 Hi, this is Dr. Don and I want to go over a simple linear regression problem that is a little bit different in that we need to look at the residuals as well as the normal things we do in finding the equation of the regression line and making a plot. So let's look at it. For given data, our X variables and our Y variable, X is the predictor variable, Y is the response variable, the thing we're trying to predict. So let's start by clicking on the icon, I'm going to open this data in StatCrunch. Okay, we have our data and we want to do the regression. So we go to Stat, regression, simple linear, we need to select our X variable, select our Y variable, and fortunately they've named those for us. We're going to leave the hypothesis test alone, but down here on this problem we don't need to actually predict any values of Y. What we do want, we want to get the fitted line plot and then I want to get a plot of residuals versus X-axis. So I'm going to hold the control key down and select that. That means I've got two things selected, fitted line plot, residuals versus X-values. And then we just click compute and we get our results. Okay, I have that expanded and we have a lot of good information about our regression. We've got our regression equation up there, Y is equal to 20.358 plus .095 times X. So that's the information we need on our regression equation. We've got our correlation coefficient of .29 and then that's all we're going to talk about right now. I'm going to click on that little arrow and go to the second term. This is our fitted line that we need to match up with the options in there. Remember you can play around with the X minimum value and I'm going to change the Y minimum value. Most often that will give you the best portrayal of the fitted line plot so that you can compare to the options in the question. Here is our fitted line and these are our actual data points. Remember the residuals are the differences between the regression line prediction for a particular point and the actual point. So there's the residual between the fitted line and a point. Here's the residual again. It's always vertical in the Y direction and here's the residual for this point. This point is almost on the line so it's residual very small. That's the residuals we're talking about. So let's look at them. Here we've got a plot of the X values in our data and these are the residuals. The difference is between the line and those actual Y plots. And what you're looking for when you're looking at a residual plot versus the X values, you're trying to see is this a random arrangement of the residuals or is there some sort of pattern going on? And here you see we've got a pattern that this is not random. Almost falling a line and then it goes down and then it goes back up. That's not random. That's the main thing I'm looking for. If it's not random that means it's not fluctuating around zero evenly, randomly and it's not fluctuating then that means it's not a good representation, not a good tool to be using for predicting Y values. So I hope this helps.