 Hi, this is Dr. Don. I have a problem on regression out of Chapter 11, Section 6, and this has to do with finding confidence intervals and prediction intervals for estimates using the linear equation that you get from regression. Now, I'm not going to go through the theory behind this. I think you can get that out of the book. What I want to show you is how to solve it using StatCrunch very, very quickly. So the first thing we're going to do is we're going to click on the icon to open the table, and then we're going to click on it again to open in StatCrunch. Okay, I have StatCrunch open, and I'm going to expand it so we can see everything. That's the cutting speed. This is the useful life of brand A and the useful life of brand B. And we want to do some estimates. And reading ahead, they wanted an estimate for 45 cutting speed, a cutting speed of 45, and then a extrapolation to a cutting speed of 100. So I'm going to show you how to do that. Let's go ahead and we're going to start with StatRegressionSimpleLinear. And we are going to first take our X variable, which is our cutting speed. That's our predictor. And then our response variable in the first one is going to be useful life brand A. We can leave everything default until we get down to this section that says prediction of Y. And I said they wanted a prediction for a Y of 40, I mean the X of 45, and then also an X of 100. So you just put those values in there separated by a comma. And they wanted 90%. So I just set that to whatever confidence level they want and click compute. And you get a table. I'm going to expand this so you can see it. We have all the information you need about linear regression. There's the intercept and slope, the equation that they want. And then they've got the ANOVA down here if you need to get into that. And it's significant with less than 0.05. But here are prediction information, our estimates. This is the predicted value of Y that they asked for. And then the confidence interval for the mean and then the prediction interval for the new estimate. As always, you need to know that theory there that the prediction interval is going to be wider than the confidence interval because it has to account for not only the variation of the mean, but also the variation associated just with that sample. So it's a larger sum variation there. And we notice here for the extrapolation, which again you have to assume that the equation holds true outside the data range, are predicted Y as a negative, and you can't have a life of negative, but you would report that value. When we get to the confidence interval and the prediction interval, the negative life doesn't make sense. So you would report zero for the lower limit. And then the upper limits you have here 1.5, zero, 2.4 for the prediction interval. That's all you have to do. If you forget about adding these predicted values, you can just go back to options, edit, and then add those values. The other thing you would have to do, of course, you need to do it for brand B, and just repeat that regression, simple linear. This time we select the X value, and then our Y value this time is brand B, and we're going to put our predicted value in there again of 45 with a 90, and click compute. And then there you've got your information you need to compare the brand A and brand B confidence intervals and prediction intervals. That's all you need. So I hope this helps.