Chapter 11.12, Problem 74E

An experiment was conducted to investigate the effect of four factors—temperature T₁, pressure P, catalyst C, and temperature T₂—on the yield Y of a chemical.

1. a The values (or levels) of the four factors used in the experiment are shown in the accompanying table. If each of the four factors is coded to produce the four variables x₁, x₂, x₃, and x₄, respectively, give the transformation relating each coded variable to its corresponding original.

1. b Fit the linear model

   Y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + β₄x₄ + ε

   to the following table of data.

1. c Do the data present sufficient evidence to indicate that T₁ contributes information for the estimation of Y? Does P? Does C? Does T2? (Test the hypotheses, respectively, that β₁ = 0, β₂ = 0, β₃ = 0, and β₄ = 0.) Give bounds for the p-value associated with each test. What would you conclude if you used α = .01 in each case?