Suppose you fit the first-order model
y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + β 4 x 4 + β 5 x 5 + ε
to n = 30 data points and obtain
SSE = .33 R2 = .92
a. Do the values of SSE and R2 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 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 = .05.