For the model y = β₀ + β₁x + β₂xd + ε, which of the following are the hypotheses for testing the individual significance of the interaction variable xd? A) H₀: xd = 0, H_A: xd ≠ 0 B) H₀: b₂ = 0, H_A: b₂ ≠ 0 C) H₀: β₂ = 0, H_A: β₂ ≠ 0 D) H₀: β₂ ≠ 0, H_A: β₂ = 0

Question

Quizplus · Accepted Answer

The hypotheses for testing the individual significance of the interaction variable xd should be in terms of β₂, which is the coefficient of xd in the regression equation. Therefore, option A and B, which use the variable xd directly, are incorrect. Option D also reverses the null and alternative hypotheses. The correct null hypothesis should be that the coefficient of xd (β₂) is equal to zero (i.e., there is no significant interaction effect of xd), and the alternative hypothesis should be that the coefficient is not equal to zero (i.e., there is a significant interaction effect of xd). Therefore, the correct choice is C.

For the Model Y = β0 + β1x + β2xd

For the Model Y = β₀ + β₁x + β₂xd