 Hi, this is Dr. Don. I have a problem at a chapter 9 about regression and in this problem we're told that we're going to be given some data that is the length in centimeters and the girth, the waistline of 12 harbor seals. We need to find the regression equation of the regression line and then construct a scatter plot, draw the regression line on it, then use the regression equation to predict the value of y for each of the given values of x. And we've got four values of x here, 140, 172, 164, 158. The last one makes the comment, if the x value is not meaningful to break y, explain why not. Well remember, we can only safely predict values of y for x's that fall within the range of our data between the minimum value and the maximum value. If the x we're trying to use is outside that range, then it's unreliable. And that means the y we get is not meaningful. I'm going to show you how to do this using Excel, basic Excel. Okay, I have the data copied into Excel. Remember in my stat lab, you can either use the little blue rectangle and open it directly in Excel, or you can copy and paste, which is what I prefer to do. I've done a little preliminary work here. I put the x values that we want to predict y for in here. And then I've labeled some cells, the min, max, r, the correlation coefficient, the intercept and the slope that we need out of our equation. Now why do I have the min and the max? Well remember, we need to only predict values of y for values of x that are in the range of our data. Now this is a small data set. You can just inspect this and find the minimum value, which I think is probably 123. But when you have more data, you need to use an equation. So I'm going to use equal min, which is the minimum function. And I'm just going to highlight that range, hit enter, and it confirms the min value is 123. Similarly, we use max. Double click that to select it, highlight the range again, and we get a max value of 168. To get the correlation coefficient, start with the equal sign again and start spelling correlation. And there's the little function correll, which is the correlation coefficient. Double click it to select it. The first array, and it doesn't matter for correlation, which you put first, then a comma, and then a second array, the second column with data of the y, and hit enter. And that gives us our correlation coefficient of 0.919, which rounds to 0.920. The intercept, again, we start with our equal. Start typing intercept. There's the formula. Double click that. This time we're going to be careful. The known y's we need to put in there first. So I'm going to highlight the y's, put a comma, and then highlight the x's, hit enter, and that gives us our intercept of 9.759. The slope, similarly, SLO, start typing slope. There's the equation. Again, y's first. Highlight that. Comma, and then our x's hit enter, and that gives us our slope, 0.695. Now to get our predicted values, we need to use that regression equation, which is, again, y is equal to the intercept plus the slope times the x value. So we just put that formula in here. Equal. I'm going to get my intercept, and we're going to use the function four key to lock that down so I can copy this formula, plus my slope, and lock that down again with the f four key times my x value. And enter, and that gives my first x value, and I can drag this down here to get the other predicted values, the y hat values, a little carrot over y tells us that's a predicted value. And remember, we need to check to see if any of these x's are outside the range. When 40 is between 123 and 168, 172 is not. So this is unreliable, not meaningful in stat crunch terminology. 64's is in that range, 158's in that range, so those are okay. So now we need to draw our graph. We can draw the graph pretty easily. We just need to select our data, and we want to have the x values in the first column for Excel, because it assumes whatever's in the first column goes on the x axis. So if I highlighted my data, I go up to insert, recommended charts, and I'm going to look and if it doesn't pop up there, go to all charts, find scatter. There's the scatter I want right there with the y and x, double click that, and it brings up the chart. Now this one doesn't look like the available charts in my stat lab, because it goes all the way to the intercept, the origin there, 00. You can also get your equation once you plot by just clicking on one of the data sets, and then right clicking and add a trend line. And it opens up. We want the linear trend line. I'm going to get it to display the equation in the R square, and click there, and there is the equation again. So you can go that way if you want, just plot and get the regression equation that way. R square remember is the square of R, so if you take the square root of that, you would get the R down here 0.919. So that's how to do this using Excel. You would have to again, you know, check this a little more closely, and you can of course, blow up your chart to make it a little bit bigger to look at the pattern to match with my stat lab. So I hope this helps.