In this video I'm going to show you how to use the TI-84 graph and calculator to calculate the correlation coefficient, the coefficient of determination, and calculate the linear regression line for a data set. And if you're using a different type of calculator like the 83 or the 85 or whatever version you have, the process will be somewhat similar but you'll have to find what keys and what buttons you're using to do different stuff. Anyways, let's go ahead and start off. The first thing that we're going to do is we're going to choose stats. And when this comes up we have to put data in so we're going to choose the edit and you can see this is in the black highlighted in black and the number one is the one we want to choose. So we can either hit the number one or we can just hit enter and that'll bring us to our list. Now if you already have data in the list to clear the list all you're going to do is go up and it highlights list number one which you can see right here. And if you just hit clear and then enter it'll clear that entire list. So let me go ahead and type in the data for list one. And these are going to be our x variables that we're typing in. And let's go ahead and go over to list two. So you'll simply click the right arrow to go over to list two and then we'll go ahead and type that data in. These are going to be our y variables. And now that I have those in I'm going to go back to the stat menu so I can actually do the calculation. So I'm going to click stat. And then when this comes up we're doing a calculation now and you can see edit is highlighted if I click the right arrow on my keypad it's going to highlight calculate. And then I can either scroll down to number four or I can hit the number four and then hit enter. And I've got linear regression selected and when I hit enter it's going to come up. And as long as you don't have anything in list number three it's automatically going to choose list one or two. Otherwise I believe it prompts you in order to get what lists you want to use. So I'm going to hit enter. And when this comes up notice it gives us our linear regression line and it gives us what the a value is which happens to be the slope. This is in the form y equals m x plus b where a is in the place of m and that's our slope and b our y intercept is 3.3. But notice it doesn't give us our correlation coefficient or our coefficient of determination. And that may be true. So we may have to go back in we may have to turn something on. So if you go to mode we will just go ahead and scroll down through mode to get the right preference is set. And when we get down a little ways you'll see that we get to this stat diagnostics right here this very second to last item in the menu and we want to turn that on. So you just highlight it so it goes over to on then you have to enter to select it now notice that's the one that's highlighted. We can go back in the stat menu we can scroll over to calculate and then scroll down to item number four which is linear regression. I'm going to go ahead and hit enter. Whoops I hit the wrong thing so let me go back into stat. Calculate and we want to go to number four which is linear regression that quadratic regression and I'm going to hit enter and it should automatically select list one and two. So I'm going to hit enter and notice now when we do this it gives us our correlation coefficient of our our our coefficient of determination which is our squared and then it gives us those values for our regression line. So we can write those down and I think one step further that we need to do is we need to go in and we need to be able to graph these and look at how that line really fits that data. We won't get into what the correlation coefficient is or coefficient of determination is in this video but that's how you would get that. So if you wanted to graph this data what we'd want to do is we'd want to copy down this information so we have our linear regression line. And then we're going to go first into stat plots so I'm going to go to second this y equals button to stat plots and notice my plots are off right now. So I'm going to hit enter for stat plots one and I'm going to turn those on and then it says what type do we want we're going to select this the scatter plot right here. We want the x list to be list one and the y list to be less to and then if we go to graph we should see those points show up on the graph and I'm going to change the window so we have a better window to view to do that. We simply click window right here. I'm going to change the x scale to negative ones since I don't have any negative values the maximum I'll change I'll keep that as 10 that's fine. And then the scale will be one the y minimum I'm going to change that to negative one and the y maximum of 10 is fine. And then I can go back to graph and you can see that I have a little bit better window to view this in. And then the last thing is we want to see how our regression line fits that data that we have. So I'm going to click y equals and I'm going to type in that information that I had for the regression line. And if you remember we had a negative 0.375 for a slope so that's going to be times x. And then we're going to have 3.3 is our y intercept so this is going to be plus 3.3. And we should have that in there and then if we go back to graph after we type that in maybe we should hit enter first so that way it saves it. But then we go back to graph and it's going to plot the line that represents that data. Remember this is our estimate traditionally in statistics we use this is our y hat our estimate of this data. Okay so here's our data points right here you can see they're fairly close to the line. That's part of the reason why we have a correlation coefficient of negative 0.9. And the reason it's negative it's downhill it's close to one so it means there's a strong correlation. And hopefully this helps you you know analyze the data a little bit quicker and check your results when you're doing your hand calculations. So good luck with the problem sets.