a. Give an example of actual variables y, x1, x2 for which you would expect

????1 ≠ 0 in the model E(yi) = ????0 + ????1xi1 but ????1 ≈ 0 in the model E(yi) =

????0 + ????1xi1 + ????2xi2 (e.g., perhaps x2 is a “lurking variable,” such that the association of x1 with y disappears when we adjust for x2).

b. Let r1 = corr(y, x∗1), r2 = corr(y, x∗2), and let R be the multiple correlation with predictors x1 and x2. For the case described in (a), explain why you would expect R to be close to |r2|.

c. For the case described in (a), which would you expect to be relatively near SSR(x1, x2): SSR(x1) or SSR(x2)? Why?