Solution Found!
Suppose you fit the regression model to n = 35 data points
Chapter 12, Problem 142SE(choose chapter or problem)
Suppose you fit the regression model
\(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{2}^{2}+\beta_{4} x_{1} x_{2}+\beta_{5} x_{1} x_{2}^{2}\)
to n = 35 data points and wish to test the null hypothesis \(H_0:\ \beta_4\ =\ \beta_5\ =\ 0\).
a. State the alternative hypothesis.
b. Explain in detail how to compute the F-statistic needed to test the null hypothesis.
c. What are the numerator and denominator degrees of freedom associated with the F-statistic in part b?
d. Give the rejection region for the test if \(\alpha\ =\ .05\).
Questions & Answers
QUESTION:
Suppose you fit the regression model
\(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{2}^{2}+\beta_{4} x_{1} x_{2}+\beta_{5} x_{1} x_{2}^{2}\)
to n = 35 data points and wish to test the null hypothesis \(H_0:\ \beta_4\ =\ \beta_5\ =\ 0\).
a. State the alternative hypothesis.
b. Explain in detail how to compute the F-statistic needed to test the null hypothesis.
c. What are the numerator and denominator degrees of freedom associated with the F-statistic in part b?
d. Give the rejection region for the test if \(\alpha\ =\ .05\).
ANSWER:Step 1 of 5
The fitted regression model is
The sample n = 35 points.
The null hypothesis is
