 Hi, this is Dr. Don. I have a problem out of Chapter 9 on correlation and regression. And in the problem, we're given some data. We're given the weight of some vehicles, the x variable. We're given the variability and breaking distance, the y variable. And we're asked to see, is there a correlation between vehicle weight and variability? Remember when we were doing correlation, in essence, we're plotting the x's and the y's. We're seeing if there's a slope. Is there a slope that is different from zero? And that is what the hypothesis test is in this case. The slope row is assumed to be zero for the null hypothesis, which is always the no difference here. Nothing happening here, alternative. And the alternative is, in this case, it is not equal to zero. There is something happening here. There is a linear relationship between the weight of the vehicle and the breaking distance, y. Now we can do this using StatCrunch, and I have a video that shows you how to do that. But I'm going to show you how to do it using Excel. And we need to do it in a way so we learn some information. They want us to use the rejection area method, so we need to get the critical values of t in this case. And it is a two-tail test because we've got not equal to zero. We just want to know, is there a slope? Is there a positive slope, or is there a negative slope statistically? Doesn't matter to us. We just want to know if there's a slope. So the critical values are two-tail, a minus, and a plus. We need to get the test statistic, which is a t, and then we need to make a conclusion. I want to show you how to do that using Excel. Remember up here on the little blue rectangle, we can open in StatCrunch, open in, copy the clipboard, open Excel. I like to copy the clipboard, it makes me easier to manipulate things. So I'm going to do that now, and open up Excel. Okay, I've got Excel open, and I've pasted the data over here in columns f and g, the weight, and the variability in the distance, or the distance y. I've added a little bit of information there so that I can go ahead and knock out the critical values. We need the alpha value, which is .05 in this case. The count, which is the number of pairs, and I've used the Excel function count in this column, is six, and the degrees of freedom for this test is just the number of pairs minus two, which would be four. And then we get the critical value of t to tail using the t.inverse to tail for the number of degrees of freedom, and the alpha, and that gives us 2.7764, which is the value that they went over here. Remember it's two tails, so it's plus and minus. Now we want to find out if the slope is different from zero. And we're going to use the data analysis tool pack, which is built into almost all versions of Excel, including the most recent versions of Excel for the Mac. And we just go up and we click on data. Okay, I'm going to up the data analysis, click on data analysis, and open up this dialog box, find the regression tool, click okay, and it gives me this dialog. I need to get the y range, I'm going to click there inside the box, I get the blinking cursor, these are my y values, and then you're going to see a lot of students make mistakes in reversing these. I'm going to click in the x range, get that blinking cursor, and then select my x values, make sure they match, you've got an even number of y values and x variables. We have labels in the first cell. I want to get a confidence interval, and it's 5% alpha, which is 95% confidence interval. My output range, I'm going to click in there, and I'm just going to move this out of the way and select J1 to where I put my output, and ignore the rest of this for right now, and click okay. And so we've got our output here, and you can expand these a little bit to read them a little bit better. We look here, we've got our multiple R, which is our correlation coefficient, which is 0.603, in case you need that. We're going to ignore the rest of this right now, since we just have a simple regression, and we look down here to the coefficients. We've got the intercept and the weight, which is the slope that we're interested in. We look across here, I'm going to expand this a little bit. We don't need this information on the confidence intervals. We're just going to look at the T statistic for our coefficient for the slope, which is the weight in this case, is 1.514, which is the value they went over here. We've got a P value for the slope of 0.204, which is greater than the alpha of 0.05, so that tells us the slope is not statistically significant. And what we can check, we've got our T statistic of 1.514, and that is not greater than the absolute value of the critical value of 2.77. So again, that tells us we do not reject, we fail to reject. There's not enough evidence at the 5% level to conclude there is a significant linear correlation. So I hope this helps.