Suppose you fit the model y = β0 + β1x1 + β2x2 + β3x1x2 + β4x1^2 + β5x2^2 + ε to n = 30 data points and get SSE = 0.46 and R^2 = 0.87.
a. Do the values of SSE and R^2 suggest that the model provides a good fit to the data? Explain.
b. Is the model of any use in predicting y? Test the null hypothesis that E(y) = β0; that is, test H0: β1 = β2 = β3 = β4 = β5 = 0 against the alternative hypothesis Ha: At least one of the parameters β1, β2, … β5 is nonzero. Use α = 0.05.