Question: Suppose that the data on a response y and three predictors . . and are such that all predictors are equally correlated, Corriz, 1] =

Suppose that the data on a response y and three predictors . . and are such that all predictors are equally correlated, Corriz, 1] = r. Transform to the new predictors =(1+2+3)

(101+23-223)

a. Determine the matrix P so that the new design matrix is written as ZXP

b. Determine the least squares estimates of y for the model y=Zy+e, in terms of the correlations, Corry, of in the model y=XB+e r,, and use this to determine the estimate

c. Comment on the situation in which r = -1/2

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