Let sx and sy denote the sample standard deviations of the observed x’s and y’s, respectively [that is, and similarly for ].

a. Show that an alternative expression for the estimated regression line is

b. This expression for the regression line can be interpreted as follows. Suppose . What then is the predicted y for an x that lies 1 SD (sx units) above the mean of the xi

’s? If r were 1, the prediction would be for y to lie 1 SD above its mean , but since , we predict a y that is only .5 SD (.5sy unit) above . Using the data in Exercise 64 for a patient whose age is 1 SD below the average age in the sample, by how many standard deviations is the patient’s predicted CBG above or below the average

CBG for the sample?