Solution Found!
Suppose you fit the regression model to n = 30 data points
Chapter 12, Problem 98E(choose chapter or problem)
Suppose you fit the regression model
\(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2}+\beta_{4} x_{1}^{2}+\beta_{5} x_{2}^{2}+\varepsilon\)
to n = 30 data points and wish to test
\(H_0:\ \beta_3=\beta_4=\beta_5=0\)
a. State the alternative hypothesis \(H_a\).
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 \(SSE_R=1,250.2\) and \(SSE_C=1,125.2\). Conduct the hypothesis test and interpret the results of your test. Test using \(\alpha\ =\ .05\).
Questions & Answers
QUESTION:
Suppose you fit the regression model
\(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2}+\beta_{4} x_{1}^{2}+\beta_{5} x_{2}^{2}+\varepsilon\)
to n = 30 data points and wish to test
\(H_0:\ \beta_3=\beta_4=\beta_5=0\)
a. State the alternative hypothesis \(H_a\).
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 \(SSE_R=1,250.2\) and \(SSE_C=1,125.2\). Conduct the hypothesis test and interpret the results of your test. Test using \(\alpha\ =\ .05\).
ANSWER:Step 1 of 4
(a) The ?rst order model equation 
n = 30 data points, and wish to test 
hypothesis is
