12.102 Why is there regression toward the mean? Refer to the relationship r = 1sx>sy2b between the...

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12.102 Why is there regression toward the mean? Refer to the relationship r = 1sx>sy2b between the slope and correlation, which is equivalently sxb = rsy.

a. Explain why an increase in x of sx units relates to a change in the predicted value of y of sxb units. (For instance, if sx = 10, it corresponds to a change in yn of 10b.)

b. Based on part

a, explain why an increase of one standard deviation in x corresponds to a change of only r standard deviations in the predicted y-variable.

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