Solution Found!
Suppose you fit the interaction modely = ?0 + ?1x1 + ?2x2
Chapter 12, Problem 36E(choose chapter or problem)
Suppose you fit the interaction model
\(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2}+\varepsilon\)
to n = 32 data points and obtain the following results:
\(\begin{array}{llll} \mathrm{SS}_{y y}=479 & \mathrm{SSE}=21 & \hat{\beta}_{3}=10 & s_{\hat{\beta}_{3}}=4 \end{array}\)
a. Find \(R^2\) and interpret its value.
b. Is the model adequate for predicting y? Test at \(\alpha\ =\ .05\).
c. Use a graph to explain the contribution of the \(x_1x_2\) term to the model.
d. Is there evidence that \(x_1\) and \(x_2\) interact? Test at \(\alpha\ =\ .05\).
Questions & Answers
QUESTION:
Suppose you fit the interaction model
\(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2}+\varepsilon\)
to n = 32 data points and obtain the following results:
\(\begin{array}{llll} \mathrm{SS}_{y y}=479 & \mathrm{SSE}=21 & \hat{\beta}_{3}=10 & s_{\hat{\beta}_{3}}=4 \end{array}\)
a. Find \(R^2\) and interpret its value.
b. Is the model adequate for predicting y? Test at \(\alpha\ =\ .05\).
c. Use a graph to explain the contribution of the \(x_1x_2\) term to the model.
d. Is there evidence that \(x_1\) and \(x_2\) interact? Test at \(\alpha\ =\ .05\).
ANSWER:Step 1 of 7
For the given information, suppose you fit the interaction model
(a) We have to the value of
The multiple coefficient of determination, 
We conclude that our model is best fit to the data