991.4, "word": " you", "probability": 0.309326171875}, {"start": 2991.4, "end": 2991.82, "word": " have", "probability": 0.9365234375}, {"start": 2991.82, "end": 2992.58, "word": " a", "probability": 0.953125}, {"start": 2992.58, "end": 2992.98, "word": " home", "probability": 0.87646484375}, {"start": 2992.98, "end": 2993.56, "word": " or", "probability": 0.8388671875}, {"start": 2993.56, "end": 2993.7, "word": " a", "probability": 0.76220703125}, {"start": 2993.7, "end": 2994.12, 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"start": 3020.13, "end": 3039.13, "text": " B0 has no practical application in this case. But B1 which is 0.1097, B1 estimates the change in the mean value of Y as a result of one unit increasing X. 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So for each one unit increased in the size, the selling price of a home increased by 109. So that means if the size increased by tenth,", "tokens": [407, 498, 1782, 2744, 6505, 538, 472, 3732, 2671, 11, 550, 264, 3218, 6505, 538, 926, 1266, 24, 3808, 13, 407, 337, 1184, 472, 4985, 6505, 294, 264, 2744, 11, 264, 6511, 3218, 295, 257, 1280, 6505, 538, 1266, 24, 13, 407, 300, 1355, 498, 264, 2744, 6505, 538, 27269, 11], "avg_logprob": -0.2391826963195434, "compression_ratio": 1.673913043478261, "no_speech_prob": 0.0, "words": [{"start": 3068.51, "end": 3068.77, "word": " So", "probability": 0.2210693359375}, {"start": 3068.77, "end": 3068.93, "word": " if", "probability": 0.8310546875}, {"start": 3068.93, "end": 3069.23, "word": " house", "probability": 0.72265625}, {"start": 3069.23, "end": 3069.53, "word": " size", "probability": 0.80517578125}, {"start": 3069.53, "end": 3069.99, "word": " increased", "probability": 0.425537109375}, {"start": 3069.99, "end": 3070.27, "word": " by", "probability": 0.96484375}, {"start": 3070.27, "end": 3070.69, "word": " one", "probability": 0.59619140625}, {"start": 3070.69, "end": 3072.01, "word": " square", "probability": 0.849609375}, {"start": 3072.01, "end": 3072.45, "word": " foot,", "probability": 0.89306640625}, {"start": 3072.77, "end": 3073.25, "word": " then", "probability": 0.83203125}, {"start": 3073.25, "end": 3073.49, "word": " the", "probability": 0.912109375}, {"start": 3073.49, "end": 3073.89, "word": " price", "probability": 0.9013671875}, {"start": 3073.89, "end": 3074.31, "word": " increased", "probability": 0.80859375}, {"start": 3074.31, "end": 3074.63, "word": " by", "probability": 0.96923828125}, {"start": 3074.63, "end": 3075.13, "word": " around", "probability": 0.9150390625}, {"start": 3075.13, "end": 3076.49, "word": " 109", "probability": 0.7335205078125}, {"start": 3076.49, "end": 3076.85, "word": " dollars.", "probability": 0.568359375}, {"start": 3077.53, "end": 3077.95, "word": " So", "probability": 0.896484375}, {"start": 3077.95, "end": 3078.19, "word": " for", "probability": 0.86962890625}, {"start": 3078.19, "end": 3078.47, "word": " each", "probability": 0.9462890625}, {"start": 3078.47, "end": 3078.73, "word": " one", "probability": 0.88720703125}, {"start": 3078.73, "end": 3079.01, "word": " unit", "probability": 0.93505859375}, {"start": 3079.01, "end": 3079.53, "word": " increased", "probability": 0.923828125}, {"start": 3079.53, "end": 3079.77, "word": " in", "probability": 0.489013671875}, {"start": 3079.77, "end": 3079.93, "word": " the", "probability": 0.85498046875}, {"start": 3079.93, "end": 3080.31, "word": " size,", "probability": 0.84521484375}, {"start": 3080.99, "end": 3081.37, "word": " the", "probability": 0.8994140625}, {"start": 3081.37, "end": 3081.65, "word": " selling", "probability": 0.8916015625}, {"start": 3081.65, "end": 3082.03, "word": " price", "probability": 0.89453125}, {"start": 3082.03, "end": 3082.21, "word": " of", "probability": 0.9091796875}, {"start": 3082.21, "end": 3082.31, "word": " a", "probability": 0.68408203125}, {"start": 3082.31, "end": 3082.55, "word": " home", "probability": 0.8935546875}, {"start": 3082.55, "end": 3082.99, "word": " increased", "probability": 0.90869140625}, {"start": 3082.99, "end": 3083.37, "word": " by", "probability": 0.9736328125}, {"start": 3083.37, "end": 3085.03, "word": " 109.", "probability": 0.9228515625}, {"start": 3085.79, "end": 3086.51, "word": " So", "probability": 0.9423828125}, {"start": 3086.51, "end": 3086.73, "word": " that", "probability": 0.9208984375}, {"start": 3086.73, "end": 3087.07, "word": " means", "probability": 0.9326171875}, {"start": 3087.07, "end": 3088.53, "word": " if", "probability": 0.76220703125}, {"start": 3088.53, "end": 3088.75, "word": " the", "probability": 0.9150390625}, {"start": 3088.75, "end": 3088.99, "word": " size", "probability": 0.853515625}, {"start": 3088.99, "end": 3089.37, "word": " increased", "probability": 0.75}, {"start": 3089.37, "end": 3089.59, "word": " by", "probability": 0.97216796875}, {"start": 3089.59, "end": 3089.99, "word": " tenth,", "probability": 0.42626953125}], "temperature": 1.0}, {"id": 116, "seek": 311930, "start": 3091.92, "end": 3119.3, "text": " It means the selling price increased by 1097.7. Make sense? So for each one unit increase in its size, the house selling price increased by 109. So we have to multiply this value by the unit we have. 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Now we can use also the regression equation line to make some prediction.", "tokens": [1692, 498, 291, 352, 646, 281, 264, 3894, 1412, 321, 362, 11, 264, 1412, 390, 1782, 3218, 2067, 380, 4714, 3808, 11, 370, 321, 362, 281, 12972, 264, 13525, 538, 257, 4714, 13, 823, 321, 393, 764, 611, 264, 24590, 5367, 1622, 281, 652, 512, 17630, 13], "avg_logprob": -0.19612630332509676, "compression_ratio": 1.510204081632653, "no_speech_prob": 0.0, "words": [{"start": 3121.74, "end": 3122.04, "word": " Here", "probability": 0.5625}, {"start": 3122.04, "end": 3122.18, "word": " if", "probability": 0.60107421875}, {"start": 3122.18, "end": 3122.28, "word": " you", "probability": 0.92431640625}, {"start": 3122.28, "end": 3122.48, "word": " go", "probability": 0.93310546875}, {"start": 3122.48, "end": 3122.96, "word": " back", "probability": 0.88330078125}, {"start": 3122.96, "end": 3123.22, "word": " to", "probability": 0.79736328125}, {"start": 3123.22, "end": 3123.3, "word": " the", "probability": 0.88720703125}, {"start": 3123.3, "end": 3123.62, "word": " previous", "probability": 0.86669921875}, {"start": 3123.62, "end": 3123.94, "word": " data", "probability": 0.92578125}, {"start": 3123.94, "end": 3124.12, "word": " we", "probability": 0.86865234375}, {"start": 3124.12, "end": 3124.42, "word": " have,", "probability": 0.8515625}, {"start": 3125.64, "end": 3125.8, "word": " the", "probability": 0.87255859375}, {"start": 3125.8, "end": 3126.08, "word": " data", "probability": 0.81591796875}, {"start": 3126.08, "end": 3126.6, "word": " was", "probability": 0.927734375}, {"start": 3126.6, "end": 3128.2, "word": " house", "probability": 0.7626953125}, {"start": 3128.2, "end": 3128.66, "word": " price", "probability": 0.89306640625}, {"start": 3128.66, "end": 3129.08, "word": " wasn't", "probability": 0.756591796875}, {"start": 3129.08, "end": 3129.5, "word": " thousand", "probability": 0.3896484375}, {"start": 3129.5, "end": 3129.94, "word": " dollars,", "probability": 0.9130859375}, {"start": 3130.38, "end": 3130.58, "word": " so", "probability": 0.93115234375}, {"start": 3130.58, "end": 3130.7, "word": " we", "probability": 0.908203125}, {"start": 3130.7, "end": 3130.88, "word": " have", "probability": 0.94140625}, {"start": 3130.88, "end": 3131.12, "word": " to", "probability": 0.96728515625}, {"start": 3131.12, "end": 3131.74, "word": " multiply", "probability": 0.90087890625}, {"start": 3131.74, "end": 3133.28, "word": " the", "probability": 0.87548828125}, {"start": 3133.28, "end": 3133.66, "word": " slope", "probability": 0.9052734375}, {"start": 3133.66, "end": 3134.2, "word": " by", "probability": 0.97216796875}, {"start": 3134.2, "end": 3135.46, "word": " a", "probability": 0.80224609375}, {"start": 3135.46, "end": 3135.84, "word": " thousand.", "probability": 0.84130859375}, {"start": 3139.48, "end": 3139.82, "word": " Now", "probability": 0.34814453125}, {"start": 3139.82, "end": 3143.72, "word": " we", "probability": 0.75244140625}, {"start": 3143.72, "end": 3144.02, "word": " can", "probability": 0.94580078125}, {"start": 3144.02, "end": 3144.28, "word": " use", "probability": 0.8740234375}, {"start": 3144.28, "end": 3144.84, "word": " also", "probability": 0.85986328125}, {"start": 3144.84, "end": 3147.44, "word": " the", "probability": 0.82373046875}, {"start": 3147.44, "end": 3147.9, "word": " regression", "probability": 0.97119140625}, {"start": 3147.9, "end": 3148.42, "word": " equation", "probability": 0.9814453125}, {"start": 3148.42, "end": 3148.98, "word": " line", "probability": 0.92431640625}, {"start": 3148.98, "end": 3150.12, "word": " to", "probability": 0.95068359375}, {"start": 3150.12, "end": 3150.38, "word": " make", "probability": 0.9404296875}, {"start": 3150.38, "end": 3150.66, "word": " some", "probability": 0.90087890625}, {"start": 3150.66, "end": 3151.12, "word": " prediction.", "probability": 0.78857421875}], "temperature": 1.0}, {"id": 118, "seek": 317589, "start": 3152.75, "end": 3175.89, "text": " For example, we can predict the price of a house with 2000 square feet. You just plug this value. So we have 98.25 plus 0.109 times 2000. That will give the house price.", "tokens": [1171, 1365, 11, 321, 393, 6069, 264, 3218, 295, 257, 1782, 365, 8132, 3732, 3521, 13, 509, 445, 5452, 341, 2158, 13, 407, 321, 362, 20860, 13, 6074, 1804, 1958, 13, 3279, 24, 1413, 8132, 13, 663, 486, 976, 264, 1782, 3218, 13], "avg_logprob": -0.17675781487063927, "compression_ratio": 1.25, "no_speech_prob": 0.0, "words": [{"start": 3152.75, "end": 3152.99, "word": " For", "probability": 0.73583984375}, {"start": 3152.99, "end": 3153.41, "word": " example,", "probability": 0.9580078125}, {"start": 3154.15, "end": 3154.43, "word": " we", "probability": 0.89208984375}, {"start": 3154.43, "end": 3154.69, "word": " can", "probability": 0.93017578125}, {"start": 3154.69, "end": 3155.11, "word": " predict", "probability": 0.76513671875}, {"start": 3155.11, "end": 3155.39, "word": " the", "probability": 0.89892578125}, {"start": 3155.39, "end": 3155.79, "word": " price", "probability": 0.92236328125}, {"start": 3155.79, "end": 3155.95, "word": " of", "probability": 0.96533203125}, {"start": 3155.95, "end": 3156.11, "word": " a", "probability": 0.95166015625}, {"start": 3156.11, "end": 3156.71, "word": " house", "probability": 0.86083984375}, {"start": 3156.71, "end": 3157.13, "word": " with", "probability": 0.8876953125}, {"start": 3157.13, "end": 3157.83, "word": " 2000", "probability": 0.64404296875}, {"start": 3157.83, "end": 3159.11, "word": " square", "probability": 0.6484375}, {"start": 3159.11, "end": 3159.49, "word": " feet.", "probability": 0.92431640625}, {"start": 3161.23, "end": 3161.87, "word": " You", "probability": 0.88818359375}, {"start": 3161.87, "end": 3162.29, "word": " just", "probability": 0.89013671875}, {"start": 3162.29, "end": 3162.89, "word": " plug", "probability": 0.86181640625}, {"start": 3162.89, "end": 3163.15, "word": " this", "probability": 0.89599609375}, {"start": 3163.15, "end": 3163.59, "word": " value.", "probability": 0.97119140625}, {"start": 3166.31, "end": 3166.55, "word": " So", "probability": 0.8798828125}, {"start": 3166.55, "end": 3166.67, "word": " we", "probability": 0.63671875}, {"start": 3166.67, "end": 3166.83, "word": " have", "probability": 0.94677734375}, {"start": 3166.83, "end": 3167.13, "word": " 98", "probability": 0.92724609375}, {"start": 3167.13, "end": 3167.95, "word": ".25", "probability": 0.97509765625}, {"start": 3167.95, "end": 3168.27, "word": " plus", "probability": 0.70703125}, {"start": 3168.27, "end": 3168.53, "word": " 0", "probability": 0.72265625}, {"start": 3168.53, "end": 3169.53, "word": ".109", "probability": 0.9881184895833334}, {"start": 3169.53, "end": 3170.51, "word": " times", "probability": 0.82080078125}, {"start": 3170.51, "end": 3171.07, "word": " 2000.", "probability": 0.83154296875}, {"start": 3171.57, "end": 3171.99, "word": " That", "probability": 0.87890625}, {"start": 3171.99, "end": 3172.21, "word": " will", "probability": 0.88134765625}, {"start": 3172.21, "end": 3172.53, "word": " give", "probability": 0.8701171875}, {"start": 3172.53, "end": 3174.91, "word": " the", "probability": 0.84423828125}, {"start": 3174.91, "end": 3175.33, "word": " house", "probability": 0.89013671875}, {"start": 3175.33, "end": 3175.89, "word": " price.", "probability": 0.8720703125}], "temperature": 1.0}, {"id": 119, "seek": 320184, "start": 3177.92, "end": 3201.84, "text": " for 2,000 square feet. So that means the predicted price for a house with 2,000 square feet is this amount multiplied by 1,000. So that will give $317,850. So that's how can we make predictions for why", "tokens": [337, 568, 11, 1360, 3732, 3521, 13, 407, 300, 1355, 264, 19147, 3218, 337, 257, 1782, 365, 568, 11, 1360, 3732, 3521, 307, 341, 2372, 17207, 538, 502, 11, 1360, 13, 407, 300, 486, 976, 1848, 18, 7773, 11, 23, 2803, 13, 407, 300, 311, 577, 393, 321, 652, 21264, 337, 983], "avg_logprob": -0.19649174190917104, "compression_ratio": 1.4225352112676057, "no_speech_prob": 0.0, "words": [{"start": 3177.92, "end": 3178.4, "word": " for", "probability": 0.59912109375}, {"start": 3178.4, "end": 3179.12, "word": " 2", "probability": 0.2509765625}, {"start": 3179.12, "end": 3179.56, "word": ",000", "probability": 0.931396484375}, {"start": 3179.56, "end": 3180.0, "word": " square", "probability": 0.85205078125}, {"start": 3180.0, "end": 3180.42, "word": " feet.", "probability": 0.94921875}, {"start": 3181.38, "end": 3181.6, "word": " So", "probability": 0.88525390625}, {"start": 3181.6, "end": 3181.84, "word": " that", "probability": 0.81005859375}, {"start": 3181.84, "end": 3182.06, "word": " means", "probability": 0.9345703125}, {"start": 3182.06, "end": 3182.22, "word": " the", "probability": 0.85205078125}, {"start": 3182.22, "end": 3182.66, "word": " predicted", "probability": 0.841796875}, {"start": 3182.66, "end": 3183.32, "word": " price", "probability": 0.91552734375}, {"start": 3183.32, "end": 3183.66, "word": " for", "probability": 0.94287109375}, {"start": 3183.66, "end": 3183.8, "word": " a", "probability": 0.96875}, {"start": 3183.8, "end": 3184.12, "word": " house", "probability": 0.8828125}, {"start": 3184.12, "end": 3184.52, "word": " with", "probability": 0.89892578125}, {"start": 3184.52, "end": 3185.92, "word": " 2", "probability": 0.91455078125}, {"start": 3185.92, "end": 3186.22, "word": ",000", "probability": 0.99853515625}, {"start": 3186.22, "end": 3186.6, "word": " square", "probability": 0.9033203125}, {"start": 3186.6, "end": 3186.9, "word": " feet", "probability": 0.9599609375}, {"start": 3186.9, "end": 3187.22, "word": " is", "probability": 0.89501953125}, {"start": 3187.22, "end": 3187.52, "word": " this", "probability": 0.94140625}, {"start": 3187.52, "end": 3187.92, "word": " amount", "probability": 0.90087890625}, {"start": 3187.92, "end": 3188.56, "word": " multiplied", "probability": 0.6650390625}, {"start": 3188.56, "end": 3189.12, "word": " by", "probability": 0.974609375}, {"start": 3189.12, "end": 3190.18, "word": " 1", "probability": 0.83251953125}, {"start": 3190.18, "end": 3190.76, "word": ",000.", "probability": 0.986328125}, {"start": 3190.88, "end": 3191.16, "word": " So", "probability": 0.94970703125}, {"start": 3191.16, "end": 3191.38, "word": " that", "probability": 0.87939453125}, {"start": 3191.38, "end": 3191.56, "word": " will", "probability": 0.40771484375}, {"start": 3191.56, "end": 3191.82, "word": " give", "probability": 0.66162109375}, {"start": 3191.82, "end": 3194.08, "word": " $317", "probability": 0.7435709635416666}, {"start": 3194.08, "end": 3196.32, "word": ",850.", "probability": 0.9384765625}, {"start": 3197.04, "end": 3197.82, "word": " So", "probability": 0.95068359375}, {"start": 3197.82, "end": 3198.14, "word": " that's", "probability": 0.952392578125}, {"start": 3198.14, "end": 3198.26, "word": " how", "probability": 0.93701171875}, {"start": 3198.26, "end": 3198.48, "word": " can", "probability": 0.7626953125}, {"start": 3198.48, "end": 3198.64, "word": " we", "probability": 0.95703125}, {"start": 3198.64, "end": 3199.0, "word": " make", "probability": 0.94140625}, {"start": 3199.0, "end": 3199.78, "word": " predictions", "probability": 0.6435546875}, {"start": 3199.78, "end": 3201.18, "word": " for", "probability": 0.93603515625}, {"start": 3201.18, "end": 3201.84, "word": " why", "probability": 0.483642578125}], "temperature": 1.0}, {"id": 120, "seek": 323158, "start": 3202.7, "end": 3231.58, "text": " I mean for house price at any given value of its size. So for this data, we have a house with 2000 square feet. So we predict its price to be around 317,850. I will stop at coefficient of correlation. 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