Specify the parameters involved in a test of the hypothesis

Question

Testing for curvature. Consider the secondorder model relating E(y) to three quantitative independent variables, x₁, x₂, and x₃:

E(y) = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + β₄x₁x₂ + β₅x₁x_{3 +} β₆x₂x_{3 +} β₇x₁^{2 +} β₈x₂2 + β9x₃2

(a) Specify the parameters involved in a test of the hypothesis that no curvature exists in the response surface.

(b) State the hypothesis of part a in terms of the model parameters.

(c) What hypothesis would you test to determine whether x3 is useful for the prediction of E(y)?