In Section 2.5.1 we noted that for linear models containing an intercept term, corr(????̂ ,

e) = 0, and plotting e against ????̂ helps detect violations of model assumptions. However, it is not helpful to plot e against y. To see why not,

using formula (2.5), show that

(a) the regression of y on e has slope 1,

(b) the regression of e on y has slope 1 − R2,

(c) corr(y,

e) = √
1 − R2.