Suppose you fit the regression model y = 0 + 1x1 + 2x2 + 3x1x2 + 4x21

Question:

Suppose you fit the regression model
y = β0 + β1x1 + β2x2 + β3x1x2 + β4x21 + β5x22+ ε
to n = 30 data points and wish to test
H0: β3 = β4 = β5 = 0
a. State the alternative hypothesis Ha.
b. Give the reduced model appropriate for conducting the test.
c. What are the numerator and denominator degrees of freedom associated with the F-statistic?
d. Suppose the SSE's for the reduced and complete models are SSER = 1,250.2 and SSEC = 1,125.2. Conduct the hypothesis test and interpret the results of your test. Test using α = .05.