Use R, SPSS, or another program to reproduce the results shown in Figure 9.5. You can modify the R code given in Section 9.4.

Section 9.4

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You might expect that we could use the covariance as a measure of the degree of rela- tionship between two variables. An immediate difficulty arises, however, in that the absolute value of covxy is also a function of the standard deviations of X and Y. For example, covxy = 20 might reflect a high degree of correlation when each variable contains little variability, but a low degree of correlation when the standard deviations are large and the scores are quite variable. To resolve this difficulty, we will divide the covariance by the standard deviations and make the result our estimate of correla- tion. (Technically, this is known as scaling the covariance by the standard deviations because we basically are changing the scale on which it is measured.) We will define what is known as the Pearson product-moment correlation coefficient (r) as COVXY SXSY The maximum value of covxy turns out to be sxsy. (This can be shown math- ematically, but just trust me.) Because the maximum of covxy is sxsy, it follows that the limits on r are 1.00. One interpretation of r, then, is that it is a measure of the degree to which the covariance approaches its maximum. An equivalent way of writing the preceding equation would be to replace the variances and covariances by their computational formulae and then simplify by can- cellation. If we do this, we will arrive at T = V[NEX - (EX)][NY (Y)] -