Chapter 12.5, Problem 12.36LM

Suppose you fit the interaction model

y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + ε

to n = 32 data points and obtain the following results:

SS_yy = 479 SSE = 21 ${\hat{\beta }}_3$ = 10 $s_{{\hat{\beta }}_3}$ = 4

1. a. Find R² and interpret its value.
2. b. Is the model adequate for predicting y? Test at α=.05.
3. c. Use a graph to explain the contribution of the x₁ x₂ term to the model.
4. d. Is there evidence that x₁ and x₂ interact? Test at α =.05.