(Data file: cakes) Refer to Problem 5.8, which uses the model given at (5.12), Estimate the optimal (X1, X2) combination that maximizes the fitted response and find the standard errors of X­1 and...

(Data file: cakes) Refer to Problem 5.8, which uses the model given at (5.12),

Estimate the optimal (X₁, X₂) combination

that maximizes the fitted response and find the standard errors of X­₁
and X­₂.

(Data file: mile) The data file gives the world record times for the one mile run (Perkiömäki, 1997). For males, the records are for the period from 1861 to 2003, and for females, for the period 1967–2003. The variables in the file are Year, year of the record, Time, the record time, in seconds, Name, the name of the runner, Country, the runner’s home country, Place, the place where the record was run (missing for many of the early records), and Gender, either male or female.