Chapter 12.6, Problem 12.53LM

Minitab was used to fit the complete second-order model

E(y) = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + β₄ $x_1^2$ + β₅ $x_2^2$

to n = 39 data points. The printout is shown on the next page.

1. a. Is there sufficient evidence to indicate that at least one of the parameters—β₁, β₂, β₃, β₄, and β₅—is nonzero? Test using α =.05.
2. b. Test H₀ : β₄ = 0 against H_a : β₄ ≠ 0. Use α =.01.
3. c. Test H₀ : β₅ = 0 against H_a : β₄ ≠ 0. Use α =.01.
4. d. Use graphs to explain the consequences of the tests in parts b and c.