If we start with (6.38) under the CLM assumptions, assume large n, and ignore the estimation error in the β̂_j, a 95% prediction interval for ŷ⁰ is [exp(–1.96ŝ) exp(logy⁰), exp(1.96ŝ) exp(logy⁰)].

The point prediction for y⁰ is ŷ⁰ 5 exp(ŝ ²/2)exp(logy⁰).

(i) For what values of ŝ will the point prediction be in the 95% prediction interval? Does this condition seem likely to hold in most applications?

(ii) Verify that the condition from part (i) is satisfied in the CEO salary example.