{"segments": [{"id": 1, "seek": 2828, "start": 6.48, "end": 28.28, "text": " Last time, I mean Tuesday, we discussed box plot and we introduced how can we use box plot to determine if any point is suspected to be an outlier by using the lower limit and upper limit.", "tokens": [5264, 565, 11, 286, 914, 10017, 11, 321, 7152, 2424, 7542, 293, 321, 7268, 577, 393, 321, 764, 2424, 7542, 281, 6997, 498, 604, 935, 307, 26439, 281, 312, 364, 484, 2753, 538, 1228, 264, 3126, 4948, 293, 6597, 4948, 13], "avg_logprob": -0.20684524448145003, "compression_ratio": 1.4104477611940298, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 6.48, "end": 7.04, "word": " Last", "probability": 0.6337890625}, {"start": 7.04, "end": 7.4, "word": " time,", "probability": 0.87939453125}, {"start": 7.6, "end": 7.64, "word": " I", "probability": 0.640625}, {"start": 7.64, "end": 7.8, "word": " mean", "probability": 0.962890625}, {"start": 7.8, "end": 8.36, "word": " Tuesday,", "probability": 0.5576171875}, {"start": 9.36, "end": 10.08, "word": " we", "probability": 0.955078125}, {"start": 10.08, "end": 10.86, "word": " discussed", "probability": 0.87451171875}, {"start": 10.86, "end": 11.86, "word": " box", "probability": 0.1781005859375}, {"start": 11.86, "end": 12.1, "word": " plot", "probability": 0.81005859375}, {"start": 12.1, "end": 13.66, "word": " and", "probability": 0.51708984375}, {"start": 13.66, "end": 14.04, "word": " we", "probability": 0.82373046875}, {"start": 14.04, "end": 15.24, "word": " introduced", "probability": 0.7802734375}, {"start": 15.24, "end": 16.12, "word": " how", "probability": 0.88916015625}, {"start": 16.12, "end": 16.38, "word": " can", "probability": 0.91552734375}, {"start": 16.38, "end": 16.66, "word": " we", "probability": 0.94677734375}, {"start": 16.66, "end": 17.72, "word": " use", "probability": 0.86962890625}, {"start": 17.72, "end": 18.0, "word": " box", "probability": 0.9287109375}, {"start": 18.0, "end": 18.42, "word": " plot", "probability": 0.97509765625}, {"start": 18.42, "end": 19.54, "word": " to", "probability": 0.9453125}, {"start": 19.54, "end": 20.02, "word": " determine", "probability": 0.92138671875}, {"start": 20.02, "end": 20.74, "word": " if", "probability": 0.94580078125}, {"start": 20.74, "end": 21.64, "word": " any", "probability": 0.8896484375}, {"start": 21.64, "end": 22.08, "word": " point", "probability": 0.97900390625}, {"start": 22.08, "end": 23.18, "word": " is", "probability": 0.9384765625}, {"start": 23.18, "end": 23.64, "word": " suspected", "probability": 0.8779296875}, {"start": 23.64, "end": 23.88, "word": " to", "probability": 0.97216796875}, {"start": 23.88, "end": 24.02, "word": " be", "probability": 0.9541015625}, {"start": 24.02, "end": 24.16, "word": " an", "probability": 0.9365234375}, {"start": 24.16, "end": 24.56, "word": " outlier", "probability": 0.950439453125}, {"start": 24.56, "end": 26.28, "word": " by", "probability": 0.30517578125}, {"start": 26.28, "end": 26.68, "word": " using", "probability": 0.92822265625}, {"start": 26.68, "end": 26.9, "word": " the", "probability": 0.88623046875}, {"start": 26.9, "end": 27.08, "word": " lower", "probability": 0.8515625}, {"start": 27.08, "end": 27.44, "word": " limit", "probability": 0.92529296875}, {"start": 27.44, "end": 27.72, "word": " and", "probability": 0.94091796875}, {"start": 27.72, "end": 27.98, "word": " upper", "probability": 0.8291015625}, {"start": 27.98, "end": 28.28, "word": " limit.", "probability": 0.83056640625}], "temperature": 1.0}, {"id": 2, "seek": 5308, "start": 29.46, "end": 53.08, "text": " And we mentioned last time that if any point is below the lower limit or is above the upper limit, that point is considered to be an outlier. So that's one of the usage of the backsplat. I mean, for this specific example, we mentioned last time 27 is an outlier.", "tokens": [400, 321, 2835, 1036, 565, 300, 498, 604, 935, 307, 2507, 264, 3126, 4948, 420, 307, 3673, 264, 6597, 4948, 11, 300, 935, 307, 4888, 281, 312, 364, 484, 2753, 13, 407, 300, 311, 472, 295, 264, 14924, 295, 264, 646, 46535, 267, 13, 286, 914, 11, 337, 341, 2685, 1365, 11, 321, 2835, 1036, 565, 7634, 307, 364, 484, 2753, 13], "avg_logprob": -0.20275297713658166, "compression_ratio": 1.623456790123457, "no_speech_prob": 0.0, "words": [{"start": 29.46, "end": 29.78, "word": " And", "probability": 0.77880859375}, {"start": 29.78, "end": 29.94, "word": " we", "probability": 0.93994140625}, {"start": 29.94, "end": 30.3, "word": " mentioned", "probability": 0.82958984375}, {"start": 30.3, "end": 30.82, "word": " last", "probability": 0.82958984375}, {"start": 30.82, "end": 31.02, "word": " time", "probability": 0.88720703125}, {"start": 31.02, "end": 31.3, "word": " that", "probability": 0.8876953125}, {"start": 31.3, "end": 31.6, "word": " if", "probability": 0.88134765625}, {"start": 31.6, "end": 31.94, "word": " any", "probability": 0.8974609375}, {"start": 31.94, "end": 32.26, "word": " point", "probability": 0.9716796875}, {"start": 32.26, "end": 32.98, "word": " is", "probability": 0.93896484375}, {"start": 32.98, "end": 33.3, "word": " below", "probability": 0.904296875}, {"start": 33.3, "end": 33.56, "word": " the", "probability": 0.916015625}, {"start": 33.56, "end": 33.88, "word": " lower", "probability": 0.859375}, {"start": 33.88, "end": 34.4, "word": " limit", "probability": 0.9638671875}, {"start": 34.4, "end": 35.3, "word": " or", "probability": 0.50439453125}, {"start": 35.3, "end": 37.18, "word": " is", "probability": 0.82763671875}, {"start": 37.18, "end": 37.6, "word": " above", "probability": 0.966796875}, {"start": 37.6, "end": 37.78, "word": " the", "probability": 0.87548828125}, {"start": 37.78, "end": 38.02, "word": " upper", "probability": 0.79638671875}, {"start": 38.02, "end": 38.58, "word": " limit,", "probability": 0.95849609375}, {"start": 39.2, "end": 39.54, "word": " that", "probability": 0.8876953125}, {"start": 39.54, "end": 39.88, "word": " point", "probability": 0.9462890625}, {"start": 39.88, "end": 40.12, "word": " is", "probability": 0.9208984375}, {"start": 40.12, "end": 40.46, "word": " considered", "probability": 0.80810546875}, {"start": 40.46, "end": 40.72, "word": " to", "probability": 0.9658203125}, {"start": 40.72, "end": 41.0, "word": " be", "probability": 0.953125}, {"start": 41.0, "end": 41.54, "word": " an", "probability": 0.92041015625}, {"start": 41.54, "end": 41.96, "word": " outlier.", "probability": 0.96240234375}, {"start": 42.86, "end": 43.0, "word": " So", "probability": 0.2032470703125}, {"start": 43.0, "end": 43.28, "word": " that's", "probability": 0.794921875}, {"start": 43.28, "end": 43.38, "word": " one", "probability": 0.88720703125}, {"start": 43.38, "end": 43.5, "word": " of", "probability": 0.94384765625}, {"start": 43.5, "end": 43.8, "word": " the", "probability": 0.9169921875}, {"start": 43.8, "end": 44.56, "word": " usage", "probability": 0.759765625}, {"start": 44.56, "end": 44.92, "word": " of", "probability": 0.970703125}, {"start": 44.92, "end": 45.2, "word": " the", "probability": 0.30322265625}, {"start": 45.2, "end": 46.1, "word": " backsplat.", "probability": 0.4542643229166667}, {"start": 46.6, "end": 46.84, "word": " I", "probability": 0.90185546875}, {"start": 46.84, "end": 46.94, "word": " mean,", "probability": 0.95751953125}, {"start": 47.0, "end": 47.1, "word": " for", "probability": 0.94775390625}, {"start": 47.1, "end": 47.32, "word": " this", "probability": 0.94580078125}, {"start": 47.32, "end": 47.88, "word": " specific", "probability": 0.8984375}, {"start": 47.88, "end": 48.34, "word": " example,", "probability": 0.9736328125}, {"start": 49.78, "end": 50.6, "word": " we", "probability": 0.9501953125}, {"start": 50.6, "end": 50.88, "word": " mentioned", "probability": 0.82568359375}, {"start": 50.88, "end": 51.14, "word": " last", "probability": 0.8623046875}, {"start": 51.14, "end": 51.36, "word": " time", "probability": 0.88671875}, {"start": 51.36, "end": 51.72, "word": " 27", "probability": 0.556640625}, {"start": 51.72, "end": 52.56, "word": " is", "probability": 0.9404296875}, {"start": 52.56, "end": 52.74, "word": " an", "probability": 0.96142578125}, {"start": 52.74, "end": 53.08, "word": " outlier.", "probability": 0.97265625}], "temperature": 1.0}, {"id": 3, "seek": 7695, "start": 54.37, "end": 76.95, "text": " And also here you can tell also the data are right skewed because the right tail exactly is much longer than the left tail. I mean the distance between or from the median and the maximum value is bigger or larger than the distance from the median to the smallest value.", "tokens": [400, 611, 510, 291, 393, 980, 611, 264, 1412, 366, 558, 8756, 26896, 570, 264, 558, 6838, 2293, 307, 709, 2854, 813, 264, 1411, 6838, 13, 286, 914, 264, 4560, 1296, 420, 490, 264, 26779, 293, 264, 6674, 2158, 307, 3801, 420, 4833, 813, 264, 4560, 490, 264, 26779, 281, 264, 16998, 2158, 13], "avg_logprob": -0.15965909632769498, "compression_ratio": 1.6981132075471699, "no_speech_prob": 0.0, "words": [{"start": 54.37, "end": 54.71, "word": " And", "probability": 0.75}, {"start": 54.71, "end": 55.03, "word": " also", "probability": 0.74169921875}, {"start": 55.03, "end": 55.35, "word": " here", "probability": 0.7890625}, {"start": 55.35, "end": 56.11, "word": " you", "probability": 0.412353515625}, {"start": 56.11, "end": 56.35, "word": " can", "probability": 0.9482421875}, {"start": 56.35, "end": 56.53, "word": " tell", "probability": 0.8671875}, {"start": 56.53, "end": 56.91, "word": " also", "probability": 0.8056640625}, {"start": 56.91, "end": 57.31, "word": " the", "probability": 0.7236328125}, {"start": 57.31, "end": 57.71, "word": " data", "probability": 0.90234375}, {"start": 57.71, "end": 58.19, "word": " are", "probability": 0.9072265625}, {"start": 58.19, "end": 58.45, "word": " right", "probability": 0.884765625}, {"start": 58.45, "end": 59.03, "word": " skewed", "probability": 0.93994140625}, {"start": 59.03, "end": 59.77, "word": " because", "probability": 0.60546875}, {"start": 59.77, "end": 61.13, "word": " the", "probability": 0.48828125}, {"start": 61.13, "end": 62.41, "word": " right", "probability": 0.64111328125}, {"start": 62.41, "end": 62.77, "word": " tail", "probability": 0.7841796875}, {"start": 62.77, "end": 63.27, "word": " exactly", "probability": 0.58740234375}, {"start": 63.27, "end": 63.95, "word": " is", "probability": 0.90283203125}, {"start": 63.95, "end": 64.29, "word": " much", "probability": 0.9150390625}, {"start": 64.29, "end": 64.77, "word": " longer", "probability": 0.93896484375}, {"start": 64.77, "end": 65.13, "word": " than", "probability": 0.94189453125}, {"start": 65.13, "end": 65.33, "word": " the", "probability": 0.91162109375}, {"start": 65.33, "end": 65.53, "word": " left", "probability": 0.94580078125}, {"start": 65.53, "end": 65.75, "word": " tail.", "probability": 0.86279296875}, {"start": 65.89, "end": 65.91, "word": " I", "probability": 0.99072265625}, {"start": 65.91, "end": 66.09, "word": " mean", "probability": 0.96630859375}, {"start": 66.09, "end": 66.29, "word": " the", "probability": 0.77490234375}, {"start": 66.29, "end": 66.69, "word": " distance", "probability": 0.943359375}, {"start": 66.69, "end": 67.13, "word": " between", "probability": 0.81591796875}, {"start": 67.13, "end": 67.91, "word": " or", "probability": 0.8525390625}, {"start": 67.91, "end": 68.31, "word": " from", "probability": 0.892578125}, {"start": 68.31, "end": 68.99, "word": " the", "probability": 0.92236328125}, {"start": 68.99, "end": 69.31, "word": " median", "probability": 0.9609375}, {"start": 69.31, "end": 70.23, "word": " and", "probability": 0.84619140625}, {"start": 70.23, "end": 70.45, "word": " the", "probability": 0.8935546875}, {"start": 70.45, "end": 70.81, "word": " maximum", "probability": 0.92041015625}, {"start": 70.81, "end": 71.37, "word": " value", "probability": 0.97509765625}, {"start": 71.37, "end": 72.37, "word": " is", "probability": 0.72021484375}, {"start": 72.37, "end": 72.81, "word": " bigger", "probability": 0.9228515625}, {"start": 72.81, "end": 73.27, "word": " or", "probability": 0.89208984375}, {"start": 73.27, "end": 73.65, "word": " larger", "probability": 0.9384765625}, {"start": 73.65, "end": 73.95, "word": " than", "probability": 0.93505859375}, {"start": 73.95, "end": 74.15, "word": " the", "probability": 0.91796875}, {"start": 74.15, "end": 74.51, "word": " distance", "probability": 0.94189453125}, {"start": 74.51, "end": 74.89, "word": " from", "probability": 0.87939453125}, {"start": 74.89, "end": 75.57, "word": " the", "probability": 0.91796875}, {"start": 75.57, "end": 75.87, "word": " median", "probability": 0.9736328125}, {"start": 75.87, "end": 76.13, "word": " to", "probability": 0.9619140625}, {"start": 76.13, "end": 76.29, "word": " the", "probability": 0.91259765625}, {"start": 76.29, "end": 76.63, "word": " smallest", "probability": 0.9306640625}, {"start": 76.63, "end": 76.95, "word": " value.", "probability": 0.865234375}], "temperature": 1.0}, {"id": 4, "seek": 9225, "start": 77.45, "end": 92.25, "text": " That means the data is not symmetric, it's quite skewed to the right. In this case, you cannot use the mean or the range as a measure of spread and median and, I'm sorry, mean as a measure of tendency.", "tokens": [663, 1355, 264, 1412, 307, 406, 32330, 11, 309, 311, 1596, 8756, 26896, 281, 264, 558, 13, 682, 341, 1389, 11, 291, 2644, 764, 264, 914, 420, 264, 3613, 382, 257, 3481, 295, 3974, 293, 26779, 293, 11, 286, 478, 2597, 11, 914, 382, 257, 3481, 295, 18187, 13], "avg_logprob": -0.18484374582767488, "compression_ratio": 1.4852941176470589, "no_speech_prob": 0.0, "words": [{"start": 77.45, "end": 77.77, "word": " That", "probability": 0.57177734375}, {"start": 77.77, "end": 78.01, "word": " means", "probability": 0.92236328125}, {"start": 78.01, "end": 78.17, "word": " the", "probability": 0.841796875}, {"start": 78.17, "end": 78.47, "word": " data", "probability": 0.9482421875}, {"start": 78.47, "end": 78.77, "word": " is", "probability": 0.94384765625}, {"start": 78.77, "end": 79.01, "word": " not", "probability": 0.94580078125}, {"start": 79.01, "end": 79.49, "word": " symmetric,", "probability": 0.86083984375}, {"start": 80.03, "end": 80.37, "word": " it's", "probability": 0.915771484375}, {"start": 80.37, "end": 80.87, "word": " quite", "probability": 0.9267578125}, {"start": 80.87, "end": 81.33, "word": " skewed", "probability": 0.96875}, {"start": 81.33, "end": 81.47, "word": " to", "probability": 0.9580078125}, {"start": 81.47, "end": 81.59, "word": " the", "probability": 0.91943359375}, {"start": 81.59, "end": 81.83, "word": " right.", "probability": 0.9208984375}, {"start": 82.43, "end": 82.69, "word": " In", "probability": 0.94873046875}, {"start": 82.69, "end": 82.89, "word": " this", "probability": 0.9462890625}, {"start": 82.89, "end": 83.15, "word": " case,", "probability": 0.91259765625}, {"start": 83.23, "end": 83.33, "word": " you", "probability": 0.94970703125}, {"start": 83.33, "end": 83.57, "word": " cannot", "probability": 0.86474609375}, {"start": 83.57, "end": 84.05, "word": " use", "probability": 0.87890625}, {"start": 84.05, "end": 84.57, "word": " the", "probability": 0.92041015625}, {"start": 84.57, "end": 84.79, "word": " mean", "probability": 0.96142578125}, {"start": 84.79, "end": 86.67, "word": " or", "probability": 0.85107421875}, {"start": 86.67, "end": 86.99, "word": " the", "probability": 0.9130859375}, {"start": 86.99, "end": 87.31, "word": " range", "probability": 0.86767578125}, {"start": 87.31, "end": 87.63, "word": " as", "probability": 0.947265625}, {"start": 87.63, "end": 87.79, "word": " a", "probability": 0.372802734375}, {"start": 87.79, "end": 87.97, "word": " measure", "probability": 0.8828125}, {"start": 87.97, "end": 88.21, "word": " of", "probability": 0.96240234375}, {"start": 88.21, "end": 88.65, "word": " spread", "probability": 0.701171875}, {"start": 88.65, "end": 89.37, "word": " and", "probability": 0.80322265625}, {"start": 89.37, "end": 89.77, "word": " median", "probability": 0.908203125}, {"start": 89.77, "end": 90.17, "word": " and,", "probability": 0.5302734375}, {"start": 90.21, "end": 90.35, "word": " I'm", "probability": 0.943603515625}, {"start": 90.35, "end": 90.49, "word": " sorry,", "probability": 0.85107421875}, {"start": 90.59, "end": 90.83, "word": " mean", "probability": 0.81640625}, {"start": 90.83, "end": 91.09, "word": " as", "probability": 0.923828125}, {"start": 91.09, "end": 91.25, "word": " a", "probability": 0.5634765625}, {"start": 91.25, "end": 91.47, "word": " measure", "probability": 0.86962890625}, {"start": 91.47, "end": 91.73, "word": " of", "probability": 0.96044921875}, {"start": 91.73, "end": 92.25, "word": " tendency.", "probability": 0.9287109375}], "temperature": 1.0}, {"id": 5, "seek": 11333, "start": 93.69, "end": 113.33, "text": " Because these measures are affected by outcomes. In this case, you have to use the median instead of the mean and IQR instead of the range because IQR is the mid-spread of the data because we just take the range from Q3 to Q1. 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So it depends on the data. For this example, 27, which was the maximum, is an outlier. But zero is not outlier in this case, because zero is above the lower limit. Let's move to the next topic, which talks about covariance and correlation. 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That means if the data set is numeric, I mean if both variables are numeric, in this case we can use the covariance to measure the strength of the linear association or relationship between two numerical variables. 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By using the sign of the covariance, you can tell if there exists positive or negative relationship between the two variables. 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It means that if X goes up, Y will go in the same position. If X goes down, also Y goes down. For example, suppose we are interested in the relationship between consumption and income. 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So for sure, the covariance between X and Y should be positive. 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I mean they move to opposite direction. That means there exists negative relationship between X and Y. For example, you score in statistics a number of missing classes. 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For example, your score in statistics and your weight. It makes sense that there is no relationship between your weight and your score. In this case, we are saying x and y are independent. I mean, they are uncorrelated.", "tokens": [682, 300, 1389, 11, 49851, 719, 1296, 2031, 293, 288, 6915, 4018, 13, 1171, 1365, 11, 428, 6175, 294, 12523, 293, 428, 3364, 13, 467, 1669, 2020, 300, 456, 307, 572, 2480, 1296, 428, 3364, 293, 428, 6175, 13, 682, 341, 1389, 11, 321, 366, 1566, 2031, 293, 288, 366, 6695, 13, 286, 914, 11, 436, 366, 6219, 284, 12004, 13], "avg_logprob": -0.1362147184629594, "compression_ratio": 1.6506024096385543, "no_speech_prob": 0.0, "words": [{"start": 381.58, "end": 381.8, "word": " In", "probability": 0.81787109375}, {"start": 381.8, "end": 382.02, "word": " that", "probability": 0.93310546875}, {"start": 382.02, "end": 382.34, "word": " case,", "probability": 0.921875}, {"start": 382.44, "end": 382.84, "word": " covariance", "probability": 0.7890625}, {"start": 382.84, "end": 383.04, "word": " between", "probability": 0.88818359375}, {"start": 383.04, "end": 383.26, "word": " x", "probability": 0.55859375}, {"start": 383.26, "end": 383.4, "word": " and", "probability": 0.94580078125}, {"start": 383.4, "end": 383.62, "word": " y", "probability": 0.99462890625}, {"start": 383.62, "end": 384.44, "word": " equals", "probability": 0.86279296875}, {"start": 384.44, "end": 384.78, "word": " zero.", "probability": 0.69580078125}, {"start": 384.88, "end": 385.0, "word": " For", "probability": 0.9697265625}, {"start": 385.0, "end": 385.42, "word": " example,", "probability": 0.9736328125}, {"start": 386.12, "end": 386.3, "word": " your", "probability": 0.861328125}, {"start": 386.3, "end": 386.82, "word": " score", "probability": 0.87158203125}, {"start": 386.82, "end": 388.4, "word": " in", "probability": 0.6796875}, {"start": 388.4, "end": 388.88, "word": " statistics", "probability": 0.8564453125}, {"start": 388.88, "end": 390.56, "word": " and", "probability": 0.79345703125}, {"start": 390.56, "end": 391.32, "word": " your", "probability": 0.8994140625}, {"start": 391.32, "end": 391.7, "word": " weight.", "probability": 0.92041015625}, {"start": 394.54, "end": 395.16, "word": " It", "probability": 0.55419921875}, {"start": 395.16, "end": 395.42, "word": " makes", "probability": 0.8212890625}, {"start": 395.42, "end": 395.7, "word": " sense", "probability": 0.82666015625}, {"start": 395.7, "end": 395.92, "word": " that", "probability": 0.91650390625}, {"start": 395.92, "end": 396.08, "word": " there", "probability": 0.91064453125}, {"start": 396.08, "end": 396.22, "word": " is", "probability": 0.89404296875}, {"start": 396.22, "end": 396.38, "word": " no", "probability": 0.94287109375}, {"start": 396.38, "end": 396.76, "word": " relationship", "probability": 0.91015625}, {"start": 396.76, "end": 397.24, "word": " between", "probability": 0.869140625}, {"start": 397.24, "end": 398.66, "word": " your", "probability": 0.89697265625}, {"start": 398.66, "end": 398.92, "word": " weight", "probability": 0.91845703125}, {"start": 398.92, "end": 399.3, "word": " and", "probability": 0.9375}, {"start": 399.3, "end": 400.44, "word": " your", "probability": 0.9052734375}, {"start": 400.44, "end": 400.88, "word": " score.", "probability": 0.87939453125}, {"start": 401.5, "end": 402.0, "word": " In", "probability": 0.85107421875}, {"start": 402.0, "end": 402.28, "word": " this", "probability": 0.9453125}, {"start": 402.28, "end": 402.68, "word": " case,", "probability": 0.91259765625}, {"start": 403.58, "end": 403.76, "word": " we", "probability": 0.955078125}, {"start": 403.76, "end": 403.92, "word": " are", "probability": 0.9306640625}, {"start": 403.92, "end": 404.36, "word": " saying", "probability": 0.75341796875}, {"start": 404.36, "end": 404.94, "word": " x", "probability": 0.939453125}, {"start": 404.94, "end": 405.14, "word": " and", "probability": 0.9453125}, {"start": 405.14, "end": 405.42, "word": " y", "probability": 0.998046875}, {"start": 405.42, "end": 405.72, "word": " are", "probability": 0.94091796875}, {"start": 405.72, "end": 406.22, "word": " independent.", "probability": 0.8857421875}, {"start": 406.48, "end": 406.62, "word": " I", "probability": 0.93408203125}, {"start": 406.62, "end": 406.76, "word": " mean,", "probability": 0.96484375}, {"start": 406.84, "end": 406.96, "word": " they", "probability": 0.88623046875}, {"start": 406.96, "end": 407.18, "word": " are", "probability": 0.9404296875}, {"start": 407.18, "end": 407.88, "word": " uncorrelated.", "probability": 0.9685872395833334}], "temperature": 1.0}, {"id": 17, "seek": 43515, "start": 408.71, "end": 435.15, "text": " Because as one variable increases, the other maybe go up or go down. Or maybe constant. So that means there exists no relationship between the two variables. In that case, the covariance between x and y equals zero. Now, by using the covariance, you can determine the direction of the relationship. I mean, you can just figure out if the relation is positive or negative.", "tokens": [1436, 382, 472, 7006, 8637, 11, 264, 661, 1310, 352, 493, 420, 352, 760, 13, 1610, 1310, 5754, 13, 407, 300, 1355, 456, 8198, 572, 2480, 1296, 264, 732, 9102, 13, 682, 300, 1389, 11, 264, 49851, 719, 1296, 2031, 293, 288, 6915, 4018, 13, 823, 11, 538, 1228, 264, 49851, 719, 11, 291, 393, 6997, 264, 3513, 295, 264, 2480, 13, 286, 914, 11, 291, 393, 445, 2573, 484, 498, 264, 9721, 307, 3353, 420, 3671, 13], "avg_logprob": -0.13706486662731895, "compression_ratio": 1.7064220183486238, "no_speech_prob": 0.0, "words": [{"start": 408.71, "end": 409.19, "word": " Because", "probability": 0.57763671875}, {"start": 409.19, "end": 409.79, "word": " as", "probability": 0.8076171875}, {"start": 409.79, "end": 410.35, "word": " one", "probability": 0.9208984375}, {"start": 410.35, "end": 410.79, "word": " variable", "probability": 0.91357421875}, {"start": 410.79, "end": 411.55, "word": " increases,", 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I mean you cannot tell if they exist.", "tokens": [583, 291, 2644, 980, 2293, 264, 3800, 295, 264, 2480, 13, 286, 914, 291, 2644, 980, 498, 436, 2514, 13], "avg_logprob": -0.2604166666666667, "compression_ratio": 1.2195121951219512, "no_speech_prob": 0.0, "words": [{"start": 435.88, "end": 436.2, "word": " But", "probability": 0.5380859375}, {"start": 436.2, "end": 436.36, "word": " you", "probability": 0.6796875}, {"start": 436.36, "end": 436.6, "word": " cannot", "probability": 0.7802734375}, {"start": 436.6, "end": 436.9, "word": " tell", "probability": 0.86767578125}, {"start": 436.9, "end": 437.52, "word": " exactly", "probability": 0.87109375}, {"start": 437.52, "end": 438.46, "word": " the", "probability": 0.8671875}, {"start": 438.46, "end": 438.98, "word": " strength", "probability": 0.857421875}, {"start": 438.98, "end": 439.52, "word": " of", "probability": 0.9677734375}, {"start": 439.52, "end": 439.64, "word": " the", "probability": 0.81494140625}, {"start": 439.64, "end": 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Any questions? So let me ask you just to summarize what I said so far. Just give me the summary or conclusion.", "tokens": [8000, 264, 3800, 295, 732, 29054, 9102, 11, 293, 291, 787, 980, 498, 456, 8198, 3353, 420, 3671, 2480, 11, 457, 291, 2644, 980, 1340, 466, 264, 3800, 295, 264, 2480, 13, 2639, 1651, 30, 407, 718, 385, 1029, 291, 445, 281, 20858, 437, 286, 848, 370, 1400, 13, 1449, 976, 385, 264, 12691, 420, 10063, 13], "avg_logprob": -0.14897629592953057, "compression_ratio": 1.5654450261780104, "no_speech_prob": 0.0, "words": [{"start": 471.91, "end": 472.41, "word": " measures", "probability": 0.60107421875}, {"start": 472.41, "end": 472.71, "word": " the", "probability": 0.91162109375}, {"start": 472.71, "end": 473.15, "word": " strength", "probability": 0.8310546875}, {"start": 473.15, "end": 473.93, "word": " of", "probability": 0.9638671875}, {"start": 473.93, "end": 474.21, "word": " two", "probability": 0.86181640625}, {"start": 474.21, "end": 474.57, "word": " numerical", "probability": 0.96044921875}, {"start": 474.57, "end": 475.09, 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So just tell the direction, not the strength of the relationship. Now, in order to determine both the direction and the strength, we can use the coefficient of correlation.", "tokens": [400, 437, 311, 466, 264, 3800, 30, 407, 445, 980, 264, 3513, 11, 406, 264, 3800, 295, 264, 2480, 13, 823, 11, 294, 1668, 281, 6997, 1293, 264, 3513, 293, 264, 3800, 11, 321, 393, 764, 264, 17619, 295, 20009, 13], "avg_logprob": -0.20200892502353304, "compression_ratio": 1.5572519083969465, "no_speech_prob": 0.0, "words": [{"start": 532.57, "end": 532.99, "word": " And", "probability": 0.57666015625}, {"start": 532.99, "end": 533.35, "word": " what's", "probability": 0.78662109375}, {"start": 533.35, "end": 533.59, "word": " about", "probability": 0.91064453125}, {"start": 533.59, "end": 534.09, "word": " the", "probability": 0.8837890625}, {"start": 534.09, "end": 534.93, "word": " strength?", "probability": 0.480712890625}, {"start": 537.95, "end": 538.27, "word": " So", "probability": 0.2529296875}, {"start": 538.27, "end": 538.69, "word": " just", "probability": 0.67431640625}, {"start": 538.69, "end": 538.99, "word": " tell", "probability": 0.7734375}, {"start": 538.99, "end": 540.03, "word": " the", "probability": 0.8583984375}, {"start": 540.03, "end": 540.63, "word": " direction,", "probability": 0.97412109375}, {"start": 541.35, "end": 542.29, "word": " not", "probability": 0.93896484375}, {"start": 542.29, "end": 542.51, "word": " the", "probability": 0.9130859375}, {"start": 542.51, "end": 542.91, "word": " strength", "probability": 0.85498046875}, {"start": 542.91, "end": 543.45, "word": " of", "probability": 0.88427734375}, {"start": 543.45, "end": 543.75, "word": " the", "probability": 0.91650390625}, {"start": 543.75, "end": 544.27, "word": " relationship.", "probability": 0.85693359375}, {"start": 545.17, "end": 545.41, "word": " Now,", "probability": 0.85400390625}, {"start": 546.63, "end": 547.01, "word": " in", "probability": 0.93359375}, {"start": 547.01, "end": 547.21, "word": " order", "probability": 0.935546875}, {"start": 547.21, "end": 547.67, "word": " to", "probability": 0.96923828125}, {"start": 547.67, "end": 548.15, "word": " determine", "probability": 0.9365234375}, {"start": 548.15, "end": 548.61, "word": " both", "probability": 0.8779296875}, {"start": 548.61, "end": 548.91, "word": " the", "probability": 0.69482421875}, {"start": 548.91, "end": 549.31, "word": " direction", "probability": 0.9658203125}, {"start": 549.31, "end": 549.61, "word": " and", "probability": 0.86474609375}, {"start": 549.61, "end": 549.73, "word": " the", "probability": 0.85400390625}, {"start": 549.73, "end": 550.07, "word": " strength,", "probability": 0.8642578125}, {"start": 550.15, "end": 550.27, "word": " we", "probability": 0.9404296875}, {"start": 550.27, "end": 550.47, "word": " can", "probability": 0.94287109375}, {"start": 550.47, "end": 550.91, "word": " use", "probability": 0.87744140625}, {"start": 550.91, "end": 552.11, "word": " the", "probability": 0.91552734375}, {"start": 552.11, "end": 553.37, "word": " coefficient", "probability": 0.7548828125}, {"start": 553.37, "end": 553.69, "word": " of", "probability": 0.9453125}, {"start": 553.69, "end": 554.11, "word": " correlation.", "probability": 0.94775390625}], "temperature": 1.0}, {"id": 24, "seek": 58200, "start": 556.16, "end": 582.0, "text": " The coefficient of correlation measures the relative strength of the linear relationship between two numerical variables. The simplest formula that can be used to compute the correlation coefficient is given by this one. Maybe this is the easiest formula you can use. I mean, it's shortcut formula for computation. There are many other formulas to compute the correlation.", "tokens": [440, 17619, 295, 20009, 8000, 264, 4972, 3800, 295, 264, 8213, 2480, 1296, 732, 29054, 9102, 13, 440, 22811, 8513, 300, 393, 312, 1143, 281, 14722, 264, 20009, 17619, 307, 2212, 538, 341, 472, 13, 2704, 341, 307, 264, 12889, 8513, 291, 393, 764, 13, 286, 914, 11, 309, 311, 24822, 8513, 337, 24903, 13, 821, 366, 867, 661, 30546, 281, 14722, 264, 20009, 13], "avg_logprob": -0.1329308646646413, "compression_ratio": 1.8195121951219513, "no_speech_prob": 0.0, "words": [{"start": 556.16, "end": 556.48, "word": " The", "probability": 0.330322265625}, {"start": 556.48, "end": 556.96, "word": " coefficient", "probability": 0.8544921875}, {"start": 556.96, "end": 557.58, "word": " of", "probability": 0.9501953125}, {"start": 557.58, "end": 558.02, "word": " correlation", "probability": 0.9140625}, {"start": 558.02, "end": 558.42, "word": " measures", "probability": 0.77490234375}, {"start": 558.42, "end": 558.84, "word": " 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And we are interested in the relationship between these two variables.", "tokens": [1171, 1365, 11, 7297, 321, 366, 1417, 466, 12126, 293, 4846, 13, 400, 321, 366, 3102, 294, 264, 2480, 1296, 613, 732, 9102, 13], "avg_logprob": -0.27109374046325685, "compression_ratio": 1.2592592592592593, "no_speech_prob": 0.0, "words": [{"start": 681.76, "end": 682.5, "word": " For", "probability": 0.06585693359375}, {"start": 682.5, "end": 683.24, "word": " example,", "probability": 0.9716796875}, {"start": 683.56, "end": 684.12, "word": " suppose", "probability": 0.83203125}, {"start": 684.12, "end": 684.3, "word": " we", "probability": 0.93115234375}, {"start": 684.3, "end": 684.4, "word": " are", "probability": 0.86865234375}, {"start": 684.4, "end": 684.74, "word": " talking", "probability": 0.84130859375}, {"start": 684.74, "end": 685.32, "word": " about", "probability": 0.90966796875}, {"start": 685.32, "end": 686.6, "word": " consumption", "probability": 0.9140625}, {"start": 686.6, "end": 692.28, "word": " and", "probability": 0.51025390625}, {"start": 692.28, "end": 692.62, "word": " input.", "probability": 0.407470703125}, {"start": 694.36, "end": 695.1, "word": " And", "probability": 0.92431640625}, {"start": 695.1, "end": 695.22, "word": " we", "probability": 0.921875}, {"start": 695.22, "end": 695.36, "word": " are", "probability": 0.92919921875}, {"start": 695.36, "end": 695.78, "word": " interested", "probability": 0.85791015625}, {"start": 695.78, "end": 696.14, "word": " in", "probability": 0.93798828125}, {"start": 696.14, "end": 696.26, "word": " the", "probability": 0.912109375}, {"start": 696.26, "end": 696.7, "word": " relationship", "probability": 0.9189453125}, {"start": 696.7, "end": 697.08, "word": " between", "probability": 0.88671875}, {"start": 697.08, "end": 697.3, "word": " these", "probability": 0.86181640625}, {"start": 697.3, "end": 697.48, "word": " two", "probability": 0.923828125}, {"start": 697.48, "end": 697.92, "word": " variables.", "probability": 0.93798828125}], "temperature": 1.0}, {"id": 29, "seek": 72778, "start": 699.6, "end": 727.78, "text": " Now, except for the variable or the independent, this one affects the other variable. As we mentioned, as your income increases, your consumption will go in the same direction, increases also. Income causes Y, or income affects Y. In this case, income is your X. Most of the time we use", "tokens": [823, 11, 3993, 337, 264, 7006, 420, 264, 6695, 11, 341, 472, 11807, 264, 661, 7006, 13, 1018, 321, 2835, 11, 382, 428, 5742, 8637, 11, 428, 12126, 486, 352, 294, 264, 912, 3513, 11, 8637, 611, 13, 682, 1102, 7700, 398, 11, 420, 5742, 11807, 398, 13, 682, 341, 1389, 11, 5742, 307, 428, 1783, 13, 4534, 295, 264, 565, 321, 764], "avg_logprob": -0.23388672131113708, "compression_ratio": 1.6589595375722543, "no_speech_prob": 0.0, "words": [{"start": 699.6, "end": 700.2, "word": " Now,", "probability": 0.73779296875}, {"start": 700.82, "end": 701.12, "word": " except", "probability": 0.413818359375}, {"start": 701.12, "end": 701.28, "word": " for", "probability": 0.295166015625}, {"start": 701.28, "end": 701.36, "word": " the", "probability": 0.3271484375}, {"start": 701.36, "end": 701.78, "word": " variable", "probability": 0.72216796875}, {"start": 701.78, "end": 702.08, "word": " or", "probability": 0.5322265625}, {"start": 702.08, "end": 702.24, "word": " the", "probability": 0.72509765625}, {"start": 702.24, "end": 702.66, "word": " independent,", "probability": 0.8671875}, {"start": 703.16, "end": 703.52, "word": " this", "probability": 0.91162109375}, {"start": 703.52, "end": 703.86, "word": " one", "probability": 0.9091796875}, {"start": 703.86, "end": 704.6, "word": " affects", "probability": 0.7568359375}, {"start": 704.6, "end": 704.9, "word": " the", "probability": 0.91455078125}, {"start": 704.9, "end": 705.14, "word": " other", "probability": 0.890625}, {"start": 705.14, "end": 705.6, "word": " variable.", "probability": 0.8525390625}, {"start": 707.76, "end": 708.36, "word": " As", "probability": 0.951171875}, {"start": 708.36, "end": 708.48, "word": " we", "probability": 0.84814453125}, {"start": 708.48, "end": 708.84, "word": " mentioned,", "probability": 0.80419921875}, {"start": 709.02, "end": 709.22, "word": " as", "probability": 0.95458984375}, {"start": 709.22, "end": 709.42, "word": " your", "probability": 0.8857421875}, {"start": 709.42, "end": 709.84, "word": " income", "probability": 0.939453125}, {"start": 709.84, "end": 710.7, "word": " increases,", "probability": 0.93310546875}, {"start": 712.04, "end": 712.32, "word": " your", "probability": 0.86865234375}, {"start": 712.32, "end": 712.8, "word": " consumption", "probability": 0.9755859375}, {"start": 712.8, "end": 713.22, "word": " will", "probability": 0.8505859375}, {"start": 713.22, "end": 713.42, "word": " go", "probability": 0.94873046875}, {"start": 713.42, "end": 713.52, "word": " in", "probability": 0.9287109375}, {"start": 713.52, "end": 713.64, "word": " the", "probability": 0.91845703125}, {"start": 713.64, "end": 713.8, "word": " same", "probability": 0.9052734375}, {"start": 713.8, "end": 714.22, "word": " direction,", "probability": 0.97021484375}, {"start": 714.4, "end": 714.7, "word": " increases", "probability": 0.6865234375}, {"start": 714.7, "end": 715.12, "word": " also.", "probability": 0.8671875}, {"start": 716.26, "end": 716.84, "word": " Income", "probability": 0.91943359375}, {"start": 716.84, "end": 718.58, "word": " causes", "probability": 0.787109375}, {"start": 718.58, "end": 718.88, "word": " Y,", "probability": 0.724609375}, {"start": 719.4, "end": 719.58, "word": " or", "probability": 0.8662109375}, {"start": 719.58, "end": 719.88, "word": " income", "probability": 0.88720703125}, {"start": 719.88, "end": 720.42, "word": " affects", "probability": 0.81640625}, {"start": 720.42, "end": 720.76, "word": " Y.", "probability": 0.99462890625}, {"start": 720.9, "end": 721.04, "word": " In", "probability": 0.955078125}, {"start": 721.04, "end": 721.26, "word": " this", "probability": 0.94384765625}, {"start": 721.26, "end": 721.56, "word": " case,", "probability": 0.9052734375}, {"start": 721.7, "end": 722.14, "word": " income", "probability": 0.94677734375}, {"start": 722.14, "end": 723.86, "word": " is", "probability": 0.87548828125}, {"start": 723.86, "end": 724.04, "word": " your", "probability": 0.84716796875}, {"start": 724.04, "end": 724.34, "word": " X.", "probability": 0.9599609375}, {"start": 726.18, "end": 726.78, "word": " Most", "probability": 0.8720703125}, {"start": 726.78, "end": 727.1, "word": " of", "probability": 0.96630859375}, {"start": 727.1, "end": 727.22, "word": " the", "probability": 0.91650390625}, {"start": 727.22, "end": 727.46, "word": " time", "probability": 0.884765625}, {"start": 727.46, "end": 727.64, "word": " we", "probability": 0.51220703125}, {"start": 727.64, "end": 727.78, "word": " use", "probability": 0.8583984375}], "temperature": 1.0}, {"id": 30, "seek": 75321, "start": 730.79, "end": 753.21, "text": " And Y for independent. So in this case, the response variable or your outcome or the dependent variable is your consumption. So Y is consumption, X is income. 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So first step, compute x bar and y bar.", "tokens": [2031, 2159, 11, 288, 2159, 11, 6666, 538, 264, 3732, 5593, 295, 732, 22927, 13, 440, 700, 472, 11, 2408, 295, 2031, 8889, 3175, 297, 2031, 2159, 13, 440, 661, 472, 11, 2408, 295, 288, 8889, 3175, 18052, 288, 8889, 13, 407, 264, 700, 551, 321, 362, 281, 360, 307, 281, 915, 264, 914, 337, 1184, 2031, 293, 288, 13, 407, 700, 1823, 11, 14722, 2031, 2159, 293, 288, 2159, 13], "avg_logprob": -0.2121310786654552, "compression_ratio": 1.7419354838709677, "no_speech_prob": 0.0, "words": [{"start": 784.97, "end": 785.33, "word": " x", "probability": 0.2286376953125}, {"start": 785.33, "end": 785.73, "word": " bar,", "probability": 0.83154296875}, {"start": 786.01, "end": 786.25, "word": " y", "probability": 0.96630859375}, {"start": 786.25, "end": 786.61, "word": " bar,", "probability": 0.96044921875}, {"start": 786.99, "end": 787.67, "word": " divided", "probability": 0.5810546875}, {"start": 787.67, "end": 787.85, "word": " by", 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So we need to compute the product of x times y. So just for example, suppose x is 10, y is 5. So x times y is 50. In addition to that, you have to compute", "tokens": [3087, 11, 498, 291, 574, 510, 11, 321, 362, 2031, 293, 288, 11, 2031, 1413, 288, 13, 407, 321, 643, 281, 14722, 264, 1674, 295, 2031, 1413, 288, 13, 407, 445, 337, 1365, 11, 7297, 2031, 307, 1266, 11, 288, 307, 1025, 13, 407, 2031, 1413, 288, 307, 2625, 13, 682, 4500, 281, 300, 11, 291, 362, 281, 14722], "avg_logprob": -0.13971354737877845, "compression_ratio": 1.4577464788732395, "no_speech_prob": 0.0, "words": [{"start": 815.39, "end": 815.91, "word": " Next,", "probability": 0.87109375}, {"start": 817.03, "end": 817.21, "word": " if", "probability": 0.93310546875}, {"start": 817.21, "end": 817.23, "word": " you", "probability": 0.95947265625}, {"start": 817.23, "end": 817.45, "word": " look", "probability": 0.96875}, {"start": 817.45, "end": 817.71, "word": " here,", "probability": 0.86328125}, {"start": 817.79, "end": 817.91, "word": " we", "probability": 0.955078125}, {"start": 817.91, "end": 818.33, "word": " have", "probability": 0.9501953125}, {"start": 818.33, "end": 818.87, "word": " x", "probability": 0.69287109375}, {"start": 818.87, "end": 819.05, "word": " and", "probability": 0.94677734375}, {"start": 819.05, "end": 819.39, "word": " y,", "probability": 0.99609375}, {"start": 820.35, "end": 820.57, "word": " x", "probability": 0.9892578125}, {"start": 820.57, "end": 820.97, "word": " times", "probability": 0.89404296875}, {"start": 820.97, "end": 821.29, "word": " y.", "probability": 0.98291015625}, {"start": 821.33, "end": 821.55, "word": " So", "probability": 0.9326171875}, {"start": 821.55, "end": 821.69, "word": " we", "probability": 0.591796875}, {"start": 821.69, "end": 821.85, "word": " need", "probability": 0.904296875}, {"start": 821.85, "end": 821.97, "word": " to", "probability": 0.958984375}, {"start": 821.97, "end": 822.25, "word": " compute", "probability": 0.441650390625}, {"start": 822.25, "end": 822.63, "word": " the", "probability": 0.89306640625}, {"start": 822.63, "end": 822.99, "word": " product", "probability": 0.95751953125}, {"start": 822.99, "end": 825.37, "word": " of", "probability": 0.90625}, {"start": 825.37, "end": 825.65, "word": " x", "probability": 0.99169921875}, {"start": 825.65, "end": 825.89, "word": " times", "probability": 0.92919921875}, {"start": 825.89, "end": 826.17, "word": " y.", "probability": 0.98828125}, {"start": 828.03, "end": 828.55, "word": " So", "probability": 0.9482421875}, {"start": 828.55, "end": 828.87, "word": " just", "probability": 0.84521484375}, {"start": 828.87, "end": 829.11, "word": " for", "probability": 0.7216796875}, {"start": 829.11, "end": 829.45, "word": " example,", "probability": 0.9755859375}, {"start": 829.57, "end": 829.83, "word": " suppose", "probability": 0.95263671875}, {"start": 829.83, "end": 830.79, "word": " x", "probability": 0.9638671875}, {"start": 830.79, "end": 830.95, "word": " is", "probability": 0.9453125}, {"start": 830.95, "end": 831.17, "word": " 10,", "probability": 0.771484375}, {"start": 831.25, "end": 831.39, "word": " y", "probability": 0.98828125}, {"start": 831.39, "end": 831.61, "word": " is", "probability": 0.95361328125}, {"start": 831.61, "end": 832.05, "word": " 5.", "probability": 0.9169921875}, {"start": 832.71, "end": 833.01, "word": " So", "probability": 0.95068359375}, {"start": 833.01, "end": 833.27, "word": " x", "probability": 0.94677734375}, {"start": 833.27, "end": 833.53, "word": " times", "probability": 0.92919921875}, {"start": 833.53, "end": 833.87, "word": " y", "probability": 0.98974609375}, {"start": 833.87, "end": 834.53, "word": " is", "probability": 0.94677734375}, {"start": 834.53, "end": 834.97, "word": " 50.", "probability": 0.68359375}, {"start": 837.81, "end": 838.33, "word": " In", "probability": 0.9287109375}, {"start": 838.33, "end": 838.65, "word": " addition", "probability": 0.9541015625}, {"start": 838.65, "end": 838.85, "word": " to", "probability": 0.966796875}, {"start": 838.85, "end": 839.05, "word": " that,", "probability": 0.939453125}, {"start": 839.09, "end": 839.17, "word": " you", "probability": 0.9365234375}, {"start": 839.17, "end": 839.35, "word": " have", "probability": 0.947265625}, {"start": 839.35, "end": 839.53, "word": " to", "probability": 0.9697265625}, {"start": 839.53, "end": 839.95, "word": " compute", "probability": 0.82568359375}], "temperature": 1.0}, {"id": 34, "seek": 87325, "start": 846.79, "end": 873.25, "text": " 100 x squared and y squared. It's like 125. Do the same calculations for the rest of the data you have. We have other data here, so we have to compute the same for the others. Then finally, just add xy, x squared, y squared.", "tokens": [2319, 2031, 8889, 293, 288, 8889, 13, 467, 311, 411, 25276, 13, 1144, 264, 912, 20448, 337, 264, 1472, 295, 264, 1412, 291, 362, 13, 492, 362, 661, 1412, 510, 11, 370, 321, 362, 281, 14722, 264, 912, 337, 264, 2357, 13, 1396, 2721, 11, 445, 909, 2031, 88, 11, 2031, 8889, 11, 288, 8889, 13], "avg_logprob": -0.2443804761819672, "compression_ratio": 1.5202702702702702, "no_speech_prob": 0.0, "words": [{"start": 846.79, "end": 847.27, "word": " 100", "probability": 0.292236328125}, {"start": 847.27, "end": 848.01, "word": " x", "probability": 0.328125}, {"start": 848.01, "end": 848.51, "word": " squared", "probability": 0.7763671875}, {"start": 848.51, "end": 849.87, "word": " and", "probability": 0.61083984375}, {"start": 849.87, "end": 850.09, "word": " y", "probability": 0.8505859375}, {"start": 850.09, "end": 850.31, "word": " squared.", "probability": 0.84033203125}, {"start": 850.49, "end": 850.55, "word": " It's", "probability": 0.6090087890625}, {"start": 850.55, "end": 850.63, "word": " like", "probability": 0.82470703125}, {"start": 850.63, "end": 852.47, "word": " 125.", "probability": 0.62353515625}, {"start": 854.81, "end": 855.45, "word": " Do", "probability": 0.93017578125}, {"start": 855.45, "end": 855.65, "word": " the", "probability": 0.91943359375}, {"start": 855.65, "end": 855.83, "word": " same", "probability": 0.8837890625}, {"start": 855.83, "end": 856.41, "word": " calculations", "probability": 0.9248046875}, {"start": 856.41, "end": 857.13, "word": " for", "probability": 0.95068359375}, {"start": 857.13, "end": 857.43, "word": " the", "probability": 0.916015625}, {"start": 857.43, "end": 858.09, "word": " rest", "probability": 0.92041015625}, {"start": 858.09, "end": 858.47, "word": " of", "probability": 0.96630859375}, {"start": 858.47, "end": 858.63, "word": " the", "probability": 0.9169921875}, {"start": 858.63, "end": 858.87, "word": " data", "probability": 0.93994140625}, {"start": 858.87, "end": 859.05, "word": " you", "probability": 0.93798828125}, {"start": 859.05, "end": 859.31, "word": " have.", "probability": 0.943359375}, {"start": 859.57, "end": 859.73, "word": " We", "probability": 0.89794921875}, {"start": 859.73, "end": 859.91, "word": " have", "probability": 0.94677734375}, {"start": 859.91, "end": 860.43, "word": " other", "probability": 0.86572265625}, {"start": 860.43, "end": 860.73, "word": " data", "probability": 0.93896484375}, {"start": 860.73, "end": 861.09, "word": " here,", "probability": 0.84716796875}, {"start": 861.59, "end": 861.87, "word": " so", "probability": 0.943359375}, {"start": 861.87, "end": 862.01, "word": " we", "probability": 0.90087890625}, {"start": 862.01, "end": 862.15, "word": " have", "probability": 0.9443359375}, {"start": 862.15, "end": 862.29, "word": " to", "probability": 0.9609375}, {"start": 862.29, "end": 862.73, "word": " compute", "probability": 0.8720703125}, {"start": 862.73, "end": 864.23, "word": " the", "probability": 0.88720703125}, {"start": 864.23, "end": 864.59, "word": " same", "probability": 0.87548828125}, {"start": 864.59, "end": 864.97, "word": " for", "probability": 0.91943359375}, {"start": 864.97, "end": 865.13, "word": " the", "probability": 0.52978515625}, {"start": 865.13, "end": 865.41, "word": " others.", "probability": 0.80859375}, {"start": 868.47, "end": 869.11, "word": " Then", "probability": 0.65771484375}, {"start": 869.11, "end": 869.51, "word": " finally,", "probability": 0.724609375}, {"start": 870.17, "end": 870.51, "word": " just", "probability": 0.8681640625}, {"start": 870.51, "end": 871.03, "word": " add", "probability": 0.8994140625}, {"start": 871.03, "end": 871.77, "word": " xy,", "probability": 0.84765625}, {"start": 872.03, "end": 872.27, "word": " x", "probability": 0.99560546875}, {"start": 872.27, "end": 872.57, "word": " squared,", "probability": 0.8134765625}, {"start": 872.69, "end": 872.89, "word": " y", "probability": 0.98828125}, {"start": 872.89, "end": 873.25, "word": " squared.", "probability": 0.83740234375}], "temperature": 1.0}, {"id": 35, "seek": 90037, "start": 875.91, "end": 900.37, "text": " The values you have here in this formula, in order to compute the coefficient. Now, this value ranges between minus one and plus one.", "tokens": [440, 4190, 291, 362, 510, 294, 341, 8513, 11, 294, 1668, 281, 14722, 264, 17619, 13, 823, 11, 341, 2158, 22526, 1296, 3175, 472, 293, 1804, 472, 13], "avg_logprob": -0.2280441851451479, "compression_ratio": 1.2523364485981308, "no_speech_prob": 0.0, "words": [{"start": 875.91, "end": 876.21, "word": " The", "probability": 0.607421875}, {"start": 876.21, "end": 876.61, "word": " values", "probability": 0.92919921875}, {"start": 876.61, "end": 876.81, "word": " you", "probability": 0.935546875}, {"start": 876.81, "end": 877.09, "word": " have", "probability": 0.9443359375}, {"start": 877.09, "end": 877.47, "word": " here", "probability": 0.84375}, {"start": 877.47, "end": 879.19, "word": " in", "probability": 0.6728515625}, {"start": 879.19, "end": 879.51, "word": " this", "probability": 0.927734375}, {"start": 879.51, "end": 880.07, "word": " formula,", "probability": 0.7119140625}, {"start": 880.47, "end": 880.65, "word": " in", "probability": 0.9287109375}, {"start": 880.65, "end": 880.83, "word": " order", "probability": 0.92236328125}, {"start": 880.83, "end": 882.05, "word": " to", "probability": 0.97216796875}, {"start": 882.05, "end": 882.79, "word": " compute", "probability": 0.90234375}, {"start": 882.79, "end": 883.99, "word": " the", "probability": 0.861328125}, {"start": 883.99, "end": 884.83, "word": " coefficient.", "probability": 0.86328125}, {"start": 894.25, "end": 895.05, "word": " Now,", "probability": 0.6123046875}, {"start": 895.99, "end": 896.45, "word": " this", "probability": 0.90771484375}, {"start": 896.45, "end": 896.93, "word": " value", "probability": 0.97802734375}, {"start": 896.93, "end": 898.51, "word": " ranges", "probability": 0.83056640625}, {"start": 898.51, "end": 898.97, "word": " between", "probability": 0.87451171875}, {"start": 898.97, "end": 899.33, "word": " minus", "probability": 0.7685546875}, {"start": 899.33, "end": 899.57, "word": " one", "probability": 0.489501953125}, {"start": 899.57, "end": 899.75, "word": " and", "probability": 0.90869140625}, {"start": 899.75, "end": 900.07, "word": " plus", "probability": 0.92236328125}, {"start": 900.07, "end": 900.37, "word": " one.", "probability": 0.8486328125}], "temperature": 1.0}, {"id": 36, "seek": 93512, "start": 906.52, "end": 935.12, "text": " So it's between minus one and plus one. That means it's never smaller than minus one or greater than one. It's between minus one and plus one. Make sense? I mean if your value is suppose you did mistake for any of these computations and R might be", "tokens": [407, 309, 311, 1296, 3175, 472, 293, 1804, 472, 13, 663, 1355, 309, 311, 1128, 4356, 813, 3175, 472, 420, 5044, 813, 472, 13, 467, 311, 1296, 3175, 472, 293, 1804, 472, 13, 4387, 2020, 30, 286, 914, 498, 428, 2158, 307, 7297, 291, 630, 6146, 337, 604, 295, 613, 2807, 763, 293, 497, 1062, 312], "avg_logprob": -0.18009867793635317, "compression_ratio": 1.631578947368421, "no_speech_prob": 0.0, "words": [{"start": 906.52, "end": 906.82, "word": " So", "probability": 0.75390625}, {"start": 906.82, "end": 907.04, "word": " it's", "probability": 0.88720703125}, {"start": 907.04, "end": 907.48, "word": " between", "probability": 0.7998046875}, {"start": 907.48, "end": 907.76, "word": " minus", "probability": 0.798828125}, {"start": 907.76, "end": 907.94, "word": " one", "probability": 0.6171875}, {"start": 907.94, "end": 908.08, "word": " and", "probability": 0.9013671875}, {"start": 908.08, "end": 908.36, "word": " plus", "probability": 0.96533203125}, {"start": 908.36, "end": 908.62, "word": " one.", "probability": 0.92919921875}, {"start": 909.74, "end": 910.38, "word": " That", "probability": 0.85546875}, {"start": 910.38, "end": 910.8, "word": " means", "probability": 0.94189453125}, {"start": 910.8, "end": 912.3, "word": " it's", "probability": 0.663818359375}, {"start": 912.3, "end": 912.66, "word": " never", "probability": 0.87353515625}, {"start": 912.66, "end": 915.84, "word": " smaller", "probability": 0.83935546875}, {"start": 915.84, "end": 916.1, "word": " than", "probability": 0.939453125}, {"start": 916.1, "end": 916.4, "word": " minus", "probability": 0.97802734375}, {"start": 916.4, "end": 916.74, "word": " one", "probability": 0.9150390625}, {"start": 916.74, "end": 918.34, "word": " or", "probability": 0.78271484375}, {"start": 918.34, "end": 918.7, "word": " greater", "probability": 0.90185546875}, {"start": 918.7, "end": 919.02, "word": " than", "probability": 0.94580078125}, {"start": 919.02, "end": 919.2, "word": " one.", "probability": 0.92578125}, {"start": 919.6, "end": 919.84, "word": " It's", "probability": 0.97509765625}, {"start": 919.84, "end": 920.2, "word": " between", "probability": 0.8876953125}, {"start": 920.2, "end": 920.52, "word": " minus", "probability": 0.98193359375}, {"start": 920.52, "end": 920.74, "word": " one", "probability": 0.91796875}, {"start": 920.74, "end": 920.9, "word": " and", "probability": 0.93701171875}, {"start": 920.9, "end": 921.2, "word": " plus", "probability": 0.95947265625}, {"start": 921.2, "end": 921.48, "word": " one.", "probability": 0.92041015625}, {"start": 924.36, "end": 925.0, "word": " Make", "probability": 0.7421875}, {"start": 925.0, "end": 925.3, "word": " sense?", "probability": 0.83544921875}, {"start": 925.94, "end": 926.08, "word": " I", "probability": 0.91064453125}, {"start": 926.08, "end": 926.22, "word": " mean", "probability": 0.9716796875}, {"start": 926.22, "end": 926.36, "word": " if", "probability": 0.533203125}, {"start": 926.36, "end": 926.56, "word": " your", "probability": 0.77978515625}, {"start": 926.56, "end": 926.94, "word": " value", "probability": 0.96533203125}, {"start": 926.94, "end": 927.26, "word": " is", "probability": 0.92041015625}, {"start": 927.26, "end": 927.92, "word": " suppose", "probability": 0.52001953125}, {"start": 927.92, "end": 928.3, "word": " you", "probability": 0.9296875}, {"start": 928.3, "end": 929.32, "word": " did", "probability": 0.849609375}, {"start": 929.32, "end": 930.02, "word": " mistake", "probability": 0.70947265625}, {"start": 930.02, "end": 930.32, "word": " for", "probability": 0.662109375}, {"start": 930.32, "end": 932.1, "word": " any", "probability": 0.837890625}, {"start": 932.1, "end": 932.58, "word": " of", "probability": 0.8798828125}, {"start": 932.58, "end": 932.76, "word": " these", "probability": 0.82275390625}, {"start": 932.76, "end": 933.44, "word": " computations", "probability": 0.953369140625}, {"start": 933.44, "end": 934.3, "word": " and", "probability": 0.64697265625}, {"start": 934.3, "end": 934.52, "word": " R", "probability": 0.5}, {"start": 934.52, "end": 934.82, "word": " might", "probability": 0.90771484375}, {"start": 934.82, "end": 935.12, "word": " be", "probability": 0.9482421875}], "temperature": 1.0}, {"id": 37, "seek": 96433, "start": 935.77, "end": 964.33, "text": " 1.15, 115. That means there is an error. Or for example, if R is negative 1.5, that means there is a mistake. So you have to find or figure out what is that mistake. So that's simple calculations. Usually in the exam, we will give the formula for the correlation coefficient, as we mentioned before. 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994.84, "text": " The sum of xy is given, sum x squared and sum y squared. Also sum of x and sum of y, in order to determine the means of x and y. For example, suppose I give sum of xi and i goes from 1 to 10 is 700, for example. You have to know that the sample size is 10, so x bar.", "tokens": [440, 2408, 295, 2031, 88, 307, 2212, 11, 2408, 2031, 8889, 293, 2408, 288, 8889, 13, 2743, 2408, 295, 2031, 293, 2408, 295, 288, 11, 294, 1668, 281, 6997, 264, 1355, 295, 2031, 293, 288, 13, 1171, 1365, 11, 7297, 286, 976, 2408, 295, 36800, 293, 741, 1709, 490, 502, 281, 1266, 307, 15204, 11, 337, 1365, 13, 509, 362, 281, 458, 300, 264, 6889, 2744, 307, 1266, 11, 370, 2031, 2159, 13], "avg_logprob": -0.25168919925754135, "compression_ratio": 1.5798816568047338, "no_speech_prob": 0.0, "words": [{"start": 967.7800000000001, "end": 968.34, "word": " The", "probability": 0.075439453125}, {"start": 968.34, "end": 968.56, "word": " sum", "probability": 0.904296875}, {"start": 968.56, "end": 968.7, "word": " of", "probability": 0.94384765625}, {"start": 968.7, "end": 968.98, "word": " xy", "probability": 0.615478515625}, {"start": 968.98, "end": 969.1, "word": " is", "probability": 0.86962890625}, {"start": 969.1, "end": 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Then use the curve to compute the coefficient of correlation. Questions? I think straightforward, maybe the easiest topic in this book is to compute the coefficient of correlation or correlation coefficient.", "tokens": [307, 15204, 6666, 538, 1266, 11, 370, 309, 311, 1614, 13, 1396, 764, 264, 7605, 281, 14722, 264, 17619, 295, 20009, 13, 27738, 30, 286, 519, 15325, 11, 1310, 264, 12889, 4829, 294, 341, 1446, 307, 281, 14722, 264, 17619, 295, 20009, 420, 20009, 17619, 13], "avg_logprob": -0.275764617514103, "compression_ratio": 1.6394557823129252, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 997.02, "end": 997.38, "word": " is", "probability": 0.42626953125}, {"start": 997.38, "end": 997.88, "word": " 700", "probability": 0.79931640625}, {"start": 997.88, "end": 998.24, "word": " divided", "probability": 0.52587890625}, {"start": 998.24, "end": 998.46, "word": " by", "probability": 0.96484375}, {"start": 998.46, "end": 998.72, "word": " 10,", "probability": 0.888671875}, {"start": 999.32, "end": 999.68, "word": " so", "probability": 0.496337890625}, {"start": 999.68, "end": 999.9, "word": " it's", "probability": 0.84326171875}, {"start": 999.9, "end": 1000.16, "word": " 7.", "probability": 0.59423828125}, {"start": 1002.4, "end": 1002.72, "word": " Then", "probability": 0.57275390625}, {"start": 1002.72, "end": 1003.06, "word": " use", "probability": 0.74365234375}, {"start": 1003.06, "end": 1003.46, "word": " the", "probability": 0.83544921875}, {"start": 1003.46, "end": 1003.86, "word": " curve", "probability": 0.39501953125}, {"start": 1003.86, "end": 1004.76, "word": " to", "probability": 0.87646484375}, {"start": 1004.76, "end": 1005.24, "word": " compute", "probability": 0.91455078125}, {"start": 1005.24, "end": 1006.18, "word": " the", "probability": 0.8974609375}, {"start": 1006.18, "end": 1006.78, "word": " coefficient", "probability": 0.92529296875}, {"start": 1006.78, "end": 1007.36, "word": " of", "probability": 0.9755859375}, {"start": 1007.36, "end": 1007.9, "word": " correlation.", "probability": 0.9794921875}, {"start": 1008.98, "end": 1009.9, "word": " Questions?", "probability": 0.576171875}, {"start": 1011.4, "end": 1011.86, "word": " I", "probability": 0.9853515625}, {"start": 1011.86, "end": 1012.0, "word": " think", "probability": 0.9228515625}, {"start": 1012.0, "end": 1012.56, "word": " straightforward,", "probability": 0.5234375}, {"start": 1012.92, "end": 1013.1, "word": " maybe", "probability": 0.90576171875}, {"start": 1013.1, "end": 1013.32, "word": " the", "probability": 0.91015625}, {"start": 1013.32, "end": 1013.7, "word": " easiest", "probability": 0.88427734375}, {"start": 1013.7, "end": 1015.54, "word": " topic", "probability": 0.94482421875}, {"start": 1015.54, "end": 1015.74, "word": " in", "probability": 0.92041015625}, {"start": 1015.74, "end": 1015.9, "word": " this", "probability": 0.87255859375}, {"start": 1015.9, "end": 1016.16, "word": " book", "probability": 0.50341796875}, {"start": 1016.16, "end": 1017.58, "word": " is", "probability": 0.72607421875}, {"start": 1017.58, "end": 1017.76, "word": " to", "probability": 0.9619140625}, {"start": 1017.76, "end": 1018.1, "word": " compute", "probability": 0.916015625}, {"start": 1018.1, "end": 1019.6, "word": " the", "probability": 0.86474609375}, {"start": 1019.6, "end": 1020.58, "word": " coefficient", "probability": 0.89599609375}, {"start": 1020.58, "end": 1021.9, "word": " of", "probability": 0.92724609375}, {"start": 1021.9, "end": 1022.98, "word": " correlation", "probability": 0.951171875}, {"start": 1022.98, "end": 1023.44, "word": " or", "probability": 0.72998046875}, {"start": 1023.44, "end": 1024.16, "word": " correlation", "probability": 0.96533203125}, {"start": 1024.16, "end": 1025.62, "word": " coefficient.", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 40, "seek": 105351, "start": 1027.01, "end": 1053.51, "text": " Now my question is, do you think outliers affect the correlation coefficient? We said last time outliers affect the mean, the range, the variance. Now the question is, do outliers affect the correlation?", "tokens": [823, 452, 1168, 307, 11, 360, 291, 519, 484, 23646, 3345, 264, 20009, 17619, 30, 492, 848, 1036, 565, 484, 23646, 3345, 264, 914, 11, 264, 3613, 11, 264, 21977, 13, 823, 264, 1168, 307, 11, 360, 484, 23646, 3345, 264, 20009, 30], "avg_logprob": -0.1691228716888211, "compression_ratio": 1.7, "no_speech_prob": 0.0, "words": [{"start": 1027.01, "end": 1027.29, "word": " Now", "probability": 0.6884765625}, {"start": 1027.29, "end": 1027.53, "word": " my", "probability": 0.7509765625}, {"start": 1027.53, "end": 1027.89, "word": " question", "probability": 0.91748046875}, {"start": 1027.89, "end": 1028.29, "word": " is,", "probability": 0.94970703125}, {"start": 1028.83, "end": 1029.07, "word": " do", "probability": 0.794921875}, {"start": 1029.07, "end": 1029.27, "word": " you", "probability": 0.9443359375}, {"start": 1029.27, "end": 1029.71, "word": " think", "probability": 0.91259765625}, {"start": 1029.71, "end": 1030.91, "word": " outliers", "probability": 0.88818359375}, {"start": 1030.91, "end": 1032.17, "word": " affect", "probability": 0.81787109375}, {"start": 1032.17, "end": 1032.65, "word": " the", "probability": 0.88623046875}, {"start": 1032.65, "end": 1033.09, "word": " correlation", "probability": 0.927734375}, {"start": 1033.09, "end": 1033.69, "word": " coefficient?", "probability": 0.92333984375}, {"start": 1037.01, "end": 1037.79, "word": " We", "probability": 0.68017578125}, {"start": 1037.79, "end": 1038.15, "word": " said", "probability": 0.94287109375}, {"start": 1038.15, "end": 1038.45, "word": " last", "probability": 0.8388671875}, {"start": 1038.45, "end": 1038.81, "word": " time", "probability": 0.890625}, {"start": 1038.81, "end": 1039.35, "word": " outliers", "probability": 0.822509765625}, {"start": 1039.35, "end": 1039.93, "word": " affect", "probability": 0.875}, {"start": 1039.93, "end": 1040.77, "word": " the", "probability": 0.89453125}, {"start": 1040.77, "end": 1041.11, "word": " mean,", "probability": 0.96240234375}, {"start": 1042.41, "end": 1043.21, "word": " the", "probability": 0.89111328125}, {"start": 1043.21, "end": 1043.63, "word": " range,", "probability": 0.88427734375}, {"start": 1044.75, "end": 1045.45, "word": " the", "probability": 0.86181640625}, {"start": 1045.45, "end": 1046.01, "word": " variance.", "probability": 0.92626953125}, {"start": 1046.71, "end": 1046.93, "word": " Now", "probability": 0.9306640625}, {"start": 1046.93, "end": 1047.13, "word": " the", "probability": 0.72119140625}, {"start": 1047.13, "end": 1047.45, "word": " question", "probability": 0.92236328125}, {"start": 1047.45, "end": 1048.03, "word": " is,", "probability": 0.95068359375}, {"start": 1048.17, "end": 1048.31, "word": " do", "probability": 0.939453125}, {"start": 1048.31, "end": 1048.99, "word": " outliers", "probability": 0.9541015625}, {"start": 1048.99, "end": 1051.15, "word": " affect", "probability": 0.68310546875}, {"start": 1051.15, "end": 1053.07, "word": " the", "probability": 0.908203125}, {"start": 1053.07, "end": 1053.51, "word": " correlation?", "probability": 0.90673828125}], "temperature": 1.0}, {"id": 41, "seek": 108121, "start": 1057.41, "end": 1081.21, "text": " Y. Exactly. The formula for R has X bar in it or Y bar. So it means outliers affect the correlation coefficient. So the answer is yes.", "tokens": [398, 13, 7587, 13, 440, 8513, 337, 497, 575, 1783, 2159, 294, 309, 420, 398, 2159, 13, 407, 309, 1355, 484, 23646, 3345, 264, 20009, 17619, 13, 407, 264, 1867, 307, 2086, 13], "avg_logprob": -0.2821691088816699, "compression_ratio": 1.238532110091743, "no_speech_prob": 0.0, "words": [{"start": 1057.41, "end": 1058.17, "word": " Y.", "probability": 0.1243896484375}, {"start": 1063.83, "end": 1064.59, "word": " Exactly.", "probability": 0.38525390625}, {"start": 1064.95, "end": 1065.69, "word": " The", "probability": 0.73486328125}, {"start": 1065.69, "end": 1066.25, "word": " formula", "probability": 0.9267578125}, {"start": 1066.25, "end": 1067.05, "word": " for", "probability": 0.91943359375}, {"start": 1067.05, "end": 1068.43, "word": " R", "probability": 0.873046875}, {"start": 1068.43, "end": 1069.91, "word": " has", "probability": 0.87060546875}, {"start": 1069.91, "end": 1070.15, "word": " X", "probability": 0.67431640625}, {"start": 1070.15, "end": 1070.41, "word": " bar", "probability": 0.8740234375}, {"start": 1070.41, "end": 1070.71, "word": " in", "probability": 0.91748046875}, {"start": 1070.71, "end": 1070.93, "word": " it", "probability": 0.95556640625}, {"start": 1070.93, "end": 1071.13, "word": " or", "probability": 0.68505859375}, {"start": 1071.13, "end": 1071.33, "word": " Y", "probability": 0.97802734375}, {"start": 1071.33, "end": 1071.57, "word": " bar.", "probability": 0.96044921875}, {"start": 1071.65, "end": 1071.77, "word": " So", "probability": 0.93017578125}, {"start": 1071.77, "end": 1071.91, "word": " it", "probability": 0.77783203125}, {"start": 1071.91, "end": 1072.65, "word": " means", "probability": 0.92626953125}, {"start": 1072.65, "end": 1073.63, "word": " outliers", "probability": 0.6708984375}, {"start": 1073.63, "end": 1076.67, "word": " affect", "probability": 0.72705078125}, {"start": 1076.67, "end": 1078.19, "word": " the", "probability": 0.8701171875}, {"start": 1078.19, "end": 1078.63, "word": " correlation", "probability": 0.90283203125}, {"start": 1078.63, "end": 1079.17, "word": " coefficient.", "probability": 0.9384765625}, {"start": 1080.05, "end": 1080.55, "word": " So", "probability": 0.93701171875}, {"start": 1080.55, "end": 1080.69, "word": " the", "probability": 0.8701171875}, {"start": 1080.69, "end": 1080.85, "word": " answer", "probability": 0.9560546875}, {"start": 1080.85, "end": 1081.07, "word": " is", "probability": 0.943359375}, {"start": 1081.07, "end": 1081.21, "word": " yes.", "probability": 0.9287109375}], "temperature": 1.0}, {"id": 42, "seek": 111086, "start": 1083.47, "end": 1110.87, "text": " Here we have x bar and y bar. Also, there is another formula to compute R. That formula is given by covariance between x and y. These two formulas are quite similar. I mean, by using this one, we can end with this formula. So this formula depends on this x is y.", "tokens": [1692, 321, 362, 2031, 2159, 293, 288, 2159, 13, 2743, 11, 456, 307, 1071, 8513, 281, 14722, 497, 13, 663, 8513, 307, 2212, 538, 49851, 719, 1296, 2031, 293, 288, 13, 1981, 732, 30546, 366, 1596, 2531, 13, 286, 914, 11, 538, 1228, 341, 472, 11, 321, 393, 917, 365, 341, 8513, 13, 407, 341, 8513, 5946, 322, 341, 2031, 307, 288, 13], "avg_logprob": -0.15344238420948386, "compression_ratio": 1.593939393939394, "no_speech_prob": 0.0, "words": [{"start": 1083.47, "end": 1083.73, "word": " Here", "probability": 0.74560546875}, {"start": 1083.73, "end": 1083.85, "word": " we", "probability": 0.79736328125}, {"start": 1083.85, "end": 1084.01, "word": " have", "probability": 0.9462890625}, {"start": 1084.01, "end": 1084.19, "word": " x", "probability": 0.58056640625}, {"start": 1084.19, "end": 1084.35, "word": " bar", "probability": 0.81005859375}, {"start": 1084.35, "end": 1084.55, "word": " and", "probability": 0.94189453125}, {"start": 1084.55, "end": 1084.71, "word": " y", "probability": 0.99755859375}, {"start": 1084.71, "end": 1084.97, "word": " bar.", "probability": 0.95263671875}, {"start": 1085.69, "end": 1086.09, "word": " Also,", "probability": 0.94580078125}, {"start": 1086.23, "end": 1086.27, "word": " there", "probability": 0.91064453125}, {"start": 1086.27, "end": 1086.41, "word": " is", "probability": 0.92041015625}, {"start": 1086.41, "end": 1086.75, "word": " another", "probability": 0.92138671875}, {"start": 1086.75, "end": 1087.21, "word": " formula", "probability": 0.919921875}, {"start": 1087.21, "end": 1087.43, "word": " to", "probability": 0.9638671875}, {"start": 1087.43, "end": 1087.91, "word": " compute", "probability": 0.8974609375}, {"start": 1087.91, "end": 1089.35, "word": " R.", "probability": 0.697265625}, {"start": 1089.63, "end": 1089.89, "word": " That", "probability": 0.9130859375}, {"start": 1089.89, "end": 1090.29, "word": " formula", "probability": 0.9130859375}, {"start": 1090.29, "end": 1090.69, "word": " is", "probability": 0.94873046875}, {"start": 1090.69, "end": 1090.91, "word": " given", "probability": 0.89306640625}, {"start": 1090.91, "end": 1091.29, "word": " by", "probability": 0.9697265625}, {"start": 1091.29, "end": 1092.41, "word": " covariance", "probability": 0.766845703125}, {"start": 1092.41, "end": 1092.75, "word": " between", "probability": 0.89501953125}, {"start": 1092.75, "end": 1092.95, "word": " x", "probability": 0.91064453125}, {"start": 1092.95, "end": 1093.09, "word": " and", "probability": 0.94677734375}, {"start": 1093.09, "end": 1093.37, "word": " y.", "probability": 0.9765625}, {"start": 1097.51, "end": 1098.03, "word": " These", "probability": 0.87841796875}, {"start": 1098.03, "end": 1098.27, "word": " two", "probability": 0.91845703125}, {"start": 1098.27, "end": 1098.73, "word": " formulas", "probability": 0.97265625}, {"start": 1098.73, "end": 1099.21, "word": " are", "probability": 0.94384765625}, {"start": 1099.21, "end": 1099.59, "word": " quite", "probability": 0.91015625}, {"start": 1099.59, "end": 1100.01, "word": " similar.", "probability": 0.96337890625}, {"start": 1101.27, "end": 1101.51, "word": " I", "probability": 0.79052734375}, {"start": 1101.51, "end": 1101.67, "word": " mean,", "probability": 0.96826171875}, {"start": 1101.75, "end": 1101.93, "word": " by", "probability": 0.96435546875}, {"start": 1101.93, "end": 1102.13, "word": " using", "probability": 0.9345703125}, {"start": 1102.13, "end": 1102.37, "word": " this", "probability": 0.9453125}, {"start": 1102.37, "end": 1102.57, "word": " one,", "probability": 0.93017578125}, {"start": 1102.63, "end": 1102.71, "word": " we", "probability": 0.94873046875}, {"start": 1102.71, "end": 1103.05, "word": " can", "probability": 0.94921875}, {"start": 1103.05, "end": 1104.79, "word": " end", "probability": 0.90869140625}, {"start": 1104.79, "end": 1104.97, "word": " with", "probability": 0.89404296875}, {"start": 1104.97, "end": 1105.23, "word": " this", "probability": 0.943359375}, {"start": 1105.23, "end": 1105.63, "word": " formula.", "probability": 0.90869140625}, {"start": 1105.81, "end": 1106.07, "word": " So", "probability": 0.90478515625}, {"start": 1106.07, "end": 1107.61, "word": " this", "probability": 0.78759765625}, {"start": 1107.61, "end": 1108.07, "word": " formula", "probability": 0.90966796875}, {"start": 1108.07, "end": 1108.71, "word": " depends", "probability": 0.90966796875}, {"start": 1108.71, "end": 1109.69, "word": " on", "probability": 0.9482421875}, {"start": 1109.69, "end": 1110.13, "word": " this", "probability": 0.65966796875}, {"start": 1110.13, "end": 1110.35, "word": " x", "probability": 0.908203125}, {"start": 1110.35, "end": 1110.51, "word": " is", "probability": 0.2369384765625}, {"start": 1110.51, "end": 1110.87, "word": " y.", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 43, "seek": 113979, "start": 1112.67, "end": 1139.79, "text": " standard deviations of X and Y. That means outlier will affect the correlation coefficient. So in case of outliers, R could be changed. That formula is called simple correlation coefficient. On the other hand, we have population correlation coefficient.", "tokens": [3832, 31219, 763, 295, 1783, 293, 398, 13, 663, 1355, 484, 2753, 486, 3345, 264, 20009, 17619, 13, 407, 294, 1389, 295, 484, 23646, 11, 497, 727, 312, 3105, 13, 663, 8513, 307, 1219, 2199, 20009, 17619, 13, 1282, 264, 661, 1011, 11, 321, 362, 4415, 20009, 17619, 13], "avg_logprob": -0.17890625596046447, "compression_ratio": 1.6933333333333334, "no_speech_prob": 0.0, "words": [{"start": 1112.67, "end": 1113.09, "word": " standard", "probability": 0.5546875}, {"start": 1113.09, "end": 1113.47, "word": " deviations", "probability": 0.6845703125}, {"start": 1113.47, "end": 1113.63, "word": " of", "probability": 0.90234375}, {"start": 1113.63, "end": 1113.79, "word": " X", "probability": 0.462158203125}, {"start": 1113.79, "end": 1113.95, "word": " and", "probability": 0.93212890625}, {"start": 1113.95, "end": 1114.21, "word": " Y.", "probability": 0.9931640625}, {"start": 1114.33, "end": 1114.59, "word": " That", "probability": 0.904296875}, {"start": 1114.59, "end": 1114.85, "word": " means", "probability": 0.92138671875}, {"start": 1114.85, "end": 1115.45, "word": " outlier", "probability": 0.71875}, {"start": 1115.45, "end": 1116.17, "word": " will", "probability": 0.8662109375}, {"start": 1116.17, "end": 1116.75, "word": " affect", "probability": 0.83203125}, {"start": 1116.75, "end": 1119.67, "word": " the", "probability": 0.70263671875}, {"start": 1119.67, "end": 1120.17, "word": " correlation", "probability": 0.92822265625}, {"start": 1120.17, "end": 1120.67, "word": " coefficient.", "probability": 0.59619140625}, {"start": 1120.93, "end": 1121.07, "word": " So", "probability": 0.908203125}, {"start": 1121.07, "end": 1121.37, "word": " in", "probability": 0.76708984375}, {"start": 1121.37, "end": 1122.35, "word": " case", "probability": 0.7041015625}, {"start": 1122.35, "end": 1122.53, "word": " of", "probability": 0.96728515625}, {"start": 1122.53, "end": 1123.13, "word": " outliers,", "probability": 0.94580078125}, {"start": 1124.29, "end": 1124.53, "word": " R", "probability": 0.923828125}, {"start": 1124.53, "end": 1124.99, "word": " could", "probability": 0.87060546875}, {"start": 1124.99, "end": 1125.19, "word": " be", "probability": 0.95166015625}, {"start": 1125.19, "end": 1125.67, "word": " changed.", "probability": 0.91552734375}, {"start": 1131.17, "end": 1131.87, "word": " That", "probability": 0.8818359375}, {"start": 1131.87, "end": 1132.23, "word": " formula", "probability": 0.90380859375}, {"start": 1132.23, "end": 1132.49, "word": " is", "probability": 0.8544921875}, {"start": 1132.49, "end": 1132.79, "word": " called", "probability": 0.8984375}, {"start": 1132.79, "end": 1133.39, "word": " simple", "probability": 0.8203125}, {"start": 1133.39, "end": 1135.53, "word": " correlation", "probability": 0.72998046875}, {"start": 1135.53, "end": 1136.13, "word": " coefficient.", "probability": 0.94580078125}, {"start": 1137.27, "end": 1137.61, "word": " On", "probability": 0.9482421875}, {"start": 1137.61, "end": 1137.71, "word": " the", "probability": 0.92626953125}, {"start": 1137.71, "end": 1137.87, "word": " other", "probability": 0.88623046875}, {"start": 1137.87, "end": 1138.11, "word": " hand,", "probability": 0.90869140625}, {"start": 1138.15, "end": 1138.25, "word": " we", "probability": 0.9541015625}, {"start": 1138.25, "end": 1138.39, "word": " have", "probability": 0.94384765625}, {"start": 1138.39, "end": 1138.79, "word": " population", "probability": 0.9365234375}, {"start": 1138.79, "end": 1139.29, "word": " correlation", "probability": 0.92333984375}, {"start": 1139.29, "end": 1139.79, "word": " coefficient.", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 44, "seek": 116976, "start": 1141.14, "end": 1169.76, "text": " If you remember last time, we used X bar as the sample mean and mu as population mean. Also, S square as sample variance and sigma square as population variance. Here, R is used as sample coefficient of correlation and rho, this Greek letter pronounced as rho. 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There are some features of R or Rho. The first one is unity-free. R or Rho is unity-free. That means if X represents... 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Now, in this case, there is no unity. You cannot say 0.75 years or 0.75 kilograms. It's unity-free. There is no unit for the correlation coefficient, the same as Cv. 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As I mentioned, R lies between minus one and plus one. Now, by using the value of R, you can determine two things. Number one, we can determine the direction.", "tokens": [440, 1150, 4111, 295, 497, 22526, 1296, 3175, 472, 293, 1804, 472, 13, 1018, 286, 2835, 11, 497, 9134, 1296, 3175, 472, 293, 1804, 472, 13, 823, 11, 538, 1228, 264, 2158, 295, 497, 11, 291, 393, 6997, 732, 721, 13, 5118, 472, 11, 321, 393, 6997, 264, 3513, 13], "avg_logprob": -0.1495864023180569, "compression_ratio": 1.608695652173913, "no_speech_prob": 0.0, "words": [{"start": 1226.2, "end": 1226.42, "word": " The", "probability": 0.75830078125}, {"start": 1226.42, "end": 1226.76, "word": " second", "probability": 0.89453125}, {"start": 1226.76, "end": 1227.2, "word": " feature", "probability": 0.953125}, {"start": 1227.2, "end": 1228.28, "word": " of", "probability": 0.9501953125}, {"start": 1228.28, "end": 1228.6, "word": " R", "probability": 0.77978515625}, {"start": 1228.6, "end": 1230.12, "word": " ranges", "probability": 0.77587890625}, {"start": 1230.12, "end": 1230.5, "word": " between", "probability": 0.85546875}, 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"end": 1238.08, "word": " one", "probability": 0.9169921875}, {"start": 1238.08, "end": 1238.36, "word": " and", "probability": 0.9404296875}, {"start": 1238.36, "end": 1238.9, "word": " plus", "probability": 0.96337890625}, {"start": 1238.9, "end": 1239.2, "word": " one.", "probability": 0.9267578125}, {"start": 1240.76, "end": 1241.22, "word": " Now,", "probability": 0.94189453125}, {"start": 1241.3, "end": 1241.44, "word": " by", "probability": 0.9697265625}, {"start": 1241.44, "end": 1241.8, "word": " using", "probability": 0.935546875}, {"start": 1241.8, "end": 1242.34, "word": " the", "probability": 0.90771484375}, {"start": 1242.34, "end": 1242.64, "word": " value", "probability": 0.97607421875}, {"start": 1242.64, "end": 1242.82, "word": " of", "probability": 0.94189453125}, {"start": 1242.82, "end": 1243.1, "word": " R,", "probability": 0.9931640625}, {"start": 1243.96, "end": 1244.26, "word": " you", "probability": 0.95654296875}, {"start": 1244.26, "end": 1244.5, "word": " 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there exists positive or negative so sign of R determine negative or positive relationship the direction the absolute value of R I mean absolute of R I mean ignore the sign", "tokens": [293, 3800, 538, 1228, 264, 1465, 291, 393, 6997, 498, 456, 8198, 3353, 420, 3671, 370, 1465, 295, 497, 6997, 3671, 420, 3353, 2480, 264, 3513, 264, 8236, 2158, 295, 497, 286, 914, 8236, 295, 497, 286, 914, 11200, 264, 1465], "avg_logprob": -0.24069940795501074, "compression_ratio": 1.717557251908397, "no_speech_prob": 0.0, "words": [{"start": 1252.58, "end": 1252.88, "word": " and", "probability": 0.411376953125}, {"start": 1252.88, "end": 1253.36, "word": " strength", "probability": 0.58642578125}, {"start": 1253.36, "end": 1254.18, "word": " by", "probability": 0.450439453125}, {"start": 1254.18, "end": 1254.52, "word": " using", "probability": 0.9296875}, {"start": 1254.52, "end": 1254.72, "word": " the", "probability": 0.859375}, {"start": 1254.72, "end": 1255.04, "word": " sign", "probability": 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So the absolute value of R determines the strength. So by using the sine of R, you can determine the direction, either positive or negative. By using the absolute value, you can determine the strength. We can split the strength into two parts, either strong, moderate, or weak.", "tokens": [407, 264, 8236, 2158, 295, 497, 24799, 264, 3800, 13, 407, 538, 1228, 264, 18609, 295, 497, 11, 291, 393, 6997, 264, 3513, 11, 2139, 3353, 420, 3671, 13, 3146, 1228, 264, 8236, 2158, 11, 291, 393, 6997, 264, 3800, 13, 492, 393, 7472, 264, 3800, 666, 732, 3166, 11, 2139, 2068, 11, 18174, 11, 420, 5336, 13], "avg_logprob": -0.16843220035908585, "compression_ratio": 1.793548387096774, "no_speech_prob": 0.0, "words": [{"start": 1280.66, "end": 1280.94, "word": " So", "probability": 0.5810546875}, {"start": 1280.94, "end": 1281.08, "word": " the", "probability": 0.65380859375}, {"start": 1281.08, "end": 1281.38, "word": " absolute", "probability": 0.8818359375}, {"start": 1281.38, "end": 1281.64, "word": " value", "probability": 0.98046875}, {"start": 1281.64, "end": 1281.78, "word": " of", "probability": 0.94580078125}, {"start": 1281.78, "end": 1281.98, "word": " R", "probability": 0.76416015625}, {"start": 1281.98, "end": 1282.66, "word": " determines", "probability": 0.8955078125}, {"start": 1282.66, "end": 1283.7, "word": " the", "probability": 0.83251953125}, {"start": 1283.7, "end": 1284.1, "word": " strength.", "probability": 0.85205078125}, {"start": 1287.7, "end": 1288.38, "word": " So", "probability": 0.751953125}, {"start": 1288.38, "end": 1288.54, "word": " by", "probability": 0.8447265625}, {"start": 1288.54, "end": 1288.9, "word": " using", "probability": 0.93212890625}, {"start": 1288.9, "end": 1289.5, "word": " the", "probability": 0.8583984375}, {"start": 1289.5, "end": 1289.7, "word": " sine", "probability": 0.490234375}, {"start": 1289.7, "end": 1289.84, "word": " of", "probability": 0.96826171875}, {"start": 1289.84, "end": 1289.98, "word": " R,", "probability": 0.9833984375}, {"start": 1290.02, "end": 1290.1, "word": " you", "probability": 0.84716796875}, {"start": 1290.1, "end": 1290.26, "word": " can", "probability": 0.927734375}, {"start": 1290.26, "end": 1290.56, "word": " determine", "probability": 0.92724609375}, {"start": 1290.56, "end": 1290.76, "word": " the", "probability": 0.83203125}, {"start": 1290.76, "end": 1291.24, "word": " direction,", "probability": 0.97705078125}, {"start": 1292.46, "end": 1292.7, "word": " either", "probability": 0.82763671875}, {"start": 1292.7, "end": 1293.06, "word": " positive", "probability": 0.9345703125}, {"start": 1293.06, "end": 1293.3, "word": " or", "probability": 0.9658203125}, {"start": 1293.3, "end": 1293.6, "word": " negative.", "probability": 0.94580078125}, {"start": 1295.06, "end": 1295.42, "word": " By", "probability": 0.90087890625}, {"start": 1295.42, "end": 1295.68, "word": " using", "probability": 0.9296875}, {"start": 1295.68, "end": 1295.86, "word": " the", "probability": 0.8935546875}, {"start": 1295.86, "end": 1296.14, "word": " absolute", "probability": 0.89111328125}, {"start": 1296.14, "end": 1296.56, "word": " value,", "probability": 0.9794921875}, {"start": 1296.56, "end": 1296.7, "word": " you", "probability": 0.8505859375}, {"start": 1296.7, "end": 1296.84, "word": " can", "probability": 0.93505859375}, {"start": 1296.84, "end": 1297.26, "word": " determine", "probability": 0.94140625}, {"start": 1297.26, "end": 1297.74, "word": " the", "probability": 0.90625}, {"start": 1297.74, "end": 1298.4, "word": " strength.", "probability": 0.87939453125}, {"start": 1299.74, "end": 1300.02, "word": " We", "probability": 0.92626953125}, {"start": 1300.02, "end": 1300.42, "word": " can", "probability": 0.947265625}, {"start": 1300.42, "end": 1302.04, "word": " split", "probability": 0.931640625}, {"start": 1302.04, "end": 1302.38, "word": " the", "probability": 0.892578125}, {"start": 1302.38, "end": 1302.86, "word": " strength", "probability": 0.8935546875}, {"start": 1302.86, "end": 1303.28, "word": " into", "probability": 0.8525390625}, {"start": 1303.28, "end": 1303.5, "word": " two", "probability": 0.8994140625}, {"start": 1303.5, "end": 1303.98, "word": " parts,", "probability": 0.8505859375}, {"start": 1304.56, "end": 1304.9, "word": " either", "probability": 0.94189453125}, {"start": 1304.9, "end": 1305.64, "word": " strong,", "probability": 0.88916015625}, {"start": 1307.4, "end": 1307.82, "word": " moderate,", "probability": 0.935546875}, {"start": 1308.5, "end": 1309.24, "word": " or", "probability": 0.9677734375}, {"start": 1309.24, "end": 1309.44, "word": " weak.", "probability": 0.970703125}], "temperature": 1.0}, {"id": 50, "seek": 132943, "start": 1311.77, "end": 1329.43, "text": " So weak, moderate, and strong by using the absolute value of R. The closer to minus one, if R is close to minus one, the stronger the negative relationship between X and Y. For example, imagine", "tokens": [407, 5336, 11, 18174, 11, 293, 2068, 538, 1228, 264, 8236, 2158, 295, 497, 13, 440, 4966, 281, 3175, 472, 11, 498, 497, 307, 1998, 281, 3175, 472, 11, 264, 7249, 264, 3671, 2480, 1296, 1783, 293, 398, 13, 1171, 1365, 11, 3811], "avg_logprob": -0.19389205053448677, "compression_ratio": 1.4057971014492754, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1311.77, "end": 1312.45, "word": " So", "probability": 0.342041015625}, {"start": 1312.45, "end": 1312.81, "word": " weak,", "probability": 0.794921875}, {"start": 1313.77, "end": 1314.03, "word": " moderate,", "probability": 0.90966796875}, {"start": 1314.79, "end": 1315.65, "word": " and", "probability": 0.93310546875}, {"start": 1315.65, "end": 1316.13, "word": " strong", "probability": 0.896484375}, {"start": 1316.13, "end": 1317.29, "word": " by", "probability": 0.501953125}, {"start": 1317.29, "end": 1317.65, "word": " using", "probability": 0.9267578125}, {"start": 1317.65, "end": 1318.17, "word": " the", "probability": 0.89453125}, {"start": 1318.17, "end": 1318.89, "word": " absolute", "probability": 0.90283203125}, {"start": 1318.89, "end": 1319.13, "word": " value", "probability": 0.98291015625}, {"start": 1319.13, "end": 1319.31, "word": " of", "probability": 0.77978515625}, {"start": 1319.31, "end": 1319.51, "word": " R.", "probability": 0.7587890625}, {"start": 1320.11, "end": 1320.57, "word": " The", "probability": 0.8603515625}, {"start": 1320.57, "end": 1320.91, "word": " closer", "probability": 0.91796875}, {"start": 1320.91, "end": 1321.15, "word": " to", "probability": 0.96484375}, {"start": 1321.15, "end": 1321.41, "word": " minus", "probability": 0.7548828125}, {"start": 1321.41, "end": 1321.75, "word": " one,", "probability": 0.6064453125}, {"start": 1322.85, "end": 1323.03, "word": " if", "probability": 0.86962890625}, {"start": 1323.03, "end": 1323.23, "word": " R", "probability": 0.98193359375}, {"start": 1323.23, "end": 1323.37, "word": " is", "probability": 0.93115234375}, {"start": 1323.37, "end": 1323.69, "word": " close", "probability": 0.865234375}, {"start": 1323.69, "end": 1323.87, "word": " to", "probability": 0.96435546875}, {"start": 1323.87, "end": 1324.07, "word": " minus", "probability": 0.97607421875}, {"start": 1324.07, "end": 1324.37, "word": " one,", "probability": 0.91845703125}, {"start": 1324.95, "end": 1325.09, "word": " the", "probability": 0.900390625}, {"start": 1325.09, "end": 1325.53, "word": " stronger", "probability": 0.7685546875}, {"start": 1325.53, "end": 1325.93, "word": " the", "probability": 0.8251953125}, {"start": 1325.93, "end": 1326.33, "word": " negative", "probability": 0.94580078125}, {"start": 1326.33, "end": 1327.01, "word": " relationship", "probability": 0.92041015625}, {"start": 1327.01, "end": 1327.35, "word": " between", "probability": 0.81640625}, {"start": 1327.35, "end": 1327.55, "word": " X", "probability": 0.69482421875}, {"start": 1327.55, "end": 1327.73, "word": " and", "probability": 0.9482421875}, {"start": 1327.73, "end": 1327.91, "word": " Y.", "probability": 0.99072265625}, {"start": 1327.97, "end": 1328.13, "word": " For", "probability": 0.93798828125}, {"start": 1328.13, "end": 1328.51, "word": " example,", "probability": 0.97607421875}, {"start": 1329.01, "end": 1329.43, "word": " imagine", "probability": 0.89794921875}], "temperature": 1.0}, {"id": 51, "seek": 137043, "start": 1342.67, "end": 1370.43, "text": " And as we mentioned, R ranges between minus 1 and plus 1. So if R is close to minus 1, it's a strong relationship. Strong linked relationship. The closer to 1, the stronger the positive relationship. I mean, if R is close. Strong positive.", "tokens": [400, 382, 321, 2835, 11, 497, 22526, 1296, 3175, 502, 293, 1804, 502, 13, 407, 498, 497, 307, 1998, 281, 3175, 502, 11, 309, 311, 257, 2068, 2480, 13, 22792, 9408, 2480, 13, 440, 4966, 281, 502, 11, 264, 7249, 264, 3353, 2480, 13, 286, 914, 11, 498, 497, 307, 1998, 13, 22792, 3353, 13], "avg_logprob": -0.25139509833284784, "compression_ratio": 1.6783216783216783, "no_speech_prob": 0.0, "words": [{"start": 1342.67, "end": 1342.97, "word": " And", "probability": 0.5986328125}, {"start": 1342.97, "end": 1343.17, "word": " as", "probability": 0.6259765625}, {"start": 1343.17, "end": 1343.77, "word": " we", "probability": 0.57421875}, {"start": 1343.77, "end": 1344.11, "word": " mentioned,", "probability": 0.79638671875}, {"start": 1344.25, "end": 1344.51, "word": " R", "probability": 0.70703125}, {"start": 1344.51, "end": 1345.25, "word": " ranges", "probability": 0.7275390625}, {"start": 1345.25, "end": 1345.57, "word": " between", "probability": 0.75390625}, {"start": 1345.57, "end": 1345.83, "word": " minus", "probability": 0.433837890625}, {"start": 1345.83, "end": 1346.03, "word": " 1", "probability": 0.3779296875}, {"start": 1346.03, "end": 1346.13, "word": " and", "probability": 0.8486328125}, {"start": 1346.13, "end": 1346.39, "word": " plus", "probability": 0.95947265625}, {"start": 1346.39, "end": 1346.63, "word": " 1.", "probability": 0.97998046875}, {"start": 1350.07, "end": 1350.69, "word": " So", "probability": 0.912109375}, {"start": 1350.69, "end": 1350.99, "word": " if", "probability": 0.75732421875}, {"start": 1350.99, "end": 1351.19, "word": " R", "probability": 0.9921875}, {"start": 1351.19, "end": 1351.33, "word": " is", "probability": 0.93896484375}, {"start": 1351.33, "end": 1351.67, "word": " close", "probability": 0.888671875}, {"start": 1351.67, "end": 1351.87, "word": " to", "probability": 0.96923828125}, {"start": 1351.87, "end": 1352.11, "word": " minus", "probability": 0.97314453125}, {"start": 1352.11, "end": 1352.47, "word": " 1,", "probability": 0.96142578125}, {"start": 1354.15, "end": 1355.25, "word": " it's", "probability": 0.74560546875}, {"start": 1355.25, "end": 1355.37, "word": " a", "probability": 0.982421875}, {"start": 1355.37, "end": 1355.71, "word": " strong", "probability": 0.89013671875}, {"start": 1355.71, "end": 1356.43, "word": " relationship.", "probability": 0.84912109375}, {"start": 1357.77, "end": 1358.37, "word": " Strong", "probability": 0.7412109375}, {"start": 1358.37, "end": 1358.59, "word": " linked", "probability": 0.1868896484375}, {"start": 1358.59, "end": 1359.19, "word": " relationship.", "probability": 0.89599609375}, {"start": 1360.63, "end": 1361.25, "word": " The", "probability": 0.86669921875}, {"start": 1361.25, "end": 1361.59, "word": " closer", "probability": 0.92138671875}, {"start": 1361.59, "end": 1361.87, "word": " to", "probability": 0.92822265625}, {"start": 1361.87, "end": 1362.59, "word": " 1,", "probability": 0.50537109375}, {"start": 1363.85, "end": 1364.29, "word": " the", "probability": 0.90283203125}, {"start": 1364.29, "end": 1364.69, "word": " stronger", "probability": 0.84375}, {"start": 1364.69, "end": 1364.91, "word": " the", "probability": 0.85791015625}, {"start": 1364.91, "end": 1365.19, "word": " positive", "probability": 0.9375}, {"start": 1365.19, "end": 1365.81, "word": " relationship.", "probability": 0.9111328125}, {"start": 1366.03, "end": 1366.17, "word": " I", "probability": 0.94384765625}, {"start": 1366.17, "end": 1366.35, "word": " mean,", "probability": 0.9638671875}, {"start": 1366.43, "end": 1366.59, "word": " if", "probability": 0.94970703125}, {"start": 1366.59, "end": 1366.75, "word": " R", "probability": 0.99169921875}, {"start": 1366.75, "end": 1366.89, "word": " is", "probability": 0.9326171875}, {"start": 1366.89, "end": 1367.35, "word": " close.", "probability": 0.6376953125}, {"start": 1368.61, "end": 1369.23, "word": " Strong", "probability": 0.74365234375}, {"start": 1369.23, "end": 1370.43, "word": " positive.", "probability": 0.93212890625}], "temperature": 1.0}, {"id": 52, "seek": 139594, "start": 1371.5, "end": 1395.94, "text": " So strong in either direction, either to the left side or to the right side. Strong negative. On the other hand, there exists strong negative relationship. Positive. Positive. If R is close to zero, weak. Here we can say there exists weak relationship between X and Y.", "tokens": [407, 2068, 294, 2139, 3513, 11, 2139, 281, 264, 1411, 1252, 420, 281, 264, 558, 1252, 13, 22792, 3671, 13, 1282, 264, 661, 1011, 11, 456, 8198, 2068, 3671, 2480, 13, 46326, 13, 46326, 13, 759, 497, 307, 1998, 281, 4018, 11, 5336, 13, 1692, 321, 393, 584, 456, 8198, 5336, 2480, 1296, 1783, 293, 398, 13], "avg_logprob": -0.24488146860024024, "compression_ratio": 1.6918238993710693, "no_speech_prob": 0.0, "words": [{"start": 1371.5, "end": 1371.8, "word": " So", "probability": 0.79150390625}, {"start": 1371.8, "end": 1372.22, "word": " strong", "probability": 0.6083984375}, {"start": 1372.22, "end": 1372.48, "word": " in", "probability": 0.884765625}, {"start": 1372.48, "end": 1372.78, "word": " either", "probability": 0.9541015625}, {"start": 1372.78, "end": 1373.34, "word": " direction,", "probability": 0.97265625}, {"start": 1373.72, "end": 1374.02, "word": " either", "probability": 0.919921875}, {"start": 1374.02, "end": 1374.48, "word": " to", "probability": 0.92041015625}, {"start": 1374.48, "end": 1374.74, "word": " the", "probability": 0.91845703125}, {"start": 1374.74, "end": 1375.12, "word": " left", "probability": 0.9423828125}, {"start": 1375.12, "end": 1375.48, "word": " side", "probability": 0.83935546875}, {"start": 1375.48, "end": 1375.72, "word": " or", "probability": 0.86865234375}, {"start": 1375.72, "end": 1375.84, "word": " to", "probability": 0.83203125}, {"start": 1375.84, "end": 1375.98, "word": " the", "probability": 0.912109375}, {"start": 1375.98, "end": 1376.2, "word": " right", "probability": 0.9169921875}, {"start": 1376.2, "end": 1376.56, "word": " side.", "probability": 0.8623046875}, {"start": 1377.04, "end": 1377.64, "word": " Strong", "probability": 0.60791015625}, {"start": 1377.64, "end": 1377.98, "word": " negative.", "probability": 0.7080078125}, {"start": 1378.7, "end": 1378.98, "word": " On", "probability": 0.92138671875}, {"start": 1378.98, "end": 1379.08, "word": " the", "probability": 0.89111328125}, {"start": 1379.08, "end": 1379.26, "word": " other", "probability": 0.88525390625}, {"start": 1379.26, "end": 1379.56, "word": " hand,", "probability": 0.91748046875}, {"start": 1379.64, "end": 1379.72, "word": " there", "probability": 0.91015625}, {"start": 1379.72, "end": 1379.98, "word": " exists", "probability": 0.77880859375}, {"start": 1379.98, "end": 1380.28, "word": " strong", "probability": 0.81396484375}, {"start": 1380.28, "end": 1380.64, "word": " negative", "probability": 0.90576171875}, {"start": 1380.64, "end": 1381.28, "word": " relationship.", "probability": 0.83984375}, {"start": 1382.64, "end": 1382.8, "word": " Positive.", "probability": 0.6796875}, {"start": 1382.88, "end": 1382.88, "word": " Positive.", "probability": 0.6640625}, {"start": 1384.9, "end": 1385.5, "word": " If", "probability": 0.24951171875}, {"start": 1385.5, "end": 1385.82, "word": " R", "probability": 0.611328125}, {"start": 1385.82, "end": 1385.94, "word": " is", "probability": 0.498046875}, {"start": 1385.94, "end": 1386.18, "word": " close", "probability": 0.88720703125}, {"start": 1386.18, "end": 1386.38, "word": " to", "probability": 0.96923828125}, {"start": 1386.38, "end": 1386.68, "word": " zero,", "probability": 0.66650390625}, {"start": 1387.2, "end": 1388.0, "word": " weak.", "probability": 0.8662109375}, {"start": 1388.74, "end": 1389.18, "word": " Here", "probability": 0.51416015625}, {"start": 1389.18, "end": 1389.4, "word": " we", "probability": 0.6689453125}, {"start": 1389.4, "end": 1389.7, "word": " can", "probability": 0.94287109375}, {"start": 1389.7, "end": 1390.0, "word": " say", "probability": 0.8583984375}, {"start": 1390.0, "end": 1390.24, "word": " there", "probability": 0.78662109375}, {"start": 1390.24, "end": 1390.64, "word": " exists", "probability": 0.84619140625}, {"start": 1390.64, "end": 1391.1, "word": " weak", "probability": 0.86767578125}, {"start": 1391.1, "end": 1393.1, "word": " relationship", "probability": 0.9033203125}, {"start": 1393.1, "end": 1395.44, "word": " between", "probability": 0.87158203125}, {"start": 1395.44, "end": 1395.62, "word": " X", "probability": 0.6591796875}, {"start": 1395.62, "end": 1395.76, "word": " and", "probability": 0.947265625}, {"start": 1395.76, "end": 1395.94, "word": " Y.", "probability": 0.99755859375}], "temperature": 1.0}, {"id": 53, "seek": 142834, "start": 1399.26, "end": 1428.34, "text": " If R is close to 0.5 or minus 0.5, you can say there exists positive-moderate or negative-moderate relationship. So you can split or you can divide the strength of the relationship between X and Y into three parts. Strong, close to minus one of", "tokens": [759, 497, 307, 1998, 281, 1958, 13, 20, 420, 3175, 1958, 13, 20, 11, 291, 393, 584, 456, 8198, 3353, 12, 8014, 260, 473, 420, 3671, 12, 8014, 260, 473, 2480, 13, 407, 291, 393, 7472, 420, 291, 393, 9845, 264, 3800, 295, 264, 2480, 1296, 1783, 293, 398, 666, 1045, 3166, 13, 22792, 11, 1998, 281, 3175, 472, 295], "avg_logprob": -0.22886782396035116, "compression_ratio": 1.5705128205128205, "no_speech_prob": 0.0, "words": [{"start": 1399.26, "end": 1399.64, "word": " If", "probability": 0.56298828125}, {"start": 1399.64, "end": 1400.02, "word": " R", "probability": 0.67431640625}, {"start": 1400.02, "end": 1400.18, "word": " is", "probability": 0.888671875}, {"start": 1400.18, "end": 1400.76, "word": " close", "probability": 0.85009765625}, {"start": 1400.76, "end": 1401.12, "word": " to", "probability": 0.95263671875}, {"start": 1401.12, "end": 1401.4, "word": " 0", "probability": 0.26123046875}, {"start": 1401.4, "end": 1401.92, "word": ".5", "probability": 0.99267578125}, {"start": 1401.92, "end": 1405.48, "word": " or", "probability": 0.488037109375}, {"start": 1405.48, "end": 1405.86, "word": " minus", "probability": 0.49609375}, {"start": 1405.86, "end": 1406.08, "word": " 0", "probability": 0.96923828125}, {"start": 1406.08, "end": 1406.54, "word": ".5,", "probability": 0.998046875}, {"start": 1408.5, "end": 1408.9, "word": " you", "probability": 0.826171875}, {"start": 1408.9, "end": 1409.16, "word": " can", "probability": 0.9365234375}, {"start": 1409.16, "end": 1409.56, "word": " say", "probability": 0.7958984375}, {"start": 1409.56, "end": 1409.88, "word": " there", "probability": 0.6787109375}, {"start": 1409.88, "end": 1410.44, "word": " exists", "probability": 0.6162109375}, {"start": 1410.44, "end": 1412.32, "word": " positive", "probability": 0.70947265625}, {"start": 1412.32, "end": 1414.2, "word": "-moderate", "probability": 0.8070068359375}, {"start": 1414.2, "end": 1415.78, "word": " or", "probability": 0.81005859375}, {"start": 1415.78, "end": 1416.34, "word": " negative", "probability": 0.9453125}, {"start": 1416.34, "end": 1416.84, "word": "-moderate", "probability": 0.9771728515625}, {"start": 1416.84, "end": 1417.36, "word": " relationship.", "probability": 0.8779296875}, {"start": 1418.08, "end": 1418.84, "word": " So", "probability": 0.92626953125}, {"start": 1418.84, "end": 1419.02, "word": " you", "probability": 0.7373046875}, {"start": 1419.02, "end": 1419.24, "word": " can", "probability": 0.9384765625}, {"start": 1419.24, "end": 1419.64, "word": " split", "probability": 0.91748046875}, {"start": 1419.64, "end": 1420.12, "word": " or", "probability": 0.80419921875}, {"start": 1420.12, "end": 1420.28, "word": " you", "probability": 0.9111328125}, {"start": 1420.28, "end": 1420.48, "word": " can", "probability": 0.9384765625}, {"start": 1420.48, "end": 1420.86, "word": " divide", "probability": 0.9375}, {"start": 1420.86, "end": 1421.24, "word": " the", "probability": 0.9150390625}, {"start": 1421.24, "end": 1421.78, "word": " strength", "probability": 0.8046875}, {"start": 1421.78, "end": 1422.2, "word": " of", "probability": 0.96728515625}, {"start": 1422.2, "end": 1422.36, "word": " the", "probability": 0.91357421875}, {"start": 1422.36, "end": 1422.82, "word": " relationship", "probability": 0.9072265625}, {"start": 1422.82, "end": 1423.16, "word": " between", "probability": 0.90869140625}, {"start": 1423.16, "end": 1423.36, "word": " X", "probability": 0.609375}, {"start": 1423.36, "end": 1423.48, "word": " and", "probability": 0.93994140625}, {"start": 1423.48, "end": 1423.64, "word": " Y", "probability": 0.99560546875}, {"start": 1423.64, "end": 1423.86, "word": " into", "probability": 0.85400390625}, {"start": 1423.86, "end": 1424.1, "word": " three", "probability": 0.85791015625}, {"start": 1424.1, "end": 1424.54, "word": " parts.", "probability": 0.83642578125}, {"start": 1425.86, "end": 1426.62, "word": " Strong,", "probability": 0.88427734375}, {"start": 1427.1, "end": 1427.48, "word": " close", "probability": 0.85595703125}, {"start": 1427.48, "end": 1427.7, "word": " to", "probability": 0.96875}, {"start": 1427.7, "end": 1427.96, "word": " minus", "probability": 0.95654296875}, {"start": 1427.96, "end": 1428.18, "word": " one", "probability": 0.62890625}, {"start": 1428.18, "end": 1428.34, "word": " of", "probability": 0.307373046875}], "temperature": 1.0}, {"id": 54, "seek": 145650, "start": 1428.48, "end": 1456.5, "text": " Plus one, weak, close to zero, moderate, close to 0.5. 0.5 is halfway between 0 and 1, and minus 0.5 is also halfway between minus 1 and 0. Now for example, what's about if R equals minus 0.5? Suppose R1 is minus 0.5.", "tokens": [7721, 472, 11, 5336, 11, 1998, 281, 4018, 11, 18174, 11, 1998, 281, 1958, 13, 20, 13, 1958, 13, 20, 307, 15461, 1296, 1958, 293, 502, 11, 293, 3175, 1958, 13, 20, 307, 611, 15461, 1296, 3175, 502, 293, 1958, 13, 823, 337, 1365, 11, 437, 311, 466, 498, 497, 6915, 3175, 1958, 13, 20, 30, 21360, 497, 16, 307, 3175, 1958, 13, 20, 13], "avg_logprob": -0.2428977293047038, "compression_ratio": 1.4931506849315068, "no_speech_prob": 0.0, "words": [{"start": 1428.48, "end": 1428.8, "word": " Plus", "probability": 0.1549072265625}, {"start": 1428.8, "end": 1429.2, "word": " one,", "probability": 0.66552734375}, {"start": 1429.86, "end": 1430.7, "word": " weak,", "probability": 0.92431640625}, {"start": 1431.06, "end": 1431.64, "word": " close", "probability": 0.4580078125}, {"start": 1431.64, "end": 1431.8, "word": " to", "probability": 0.9658203125}, {"start": 1431.8, "end": 1432.06, "word": " zero,", "probability": 0.86181640625}, {"start": 1433.32, "end": 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"probability": 0.93994140625}, {"start": 1442.74, "end": 1443.06, "word": " and", "probability": 0.92822265625}, {"start": 1443.06, "end": 1443.44, "word": " minus", "probability": 0.73779296875}, {"start": 1443.44, "end": 1443.68, "word": " 0", "probability": 0.98193359375}, {"start": 1443.68, "end": 1444.06, "word": ".5", "probability": 0.998779296875}, {"start": 1444.06, "end": 1444.32, "word": " is", "probability": 0.9287109375}, {"start": 1444.32, "end": 1444.58, "word": " also", "probability": 0.85986328125}, {"start": 1444.58, "end": 1444.98, "word": " halfway", "probability": 0.58740234375}, {"start": 1444.98, "end": 1445.34, "word": " between", "probability": 0.86865234375}, {"start": 1445.34, "end": 1445.68, "word": " minus", "probability": 0.8818359375}, {"start": 1445.68, "end": 1445.88, "word": " 1", "probability": 0.77587890625}, {"start": 1445.88, "end": 1446.02, "word": " and", "probability": 0.93212890625}, {"start": 1446.02, "end": 1446.3, "word": " 0.", "probability": 0.91259765625}, {"start": 1447.82, "end": 1448.5, "word": " Now", "probability": 0.9052734375}, {"start": 1448.5, "end": 1448.7, "word": " for", "probability": 0.5263671875}, {"start": 1448.7, "end": 1449.04, "word": " example,", "probability": 0.978515625}, {"start": 1449.92, "end": 1450.86, "word": " what's", "probability": 0.854248046875}, {"start": 1450.86, "end": 1451.1, "word": " about", "probability": 0.89990234375}, {"start": 1451.1, "end": 1451.32, "word": " if", "probability": 0.923828125}, {"start": 1451.32, "end": 1451.7, "word": " R", "probability": 0.73095703125}, {"start": 1451.7, "end": 1453.74, "word": " equals", "probability": 0.4697265625}, {"start": 1453.74, "end": 1454.18, "word": " minus", "probability": 0.9736328125}, {"start": 1454.18, "end": 1454.4, "word": " 0", "probability": 0.96923828125}, {"start": 1454.4, "end": 1454.7, "word": ".5?", "probability": 0.9892578125}, {"start": 1454.8, "end": 1455.04, "word": " Suppose", "probability": 0.8046875}, {"start": 1455.04, "end": 1455.46, "word": " R1", "probability": 0.948486328125}, {"start": 1455.46, "end": 1455.58, "word": " is", "probability": 0.91845703125}, {"start": 1455.58, "end": 1455.88, "word": " minus", "probability": 0.9794921875}, {"start": 1455.88, "end": 1456.18, "word": " 0", "probability": 0.98974609375}, {"start": 1456.18, "end": 1456.5, "word": ".5.", "probability": 0.998046875}], "temperature": 1.0}, {"id": 55, "seek": 147842, "start": 1460.18, "end": 1478.42, "text": " strong negative or equal minus point eight strong negative which is more strong nine nine because this value is close closer to minus one than", "tokens": [2068, 3671, 420, 2681, 3175, 935, 3180, 2068, 3671, 597, 307, 544, 2068, 4949, 4949, 570, 341, 2158, 307, 1998, 4966, 281, 3175, 472, 813], "avg_logprob": -0.3686899176010719, "compression_ratio": 1.5212765957446808, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1460.18, "end": 1460.58, "word": " strong", "probability": 0.162109375}, {"start": 1460.58, "end": 1460.98, "word": " negative", "probability": 0.7353515625}, {"start": 1460.98, "end": 1463.48, "word": " or", "probability": 0.46435546875}, {"start": 1463.48, "end": 1464.84, "word": " equal", "probability": 0.74072265625}, {"start": 1464.84, "end": 1465.24, "word": " minus", "probability": 0.7158203125}, {"start": 1465.24, "end": 1465.56, "word": " point", "probability": 0.61474609375}, {"start": 1465.56, "end": 1465.88, "word": " eight", "probability": 0.56103515625}, {"start": 1465.88, "end": 1467.4, "word": " strong", "probability": 0.56396484375}, {"start": 1467.4, "end": 1468.4, "word": " negative", "probability": 0.89892578125}, {"start": 1468.4, "end": 1469.28, "word": " which", "probability": 0.609375}, {"start": 1469.28, "end": 1469.5, "word": " is", "probability": 0.953125}, {"start": 1469.5, "end": 1469.84, "word": " more", "probability": 0.93017578125}, {"start": 1469.84, "end": 1470.32, "word": " strong", 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Even this value is greater than minus 0.9, but minus 0.9 is close to minus 1, more closer to minus 1 than minus 0.8. On the other hand, if R equals 0.75, that means there exists positive relationship. If R equals 0.85, also there exists positive.", "tokens": [2829, 301, 1958, 13, 23, 13, 2754, 341, 2158, 307, 5044, 813, 3175, 1958, 13, 24, 11, 457, 3175, 1958, 13, 24, 307, 1998, 281, 3175, 502, 11, 544, 4966, 281, 3175, 502, 813, 3175, 1958, 13, 23, 13, 1282, 264, 661, 1011, 11, 498, 497, 6915, 1958, 13, 11901, 11, 300, 1355, 456, 8198, 3353, 2480, 13, 759, 497, 6915, 1958, 13, 19287, 11, 611, 456, 8198, 3353, 13], "avg_logprob": -0.17418574489338298, "compression_ratio": 1.664516129032258, "no_speech_prob": 0.0, "words": [{"start": 1479.13, "end": 1479.67, "word": " Minus", "probability": 0.58355712890625}, {"start": 1479.67, "end": 1479.89, "word": " 0", "probability": 0.56591796875}, {"start": 1479.89, "end": 1480.21, "word": ".8.", "probability": 0.984619140625}, {"start": 1480.63, "end": 1480.91, "word": " Even", "probability": 0.7734375}, {"start": 1480.91, "end": 1481.49, "word": " this", "probability": 0.8642578125}, {"start": 1481.49, "end": 1481.91, "word": " value", 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{"id": 57, "seek": 153080, "start": 1508.08, "end": 1530.8, "text": " But R2 is stronger than R1, because 0.85 is closer to plus 1 than 0.7. So we can say that there exists strong relationship between X and Y, and this relationship is positive. So again, by using the sign, you can tell the direction.", "tokens": [583, 497, 17, 307, 7249, 813, 497, 16, 11, 570, 1958, 13, 19287, 307, 4966, 281, 1804, 502, 813, 1958, 13, 22, 13, 407, 321, 393, 584, 300, 456, 8198, 2068, 2480, 1296, 1783, 293, 398, 11, 293, 341, 2480, 307, 3353, 13, 407, 797, 11, 538, 1228, 264, 1465, 11, 291, 393, 980, 264, 3513, 13], "avg_logprob": -0.21080280300872078, "compression_ratio": 1.4320987654320987, "no_speech_prob": 0.0, "words": [{"start": 1508.08, "end": 1508.48, "word": " But", "probability": 0.183837890625}, {"start": 1508.48, "end": 1510.26, "word": " R2", "probability": 0.723876953125}, {"start": 1510.26, "end": 1510.78, "word": " is", "probability": 0.921875}, {"start": 1510.78, "end": 1511.58, "word": " stronger", "probability": 0.78955078125}, {"start": 1511.58, "end": 1511.92, "word": " than", "probability": 0.8994140625}, {"start": 1511.92, "end": 1512.42, "word": " R1,", "probability": 0.966796875}, {"start": 1512.54, "end": 1513.0, "word": " because", "probability": 0.869140625}, {"start": 1513.0, "end": 1513.24, "word": " 0", "probability": 0.87744140625}, {"start": 1513.24, "end": 1513.54, "word": ".85", "probability": 0.989501953125}, {"start": 1513.54, "end": 1514.16, "word": " is", "probability": 0.94384765625}, {"start": 1514.16, "end": 1514.76, "word": " closer", "probability": 0.90576171875}, {"start": 1514.76, "end": 1515.62, "word": " to", "probability": 0.93115234375}, {"start": 1515.62, "end": 1516.18, "word": " plus", "probability": 0.67138671875}, {"start": 1516.18, "end": 1516.56, "word": " 1", "probability": 0.521484375}, {"start": 1516.56, "end": 1518.16, "word": " than", "probability": 0.796875}, {"start": 1518.16, "end": 1518.44, "word": " 0", "probability": 0.70703125}, {"start": 1518.44, "end": 1518.76, "word": ".7.", "probability": 0.660888671875}, {"start": 1519.74, "end": 1520.2, "word": " So", "probability": 0.92236328125}, {"start": 1520.2, "end": 1520.34, "word": " we", "probability": 0.638671875}, {"start": 1520.34, "end": 1520.52, "word": " can", "probability": 0.9501953125}, {"start": 1520.52, "end": 1520.74, "word": " say", "probability": 0.9072265625}, {"start": 1520.74, "end": 1520.98, "word": " that", "probability": 0.91455078125}, {"start": 1520.98, "end": 1521.14, "word": " there", "probability": 0.8837890625}, {"start": 1521.14, "end": 1521.52, "word": " exists", "probability": 0.7783203125}, {"start": 1521.52, "end": 1522.52, "word": " strong", "probability": 0.5087890625}, {"start": 1522.52, "end": 1523.06, "word": " relationship", "probability": 0.9208984375}, {"start": 1523.06, "end": 1523.44, "word": " between", "probability": 0.87451171875}, {"start": 1523.44, "end": 1523.66, "word": " X", "probability": 0.5166015625}, {"start": 1523.66, "end": 1523.8, "word": " and", "probability": 0.94189453125}, {"start": 1523.8, "end": 1523.96, "word": " Y,", "probability": 0.99267578125}, {"start": 1524.02, "end": 1524.12, "word": " and", "probability": 0.92724609375}, {"start": 1524.12, "end": 1524.3, "word": " this", "probability": 0.931640625}, {"start": 1524.3, "end": 1524.74, "word": " relationship", "probability": 0.9111328125}, {"start": 1524.74, "end": 1524.98, "word": " is", "probability": 0.9443359375}, {"start": 1524.98, "end": 1525.22, "word": " positive.", "probability": 0.7763671875}, {"start": 1526.36, "end": 1526.68, "word": " So", "probability": 0.95361328125}, {"start": 1526.68, "end": 1527.06, "word": " again,", "probability": 0.85888671875}, {"start": 1527.12, "end": 1527.26, "word": " by", "probability": 0.966796875}, {"start": 1527.26, "end": 1527.56, "word": " using", "probability": 0.9326171875}, {"start": 1527.56, "end": 1527.9, "word": " the", "probability": 0.9150390625}, {"start": 1527.9, "end": 1528.4, "word": " sign,", "probability": 0.81787109375}, {"start": 1528.5, "end": 1528.56, "word": " you", "probability": 0.94677734375}, {"start": 1528.56, "end": 1528.76, "word": " can", "probability": 0.943359375}, {"start": 1528.76, "end": 1529.08, "word": " tell", "probability": 0.88427734375}, {"start": 1529.08, "end": 1529.96, "word": " the", "probability": 0.82763671875}, {"start": 1529.96, "end": 1530.8, "word": " direction.", "probability": 0.92919921875}], "temperature": 1.0}, {"id": 58, "seek": 156193, "start": 1532.23, "end": 1561.93, "text": " The absolute value can tell the strength of the relationship between X and Y. So there are five features of R, unity-free. Ranges between minus one and plus one. Closer to minus one, it means stronger negative. Closer to plus one, stronger positive. Close to zero, it means there is no relationship. Or the weaker, the relationship between X and Y.", "tokens": [440, 8236, 2158, 393, 980, 264, 3800, 295, 264, 2480, 1296, 1783, 293, 398, 13, 407, 456, 366, 1732, 4122, 295, 497, 11, 18205, 12, 10792, 13, 497, 10350, 1296, 3175, 472, 293, 1804, 472, 13, 2033, 22150, 281, 3175, 472, 11, 309, 1355, 7249, 3671, 13, 2033, 22150, 281, 1804, 472, 11, 7249, 3353, 13, 16346, 281, 4018, 11, 309, 1355, 456, 307, 572, 2480, 13, 1610, 264, 24286, 11, 264, 2480, 1296, 1783, 293, 398, 13], "avg_logprob": -0.19422468392154837, "compression_ratio": 1.8368421052631578, "no_speech_prob": 0.0, "words": [{"start": 1532.23, "end": 1532.53, "word": " The", "probability": 0.36328125}, {"start": 1532.53, "end": 1532.97, "word": " absolute", "probability": 0.86376953125}, {"start": 1532.97, "end": 1533.33, "word": " value", "probability": 0.95458984375}, {"start": 1533.33, "end": 1533.63, "word": " can", "probability": 0.84130859375}, {"start": 1533.63, "end": 1533.95, "word": " tell", "probability": 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straightforward to determine if it's perfect by using scatterplot. Also, by scatterplot, you can tell the direction of the relationship. For the second scatterplot, it seems to be that there exists negative relationship between X and Y. In this one, also there exists a relationship", "tokens": [407, 309, 311, 15325, 281, 6997, 498, 309, 311, 2176, 538, 1228, 34951, 564, 310, 13, 2743, 11, 538, 34951, 564, 310, 11, 291, 393, 980, 264, 3513, 295, 264, 2480, 13, 1171, 264, 1150, 34951, 564, 310, 11, 309, 2544, 281, 312, 300, 456, 8198, 3671, 2480, 1296, 1783, 293, 398, 13, 682, 341, 472, 11, 611, 456, 8198, 257, 2480], "avg_logprob": -0.16344245842524938, "compression_ratio": 1.6724137931034482, "no_speech_prob": 0.0, "words": [{"start": 1675.11, "end": 1675.47, "word": " So", "probability": 0.8583984375}, {"start": 1675.47, "end": 1675.81, "word": " it's", "probability": 0.845458984375}, {"start": 1675.81, "end": 1677.05, "word": " straightforward", "probability": 0.7041015625}, {"start": 1677.05, "end": 1677.35, "word": " to", "probability": 0.92333984375}, {"start": 1677.35, "end": 1677.59, "word": " determine", "probability": 0.89599609375}, {"start": 1677.59, "end": 1677.79, "word": " if", "probability": 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For example, if Y is 20 and X is 1. X is 1, Y is 20. X increases to 2, for example. Y is still 20. So that means there is no relationship between X and Y. It's a constant. Y equals a constant value. 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So that means there is no relationship between X and Y. Let's see how can we compute the correlation between two variables. For example, suppose we have data for father's height and son's height.", "tokens": [398, 486, 362, 5754, 2158, 13, 407, 300, 1355, 456, 307, 572, 2480, 1296, 1783, 293, 398, 13, 961, 311, 536, 577, 393, 321, 14722, 264, 20009, 1296, 732, 9102, 13, 1171, 1365, 11, 7297, 321, 362, 1412, 337, 3086, 311, 6681, 293, 1872, 311, 6681, 13], "avg_logprob": -0.1234537772834301, "compression_ratio": 1.4545454545454546, "no_speech_prob": 0.0, "words": [{"start": 1786.69, "end": 1787.27, "word": " Y", "probability": 0.47802734375}, {"start": 1787.27, "end": 1787.93, "word": " will", "probability": 0.880859375}, {"start": 1787.93, "end": 1788.35, "word": " have", "probability": 0.9423828125}, {"start": 1788.35, "end": 1789.25, "word": " constant", "probability": 0.837890625}, {"start": 1789.25, "end": 1789.69, "word": " value.", "probability": 0.9736328125}, {"start": 1790.17, "end": 1790.27, "word": " So", "probability": 0.89892578125}, {"start": 1790.27, "end": 1790.49, "word": " that", "probability": 0.82373046875}, {"start": 1790.49, "end": 1790.77, "word": " means", "probability": 0.9306640625}, {"start": 1790.77, "end": 1790.97, "word": " there", "probability": 0.83447265625}, {"start": 1790.97, "end": 1791.21, "word": " is", "probability": 0.916015625}, {"start": 1791.21, "end": 1791.69, "word": " no", "probability": 0.935546875}, {"start": 1791.69, "end": 1792.17, "word": " relationship", "probability": 0.9130859375}, {"start": 1792.17, "end": 1792.71, "word": " between", "probability": 0.90283203125}, {"start": 1792.71, "end": 1794.33, "word": " X", "probability": 0.7333984375}, {"start": 1794.33, "end": 1794.53, "word": " and", "probability": 0.92919921875}, {"start": 1794.53, "end": 1794.79, "word": " Y.", "probability": 0.98828125}, {"start": 1796.49, "end": 1797.35, "word": " Let's", "probability": 0.943115234375}, {"start": 1797.35, "end": 1797.45, "word": " see", "probability": 0.91162109375}, {"start": 1797.45, "end": 1797.57, "word": " how", "probability": 0.9208984375}, {"start": 1797.57, "end": 1797.77, "word": " can", "probability": 0.7275390625}, {"start": 1797.77, "end": 1797.91, "word": " we", "probability": 0.9482421875}, {"start": 1797.91, "end": 1798.43, "word": " compute", "probability": 0.88525390625}, {"start": 1798.43, "end": 1801.15, "word": " the", "probability": 0.76904296875}, {"start": 1801.15, "end": 1801.85, "word": " correlation", "probability": 0.888671875}, {"start": 1801.85, "end": 1803.67, "word": " between", "probability": 0.87939453125}, {"start": 1803.67, "end": 1803.99, "word": " two", "probability": 0.90576171875}, {"start": 1803.99, "end": 1804.43, "word": " variables.", "probability": 0.94482421875}, {"start": 1804.79, "end": 1804.95, "word": " For", "probability": 0.95654296875}, {"start": 1804.95, "end": 1805.39, "word": " example,", "probability": 0.9736328125}, {"start": 1806.97, "end": 1807.35, "word": " suppose", "probability": 0.88720703125}, {"start": 1807.35, "end": 1807.53, "word": " we", "probability": 0.943359375}, {"start": 1807.53, "end": 1807.69, "word": " have", "probability": 0.94091796875}, {"start": 1807.69, "end": 1808.07, "word": " data", "probability": 0.9384765625}, {"start": 1808.07, "end": 1809.07, "word": " for", "probability": 0.9404296875}, {"start": 1809.07, "end": 1809.89, "word": " father's", "probability": 0.828369140625}, {"start": 1809.89, "end": 1810.29, "word": " height", "probability": 0.978515625}, {"start": 1810.29, "end": 1811.41, "word": " and", "probability": 0.92041015625}, {"start": 1811.41, "end": 1811.87, "word": " son's", "probability": 0.949462890625}, {"start": 1811.87, "end": 1812.15, "word": " height.", "probability": 0.95556640625}], "temperature": 1.0}, {"id": 68, "seek": 183923, "start": 1813.37, "end": 1839.23, "text": " And we are interested to see if father's height affects his son's height. So we have data for 10 observations here. Father number one, his height is 64 inches. And you know that inch equals 2.5.", "tokens": [400, 321, 366, 3102, 281, 536, 498, 3086, 311, 6681, 11807, 702, 1872, 311, 6681, 13, 407, 321, 362, 1412, 337, 1266, 18163, 510, 13, 7085, 1230, 472, 11, 702, 6681, 307, 12145, 8478, 13, 400, 291, 458, 300, 7227, 6915, 568, 13, 20, 13], "avg_logprob": -0.17663043154322583, "compression_ratio": 1.3541666666666667, "no_speech_prob": 0.0, "words": [{"start": 1813.37, "end": 1813.69, "word": " And", "probability": 0.74560546875}, {"start": 1813.69, "end": 1813.81, "word": " we", "probability": 0.8984375}, {"start": 1813.81, "end": 1813.93, "word": " are", "probability": 0.900390625}, {"start": 1813.93, "end": 1814.39, "word": " interested", "probability": 0.87255859375}, {"start": 1814.39, "end": 1814.93, "word": " to", "probability": 0.9296875}, {"start": 1814.93, "end": 1815.19, "word": " see", "probability": 0.92236328125}, {"start": 1815.19, "end": 1815.51, "word": " if", "probability": 0.947265625}, {"start": 1815.51, "end": 1816.11, "word": " father's", "probability": 0.817626953125}, {"start": 1816.11, "end": 1816.51, "word": " height", "probability": 0.96337890625}, {"start": 1816.51, "end": 1817.61, "word": " affects", "probability": 0.68798828125}, {"start": 1817.61, "end": 1818.01, "word": " his", "probability": 0.9599609375}, {"start": 1818.01, "end": 1818.39, "word": " son's", "probability": 0.915771484375}, {"start": 1818.39, "end": 1818.65, "word": " height.", "probability": 0.94384765625}, {"start": 1819.63, "end": 1820.03, "word": " So", "probability": 0.8623046875}, {"start": 1820.03, "end": 1820.13, "word": " we", "probability": 0.7255859375}, {"start": 1820.13, "end": 1820.25, "word": " have", "probability": 0.947265625}, {"start": 1820.25, "end": 1820.59, "word": " data", "probability": 0.9423828125}, {"start": 1820.59, "end": 1821.11, "word": " for", "probability": 0.818359375}, {"start": 1821.11, "end": 1821.73, "word": " 10", "probability": 0.5224609375}, {"start": 1821.73, "end": 1823.85, "word": " observations", "probability": 0.7841796875}, {"start": 1823.85, "end": 1824.27, "word": " here.", "probability": 0.8427734375}, {"start": 1825.45, "end": 1825.81, "word": " Father", "probability": 0.81689453125}, {"start": 1825.81, "end": 1826.03, "word": " number", "probability": 0.7646484375}, {"start": 1826.03, "end": 1826.37, "word": " one,", "probability": 0.66162109375}, {"start": 1827.39, "end": 1827.87, "word": " his", "probability": 0.96435546875}, {"start": 1827.87, "end": 1828.61, "word": " height", "probability": 0.95556640625}, {"start": 1828.61, "end": 1830.21, "word": " is", "probability": 0.9375}, {"start": 1830.21, "end": 1830.89, "word": " 64", "probability": 0.953125}, {"start": 1830.89, "end": 1831.55, "word": " inches.", "probability": 0.87646484375}, {"start": 1831.75, "end": 1831.93, "word": " And", "probability": 0.95361328125}, {"start": 1831.93, "end": 1832.09, "word": " you", "probability": 0.87548828125}, {"start": 1832.09, "end": 1832.25, "word": " know", "probability": 0.88916015625}, {"start": 1832.25, "end": 1832.45, "word": " that", "probability": 0.92529296875}, {"start": 1832.45, "end": 1832.71, "word": " inch", "probability": 0.859375}, {"start": 1832.71, "end": 1833.29, "word": " equals", "probability": 0.9248046875}, {"start": 1833.29, "end": 1838.57, "word": " 2", "probability": 0.27001953125}, {"start": 1838.57, "end": 1839.23, "word": ".5.", "probability": 0.987548828125}], "temperature": 1.0}, {"id": 69, "seek": 186692, "start": 1843.52, "end": 1866.92, "text": " So X is 64, Sun's height is 65. X is 68, Sun's height is 67 and so on. Sometimes, if the dataset is small enough, as in this example, we have just 10 observations, you can tell the direction.", "tokens": [407, 1783, 307, 12145, 11, 6163, 311, 6681, 307, 11624, 13, 1783, 307, 23317, 11, 6163, 311, 6681, 307, 23879, 293, 370, 322, 13, 4803, 11, 498, 264, 28872, 307, 1359, 1547, 11, 382, 294, 341, 1365, 11, 321, 362, 445, 1266, 18163, 11, 291, 393, 980, 264, 3513, 13], "avg_logprob": -0.2345281927024617, "compression_ratio": 1.411764705882353, "no_speech_prob": 0.0, "words": [{"start": 1843.52, "end": 1844.18, "word": " So", "probability": 0.26318359375}, {"start": 1844.18, "end": 1844.48, "word": " X", "probability": 0.423583984375}, {"start": 1844.48, "end": 1844.62, "word": " is", "probability": 0.67431640625}, {"start": 1844.62, "end": 1845.16, "word": " 64,", "probability": 0.83154296875}, {"start": 1846.04, "end": 1846.48, "word": " Sun's", "probability": 0.85546875}, {"start": 1846.48, "end": 1846.64, "word": " height", "probability": 0.892578125}, {"start": 1846.64, "end": 1846.82, "word": " is", "probability": 0.8662109375}, {"start": 1846.82, "end": 1847.24, "word": " 65.", "probability": 0.97607421875}, {"start": 1849.38, "end": 1850.04, "word": " X", "probability": 0.93994140625}, {"start": 1850.04, "end": 1850.16, "word": " is", "probability": 0.4755859375}, {"start": 1850.16, "end": 1850.74, "word": " 68,", "probability": 0.98583984375}, {"start": 1852.32, "end": 1852.92, "word": " Sun's", "probability": 0.954833984375}, {"start": 1852.92, "end": 1853.12, "word": " height", "probability": 0.9462890625}, {"start": 1853.12, "end": 1853.34, "word": " is", "probability": 0.92724609375}, {"start": 1853.34, "end": 1853.8, "word": " 67", "probability": 0.95263671875}, {"start": 1853.8, "end": 1854.02, "word": " and", "probability": 0.6279296875}, {"start": 1854.02, "end": 1854.18, "word": " so", "probability": 0.94921875}, {"start": 1854.18, "end": 1854.4, "word": " on.", "probability": 0.94921875}, {"start": 1855.26, "end": 1855.92, "word": " Sometimes,", "probability": 0.8876953125}, {"start": 1856.94, "end": 1858.26, "word": " if", "probability": 0.9287109375}, {"start": 1858.26, "end": 1858.46, "word": " the", "probability": 0.91064453125}, {"start": 1858.46, "end": 1858.82, "word": " dataset", "probability": 0.57958984375}, {"start": 1858.82, "end": 1859.14, "word": " is", "probability": 0.95068359375}, {"start": 1859.14, "end": 1859.46, "word": " small", "probability": 0.9365234375}, {"start": 1859.46, "end": 1859.9, "word": " enough,", "probability": 0.8515625}, {"start": 1861.22, "end": 1861.42, "word": " as", "probability": 0.83251953125}, {"start": 1861.42, "end": 1861.56, "word": " in", "probability": 0.8818359375}, {"start": 1861.56, "end": 1861.74, "word": " this", "probability": 0.94140625}, {"start": 1861.74, "end": 1862.08, "word": " example,", "probability": 0.96435546875}, {"start": 1862.16, "end": 1862.26, "word": " we", "probability": 0.7646484375}, {"start": 1862.26, "end": 1862.36, "word": " have", "probability": 0.9130859375}, {"start": 1862.36, "end": 1862.6, "word": " just", "probability": 0.87548828125}, {"start": 1862.6, "end": 1862.78, "word": " 10", "probability": 0.67236328125}, {"start": 1862.78, "end": 1863.28, "word": " observations,", "probability": 0.7958984375}, {"start": 1864.46, "end": 1864.7, "word": " you", "probability": 0.9306640625}, {"start": 1864.7, "end": 1864.94, "word": " can", "probability": 0.94677734375}, {"start": 1864.94, "end": 1865.26, "word": " tell", "probability": 0.8984375}, {"start": 1865.26, "end": 1866.36, "word": " the", "probability": 0.8564453125}, {"start": 1866.36, "end": 1866.92, "word": " direction.", "probability": 0.96728515625}], "temperature": 1.0}, {"id": 70, "seek": 189322, "start": 1868.4, "end": 1893.22, "text": " I mean, you can say, yes, for this specific example, there exists positive relationship between x and y. But if the data set is large, it's very hard to figure out if the relation is positive or negative. So we have to find or to compute the coefficient of correlation in order to see there exists positive, negative, strong, weak, or moderate.", "tokens": [286, 914, 11, 291, 393, 584, 11, 2086, 11, 337, 341, 2685, 1365, 11, 456, 8198, 3353, 2480, 1296, 2031, 293, 288, 13, 583, 498, 264, 1412, 992, 307, 2416, 11, 309, 311, 588, 1152, 281, 2573, 484, 498, 264, 9721, 307, 3353, 420, 3671, 13, 407, 321, 362, 281, 915, 420, 281, 14722, 264, 17619, 295, 20009, 294, 1668, 281, 536, 456, 8198, 3353, 11, 3671, 11, 2068, 11, 5336, 11, 420, 18174, 13], "avg_logprob": -0.13384046523194565, "compression_ratio": 1.6995073891625616, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1868.4, "end": 1868.64, "word": " I", "probability": 0.81591796875}, {"start": 1868.64, "end": 1868.78, "word": " mean,", "probability": 0.9501953125}, {"start": 1868.88, "end": 1868.9, "word": " you", "probability": 0.90380859375}, {"start": 1868.9, "end": 1869.06, "word": " can", "probability": 0.943359375}, 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pick random numbers here for example 64 father's height his son's height 65 if we move up here to 70 for father's height his son's height is going to be 72 so as father heights increases", "tokens": [457, 797, 291, 393, 980, 490, 341, 2199, 1365, 2086, 456, 307, 257, 3353, 2480, 570, 445, 498, 291, 1888, 4974, 3547, 510, 337, 1365, 12145, 3086, 311, 6681, 702, 1872, 311, 6681, 11624, 498, 321, 1286, 493, 510, 281, 5285, 337, 3086, 311, 6681, 702, 1872, 311, 6681, 307, 516, 281, 312, 18731, 370, 382, 3086, 25930, 8637], "avg_logprob": -0.18476562922199566, "compression_ratio": 1.7380952380952381, "no_speech_prob": 0.0, "words": [{"start": 1893.98, "end": 1894.32, "word": " but", "probability": 0.2442626953125}, {"start": 1894.32, "end": 1894.66, "word": " again", "probability": 0.9033203125}, {"start": 1894.66, "end": 1894.92, "word": " you", "probability": 0.74365234375}, {"start": 1894.92, "end": 1895.14, "word": " can", "probability": 0.9423828125}, {"start": 1895.14, "end": 1895.34, 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{"start": 1920.16, "end": 1920.66, "word": " heights", "probability": 0.59228515625}, {"start": 1920.66, "end": 1921.22, "word": " increases", "probability": 0.912109375}], "temperature": 1.0}, {"id": 72, "seek": 194078, "start": 1922.3, "end": 1940.78, "text": " Also, son's height increases. For example, 77, father's height. His son's height is 76. So that means there exists positive relationship. Make sense? But again, for large data, you cannot tell that.", "tokens": [2743, 11, 1872, 311, 6681, 8637, 13, 1171, 1365, 11, 25546, 11, 3086, 311, 6681, 13, 2812, 1872, 311, 6681, 307, 24733, 13, 407, 300, 1355, 456, 8198, 3353, 2480, 13, 4387, 2020, 30, 583, 797, 11, 337, 2416, 1412, 11, 291, 2644, 980, 300, 13], "avg_logprob": -0.22855717831469596, "compression_ratio": 1.3724137931034484, "no_speech_prob": 0.0, "words": [{"start": 1922.3, "end": 1922.94, "word": " Also,", "probability": 0.6875}, {"start": 1923.86, "end": 1924.28, "word": " son's", "probability": 0.6654052734375}, {"start": 1924.28, "end": 1924.54, "word": " height", "probability": 0.96533203125}, {"start": 1924.54, "end": 1925.02, "word": " increases.", "probability": 0.8720703125}, {"start": 1926.32, "end": 1926.84, "word": " For", "probability": 0.95654296875}, {"start": 1926.84, "end": 1927.6, "word": " example,", "probability": 0.916015625}, {"start": 1927.8, "end": 1928.64, "word": " 77,", "probability": 0.75634765625}, {"start": 1928.84, "end": 1929.76, "word": " father's", "probability": 0.73876953125}, {"start": 1929.76, "end": 1930.2, "word": " height.", "probability": 0.978515625}, {"start": 1930.88, "end": 1931.06, "word": " His", "probability": 0.806640625}, {"start": 1931.06, "end": 1931.42, "word": " son's", "probability": 0.949951171875}, {"start": 1931.42, "end": 1931.7, "word": " height", "probability": 0.95703125}, {"start": 1931.7, "end": 1932.1, "word": " is", "probability": 0.947265625}, {"start": 1932.1, "end": 1932.74, "word": " 76.", "probability": 0.955078125}, {"start": 1933.3, "end": 1933.74, "word": " So", "probability": 0.92724609375}, {"start": 1933.74, "end": 1933.94, "word": " that", "probability": 0.82763671875}, {"start": 1933.94, "end": 1934.14, "word": " means", "probability": 0.9326171875}, {"start": 1934.14, "end": 1934.3, "word": " there", "probability": 0.845703125}, {"start": 1934.3, "end": 1934.58, "word": " exists", "probability": 0.80712890625}, {"start": 1934.58, "end": 1935.16, "word": " positive", "probability": 0.89599609375}, {"start": 1935.16, "end": 1935.78, "word": " relationship.", "probability": 0.73779296875}, {"start": 1936.78, "end": 1937.0, "word": " Make", "probability": 0.6787109375}, {"start": 1937.0, "end": 1937.32, "word": " sense?", "probability": 0.826171875}, {"start": 1938.54, "end": 1939.0, "word": " But", "probability": 0.90380859375}, {"start": 1939.0, "end": 1939.22, "word": " again,", "probability": 0.8916015625}, {"start": 1939.32, "end": 1939.42, "word": " for", "probability": 0.94580078125}, {"start": 1939.42, "end": 1939.74, "word": " large", "probability": 0.91162109375}, {"start": 1939.74, "end": 1939.98, "word": " data,", "probability": 0.95556640625}, {"start": 1940.02, "end": 1940.14, "word": " you", "probability": 0.9580078125}, {"start": 1940.14, "end": 1940.36, "word": " cannot", "probability": 0.880859375}, {"start": 1940.36, "end": 1940.58, "word": " tell", "probability": 0.7626953125}, {"start": 1940.58, "end": 1940.78, "word": " that.", "probability": 0.61865234375}], "temperature": 1.0}, {"id": 73, "seek": 197791, "start": 1951.71, "end": 1977.91, "text": " If, again, by using this data, small data, you can determine just the length, the strength, I'm sorry, the strength of a relationship or the direction of the relationship. Just pick any number at random. For example, if we pick this number. 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For father's height 70, his son's height increases up to 72. Similarly, 72 father's height, his son's height 75. So that means X increases, Y also increases. So that means there exists both of them.", "tokens": [823, 7297, 321, 1888, 1071, 1230, 300, 307, 5044, 813, 23317, 11, 550, 718, 311, 536, 437, 486, 1051, 13, 1171, 3086, 311, 6681, 5285, 11, 702, 1872, 311, 6681, 8637, 493, 281, 18731, 13, 13157, 11, 18731, 3086, 311, 6681, 11, 702, 1872, 311, 6681, 9562, 13, 407, 300, 1355, 1783, 8637, 11, 398, 611, 8637, 13, 407, 300, 1355, 456, 8198, 1293, 295, 552, 13], "avg_logprob": -0.24701287991860332, "compression_ratio": 1.6685714285714286, "no_speech_prob": 0.0, "words": [{"start": 1979.94, "end": 1980.18, "word": " Now", "probability": 0.5439453125}, {"start": 1980.18, "end": 1980.54, "word": " suppose", "probability": 0.548828125}, {"start": 1980.54, "end": 1980.7, "word": " we", "probability": 0.86669921875}, {"start": 1980.7, "end": 1980.9, "word": " pick", "probability": 0.83984375}, {"start": 1980.9, "end": 1981.2, "word": " another", "probability": 0.90869140625}, {"start": 1981.2, "end": 1981.48, "word": " number", "probability": 0.9375}, {"start": 1981.48, "end": 1981.72, "word": " that", "probability": 0.81298828125}, {"start": 1981.72, "end": 1981.86, "word": " is", "probability": 0.80322265625}, {"start": 1981.86, "end": 1982.18, "word": " greater", "probability": 0.888671875}, {"start": 1982.18, "end": 1982.46, "word": " than", "probability": 0.9384765625}, {"start": 1982.46, "end": 1982.92, "word": " 68,", "probability": 0.9326171875}, {"start": 1983.1, "end": 1983.2, "word": " then", "probability": 0.533203125}, {"start": 1983.2, "end": 1983.44, "word": " let's", "probability": 0.92041015625}, {"start": 1983.44, "end": 1983.58, "word": " see", "probability": 0.92041015625}, {"start": 1983.58, "end": 1983.74, "word": " what", "probability": 0.9443359375}, {"start": 1983.74, "end": 1983.9, "word": " will", "probability": 0.84619140625}, {"start": 1983.9, "end": 1984.18, "word": " happen.", "probability": 0.90966796875}, {"start": 1985.58, "end": 1985.84, "word": " For", "probability": 0.92822265625}, {"start": 1985.84, "end": 1986.92, "word": " father's", "probability": 0.4959716796875}, {"start": 1986.92, "end": 1987.06, "word": " height", "probability": 0.76904296875}, {"start": 1987.06, "end": 1987.64, "word": " 70,", "probability": 0.701171875}, {"start": 1988.98, "end": 1989.44, "word": " his", "probability": 0.951171875}, {"start": 1989.44, "end": 1989.8, "word": " son's", "probability": 0.8896484375}, {"start": 1989.8, "end": 1990.04, "word": " height", "probability": 0.97216796875}, {"start": 1990.04, "end": 1990.64, "word": " increases", "probability": 0.88037109375}, {"start": 1990.64, "end": 1991.06, "word": " up", "probability": 0.91748046875}, {"start": 1991.06, "end": 1991.26, "word": " to", "probability": 0.95361328125}, {"start": 1991.26, "end": 1991.76, "word": " 72.", "probability": 0.97509765625}, {"start": 1993.52, "end": 1994.1, "word": " Similarly,", "probability": 0.7294921875}, {"start": 1994.54, "end": 1995.2, "word": " 72", "probability": 0.87646484375}, {"start": 1995.2, "end": 1996.38, "word": " father's", "probability": 0.723876953125}, {"start": 1996.38, "end": 1996.64, "word": " height,", "probability": 0.95654296875}, {"start": 1996.74, "end": 1996.9, "word": " his", "probability": 0.93115234375}, {"start": 1996.9, "end": 1997.16, "word": " son's", "probability": 0.9384765625}, {"start": 1997.16, "end": 1997.24, "word": " height", "probability": 0.91064453125}, {"start": 1997.24, "end": 1997.82, "word": " 75.", "probability": 0.59912109375}, {"start": 1998.74, "end": 1999.02, "word": " So", "probability": 0.861328125}, {"start": 1999.02, "end": 1999.26, "word": " that", "probability": 0.88818359375}, {"start": 1999.26, "end": 1999.6, "word": " means", "probability": 0.93212890625}, {"start": 1999.6, "end": 1999.98, "word": " X", "probability": 0.52734375}, {"start": 1999.98, "end": 2000.54, "word": " increases,", "probability": 0.92626953125}, {"start": 2001.32, "end": 2001.58, "word": " Y", "probability": 0.9765625}, {"start": 2001.58, "end": 2002.06, "word": " also", "probability": 0.88232421875}, {"start": 2002.06, "end": 2002.54, "word": " increases.", "probability": 0.828125}, {"start": 2002.8, "end": 2002.94, "word": " So", "probability": 0.93310546875}, {"start": 2002.94, "end": 2003.76, "word": " that", "probability": 0.8642578125}, {"start": 2003.76, "end": 2004.0, "word": " means", "probability": 0.92333984375}, {"start": 2004.0, "end": 2004.16, "word": " there", "probability": 0.73291015625}, {"start": 2004.16, "end": 2004.6, "word": " exists", "probability": 0.66796875}, {"start": 2004.6, "end": 2005.34, "word": " both", "probability": 0.65234375}, {"start": 2005.34, "end": 2005.74, "word": " of", "probability": 0.2100830078125}, {"start": 2005.74, "end": 2005.82, "word": " them.", "probability": 0.56201171875}], "temperature": 1.0}, {"id": 75, "seek": 203455, "start": 2008.55, "end": 2034.55, "text": " For sure it is hard to tell this direction if the data is large. Because maybe you will find as X increases for one point, Y maybe decreases for that point. So it depends on the data you have. Anyway, let's see how can we compute R. 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"probability": 0.8938802083333334}, {"start": 2087.16, "end": 2087.6, "word": " Seventy", "probability": 0.83203125}, {"start": 2087.6, "end": 2087.96, "word": "-five.", "probability": 0.887451171875}, {"start": 2088.98, "end": 2089.44, "word": " Seventy", "probability": 0.9173177083333334}, {"start": 2089.44, "end": 2089.8, "word": "-seven.", "probability": 0.93359375}], "temperature": 1.0}, {"id": 78, "seek": 211937, "start": 2117.23, "end": 2119.37, "text": " So first we have to compute it.", "tokens": [407, 700, 321, 362, 281, 14722, 309, 13], "avg_logprob": -0.5125868055555556, "compression_ratio": 0.8, "no_speech_prob": 0.0, "words": [{"start": 2117.23, "end": 2117.73, "word": " So", "probability": 0.1414794921875}, {"start": 2117.73, "end": 2118.23, "word": " first", "probability": 0.77294921875}, {"start": 2118.23, "end": 2118.47, "word": " we", "probability": 0.479248046875}, {"start": 2118.47, "end": 2118.65, "word": " have", "probability": 0.93701171875}, {"start": 2118.65, 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"probability": 0.91650390625}, {"start": 2163.72, "end": 2164.04, "word": " sum", "probability": 0.919921875}, {"start": 2164.04, "end": 2164.18, "word": " of", "probability": 0.9736328125}, {"start": 2164.18, "end": 2164.6, "word": " XY", "probability": 0.63671875}, {"start": 2164.6, "end": 2165.1, "word": " sum", "probability": 0.480224609375}, {"start": 2165.1, "end": 2165.32, "word": " X", "probability": 0.5732421875}, {"start": 2165.32, "end": 2165.7, "word": " squared", "probability": 0.50732421875}, {"start": 2165.7, "end": 2166.72, "word": " and", "probability": 0.9482421875}, {"start": 2166.72, "end": 2167.06, "word": " Y", "probability": 0.8544921875}, {"start": 2167.06, "end": 2167.6, "word": " squared", "probability": 0.7236328125}, {"start": 2167.6, "end": 2168.4, "word": " now", "probability": 0.348388671875}, {"start": 2168.4, "end": 2168.58, "word": " the", "probability": 0.89892578125}, {"start": 2168.58, "end": 2169.06, "word": " summation", "probability": 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So that is this sum divided by n, where n is 10 in this case. So this is the first step. Let's see how can we compute R. R, we have sum of x, y.", "tokens": [492, 362, 281, 14722, 264, 914, 295, 2031, 293, 288, 13, 407, 300, 307, 341, 2408, 6666, 538, 297, 11, 689, 297, 307, 1266, 294, 341, 1389, 13, 407, 341, 307, 264, 700, 1823, 13, 961, 311, 536, 577, 393, 321, 14722, 497, 13, 497, 11, 321, 362, 2408, 295, 2031, 11, 288, 13], "avg_logprob": -0.2254261396147988, "compression_ratio": 1.3805970149253732, "no_speech_prob": 0.0, "words": [{"start": 2180.38, "end": 2180.68, "word": " We", "probability": 0.53955078125}, {"start": 2180.68, "end": 2180.9, "word": " have", "probability": 0.86669921875}, {"start": 2180.9, "end": 2181.04, "word": " to", "probability": 0.9609375}, {"start": 2181.04, "end": 2181.38, "word": " compute", "probability": 0.9228515625}, {"start": 2181.38, "end": 2182.58, "word": " the", "probability": 0.74951171875}, {"start": 2182.58, "end": 2182.76, "word": " mean", "probability": 0.94287109375}, {"start": 2182.76, "end": 2182.9, "word": " of", "probability": 0.958984375}, {"start": 2182.9, "end": 2183.2, "word": " x", "probability": 0.5986328125}, {"start": 2183.2, "end": 2185.04, "word": " and", "probability": 0.85498046875}, {"start": 2185.04, "end": 2185.36, "word": " y.", "probability": 0.96826171875}, {"start": 2186.3, "end": 2186.42, "word": " So", "probability": 0.78125}, {"start": 2186.42, "end": 2186.66, "word": " that", "probability": 0.76123046875}, {"start": 2186.66, "end": 2187.04, "word": " is", "probability": 0.927734375}, {"start": 2187.04, "end": 2188.16, "word": " this", "probability": 0.68359375}, {"start": 2188.16, "end": 2188.52, "word": " sum", "probability": 0.9267578125}, {"start": 2188.52, "end": 2189.24, "word": " divided", "probability": 0.6787109375}, {"start": 2189.24, "end": 2189.5, "word": " by", "probability": 0.97119140625}, {"start": 2189.5, "end": 2189.82, "word": " n,", "probability": 0.611328125}, {"start": 2189.96, "end": 2190.06, "word": " where", "probability": 0.3466796875}, {"start": 2190.06, "end": 2190.18, "word": " n", "probability": 0.95458984375}, {"start": 2190.18, "end": 2190.5, "word": " is", "probability": 0.9013671875}, {"start": 2190.5, "end": 2190.78, "word": " 10", "probability": 0.67333984375}, {"start": 2190.78, "end": 2190.9, "word": " in", "probability": 0.87255859375}, {"start": 2190.9, "end": 2191.08, "word": " this", "probability": 0.94580078125}, {"start": 2191.08, "end": 2191.38, "word": " case.", "probability": 0.90771484375}, {"start": 2194.6, "end": 2195.2, "word": " So", "probability": 0.87646484375}, {"start": 2195.2, "end": 2195.36, "word": " this", "probability": 0.86767578125}, {"start": 2195.36, "end": 2195.46, "word": " is", "probability": 0.94580078125}, {"start": 2195.46, "end": 2195.56, "word": " the", "probability": 0.91552734375}, {"start": 2195.56, "end": 2195.76, "word": " first", "probability": 0.884765625}, {"start": 2195.76, "end": 2196.1, "word": " step.", "probability": 0.94189453125}, {"start": 2201.82, "end": 2202.42, "word": " Let's", "probability": 0.941162109375}, {"start": 2202.42, "end": 2202.54, "word": " see", "probability": 0.8603515625}, {"start": 2202.54, "end": 2202.64, "word": " how", "probability": 0.88330078125}, {"start": 2202.64, "end": 2202.78, "word": " can", "probability": 0.67333984375}, {"start": 2202.78, "end": 2202.9, "word": " we", "probability": 0.92724609375}, {"start": 2202.9, "end": 2203.22, "word": " compute", "probability": 0.93896484375}, {"start": 2203.22, "end": 2203.56, "word": " R.", "probability": 0.73388671875}, {"start": 2204.58, "end": 2205.18, "word": " R,", "probability": 0.634765625}, {"start": 2206.32, "end": 2207.7, "word": " we", "probability": 0.93701171875}, {"start": 2207.7, "end": 2208.0, "word": " have", "probability": 0.9443359375}, {"start": 2208.0, "end": 2208.74, "word": " sum", "probability": 0.77734375}, {"start": 2208.74, "end": 2208.9, "word": " of", "probability": 0.9638671875}, {"start": 2208.9, "end": 2209.08, "word": " x,", "probability": 0.927734375}, {"start": 2209.18, "end": 2209.38, "word": " y.", "probability": 0.75}], "temperature": 1.0}, {"id": 82, "seek": 223542, "start": 2211.42, "end": 2235.42, "text": " minus n is 10 times x bar times y bar. This is the first quantity. The other one is square root of sum x squared minus n x bar squared.", "tokens": [3175, 297, 307, 1266, 1413, 2031, 2159, 1413, 288, 2159, 13, 639, 307, 264, 700, 11275, 13, 440, 661, 472, 307, 3732, 5593, 295, 2408, 2031, 8889, 3175, 297, 2031, 2159, 8889, 13], "avg_logprob": -0.28883271269938526, "compression_ratio": 1.4166666666666667, "no_speech_prob": 0.0, "words": [{"start": 2211.42, "end": 2211.88, "word": " minus", "probability": 0.224609375}, {"start": 2211.88, "end": 2212.18, "word": " n", "probability": 0.6376953125}, {"start": 2212.18, "end": 2212.38, "word": " is", "probability": 0.701171875}, {"start": 2212.38, "end": 2212.66, "word": " 10", "probability": 0.61279296875}, {"start": 2212.66, "end": 2214.76, "word": " times", "probability": 0.66650390625}, {"start": 2214.76, "end": 2215.1, "word": " x", "probability": 0.84130859375}, {"start": 2215.1, "end": 2215.44, "word": " bar", "probability": 0.86083984375}, {"start": 2215.44, "end": 2217.96, "word": " times", "probability": 0.85986328125}, {"start": 2217.96, "end": 2218.24, "word": " y", "probability": 0.9765625}, {"start": 2218.24, "end": 2218.5, "word": " bar.", "probability": 0.94921875}, {"start": 2220.14, "end": 2220.78, "word": " This", "probability": 0.7880859375}, {"start": 2220.78, "end": 2220.9, "word": " is", "probability": 0.94873046875}, {"start": 2220.9, "end": 2221.0, "word": " the", "probability": 0.9033203125}, {"start": 2221.0, "end": 2221.24, "word": " first", "probability": 0.8681640625}, {"start": 2221.24, "end": 2221.64, "word": " quantity.", "probability": 0.45166015625}, {"start": 2221.94, "end": 2222.1, "word": " The", "probability": 0.841796875}, {"start": 2222.1, "end": 2222.32, "word": " other", "probability": 0.8896484375}, {"start": 2222.32, "end": 2222.52, "word": " one", "probability": 0.9228515625}, {"start": 2222.52, "end": 2222.78, "word": " is", "probability": 0.9541015625}, {"start": 2222.78, "end": 2223.1, "word": " square", "probability": 0.75537109375}, {"start": 2223.1, "end": 2223.32, "word": " root", "probability": 0.9326171875}, {"start": 2223.32, "end": 2223.7, "word": " of", "probability": 0.9775390625}, {"start": 2223.7, "end": 2228.58, "word": " sum", "probability": 0.4619140625}, {"start": 2228.58, "end": 2228.84, "word": " x", "probability": 0.95166015625}, {"start": 2228.84, "end": 2230.16, "word": " squared", "probability": 0.390380859375}, {"start": 2230.16, "end": 2233.12, "word": " minus", "probability": 0.966796875}, {"start": 2233.12, "end": 2233.92, "word": " n", "probability": 0.72216796875}, {"start": 2233.92, "end": 2234.5, "word": " x", "probability": 0.83984375}, {"start": 2234.5, "end": 2234.86, "word": " bar", "probability": 0.943359375}, {"start": 2234.86, "end": 2235.42, "word": " squared.", "probability": 0.806640625}], "temperature": 1.0}, {"id": 83, "seek": 226698, "start": 2238.83, "end": 2266.99, "text": " times some y squared minus n times y bar squared. And we have to find the square root of this value. So square root, that will give this result. 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And finally, we'll get that result, 87%. Now, the sign is positive. 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That means there exists strong positive relationship between father's and son's height. I think the calculation is straightforward. Now, for this example, the data are given in inches. 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Do you think in this case, R will change? So if we add or multiply or divide, R will not change? 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But here I meant if we multiply this value by positive sign, plus two, plus three, and let's see how can we do that by Excel. Now this is the data we have. 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The calculations here are different. We have different sum, different sum of x, sum of y and so on, but are the same. Let's see if we multiply just x by 2.5 and y the same.", "tokens": [407, 510, 321, 12972, 1184, 2031, 538, 568, 13, 20, 293, 264, 912, 337, 288, 13, 440, 20448, 510, 366, 819, 13, 492, 362, 819, 2408, 11, 819, 2408, 295, 2031, 11, 2408, 295, 288, 293, 370, 322, 11, 457, 366, 264, 912, 13, 961, 311, 536, 498, 321, 12972, 445, 2031, 538, 568, 13, 20, 293, 288, 264, 912, 13], "avg_logprob": -0.14667338084790013, "compression_ratio": 1.644927536231884, "no_speech_prob": 0.0, "words": [{"start": 2529.34, "end": 2529.74, "word": " So", "probability": 0.79150390625}, {"start": 2529.74, "end": 2530.18, "word": " here", "probability": 0.7470703125}, {"start": 2530.18, "end": 2530.4, "word": " we", "probability": 0.8115234375}, {"start": 2530.4, "end": 2531.0, "word": " multiply", "probability": 0.492431640625}, {"start": 2531.0, "end": 2531.44, "word": " each", "probability": 0.88330078125}, {"start": 2531.44, "end": 2531.72, "word": " x", "probability": 0.7431640625}, {"start": 2531.72, "end": 2532.12, "word": " by", "probability": 0.9697265625}, {"start": 2532.12, "end": 2532.7, "word": " 2", "probability": 0.9169921875}, {"start": 2532.7, "end": 2533.4, "word": ".5", "probability": 0.9892578125}, {"start": 2533.4, "end": 2533.6, "word": " and", "probability": 0.7236328125}, {"start": 2533.6, "end": 2533.76, "word": " the", "probability": 0.8203125}, {"start": 2533.76, "end": 2533.98, "word": " same", "probability": 0.90234375}, {"start": 2533.98, "end": 2534.26, "word": " for", "probability": 0.93798828125}, {"start": 2534.26, "end": 2534.62, "word": " y.", "probability": 0.89306640625}, {"start": 2535.54, "end": 2535.92, "word": " The", "probability": 0.8720703125}, {"start": 2535.92, "end": 2536.48, "word": " calculations", "probability": 0.88427734375}, {"start": 2536.48, "end": 2536.94, "word": " here", "probability": 0.8583984375}, {"start": 2536.94, "end": 2537.14, "word": " are", "probability": 0.93896484375}, {"start": 2537.14, "end": 2537.58, "word": " different.", "probability": 0.888671875}, {"start": 2538.76, "end": 2539.1, "word": " We", "probability": 0.95263671875}, {"start": 2539.1, "end": 2539.4, "word": " have", "probability": 0.94677734375}, {"start": 2539.4, "end": 2539.9, "word": " different", "probability": 0.88037109375}, {"start": 2539.9, "end": 2540.34, "word": " sum,", "probability": 0.77880859375}, {"start": 2540.72, "end": 2541.08, "word": " different", "probability": 0.849609375}, {"start": 2541.08, "end": 2541.5, "word": " sum", "probability": 0.93701171875}, {"start": 2541.5, "end": 2541.64, "word": " of", "probability": 0.9609375}, {"start": 2541.64, "end": 2541.88, "word": " x,", "probability": 0.9853515625}, {"start": 2542.2, "end": 2542.2, "word": " sum", "probability": 0.796875}, {"start": 2542.2, "end": 2542.34, "word": " of", "probability": 0.96630859375}, {"start": 2542.34, "end": 2542.56, "word": " y", "probability": 0.99560546875}, {"start": 2542.56, "end": 2542.76, "word": " and", "probability": 0.5771484375}, {"start": 2542.76, "end": 2542.96, "word": " so", "probability": 0.95166015625}, {"start": 2542.96, "end": 2543.26, "word": " on,", "probability": 0.94775390625}, {"start": 2543.7, "end": 2544.0, "word": " but", "probability": 0.91162109375}, {"start": 2544.0, "end": 2544.52, "word": " are", "probability": 0.63037109375}, {"start": 2544.52, "end": 2545.86, "word": " the", "probability": 0.89697265625}, {"start": 2545.86, "end": 2546.1, "word": " same.", "probability": 0.91015625}, {"start": 2547.54, "end": 2548.06, "word": " Let's", "probability": 0.959228515625}, {"start": 2548.06, "end": 2548.24, "word": " see", "probability": 0.9130859375}, {"start": 2548.24, "end": 2548.44, "word": " if", "probability": 0.95166015625}, {"start": 2548.44, "end": 2548.84, "word": " we", "probability": 0.96142578125}, {"start": 2548.84, "end": 2551.04, "word": " multiply", "probability": 0.92333984375}, {"start": 2551.04, "end": 2553.28, "word": " just", "probability": 0.87548828125}, {"start": 2553.28, "end": 2553.54, "word": " x", "probability": 0.98974609375}, {"start": 2553.54, "end": 2553.76, "word": " by", "probability": 0.97705078125}, {"start": 2553.76, "end": 2553.96, "word": " 2", "probability": 0.9951171875}, {"start": 2553.96, "end": 2554.52, "word": ".5", "probability": 0.998779296875}, {"start": 2554.52, "end": 2555.54, "word": " and", "probability": 0.81298828125}, {"start": 2555.54, "end": 2556.0, "word": " y", "probability": 0.98876953125}, {"start": 2556.0, "end": 2558.58, "word": " the", "probability": 0.70849609375}, {"start": 2558.58, "end": 2558.88, "word": " same.", "probability": 0.91162109375}], "temperature": 1.0}, {"id": 94, "seek": 258848, "start": 2561.84, "end": 2588.48, "text": " So we multiplied x by 2.5 and we keep it make sense? Now let's see how outliers will affect the value of R. Let's say if we change one point in the data set support. 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The other is 2, for example. 1. I just changed half of the data. Now R was 87, it becomes 59. 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It will go from 50 to up to 63. That means any changes in x or y values will change the y. But if we add or multiply all the values by a constant, r will stay the same. 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I will move quickly to the practice problems we have. 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