Solution Found!
Suppose you fit the first-order modely = ? 0 + ? 1 x 1 + ?
Chapter 12, Problem 7E(choose chapter or problem)
Suppose you fit the first-order model
\(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+\beta_{4} x_{4}+\beta_{5} x_{5}+\varepsilon\)
to n = 30 data points and obtain
\(SSE=.33\ \ \ \ \ R^2=.92\)
a. Do the values of SSE and \(R^2\) 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 \(H_0:\ \beta_1=\ \beta_2\ =\ \beta_3\ =\ \beta_4\ =\ \beta_5\ =\ 0\) against the alternative hypothesis \(H_a:\) At least one of the parameters \(\beta_1,\ \beta_2,\ .\ .\ .\ ,\ \beta_5\) is nonzero. Use \(\alpha\ =\ .05\).
Questions & Answers
QUESTION:
Suppose you fit the first-order model
\(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+\beta_{4} x_{4}+\beta_{5} x_{5}+\varepsilon\)
to n = 30 data points and obtain
\(SSE=.33\ \ \ \ \ R^2=.92\)
a. Do the values of SSE and \(R^2\) 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 \(H_0:\ \beta_1=\ \beta_2\ =\ \beta_3\ =\ \beta_4\ =\ \beta_5\ =\ 0\) against the alternative hypothesis \(H_a:\) At least one of the parameters \(\beta_1,\ \beta_2,\ .\ .\ .\ ,\ \beta_5\) is nonzero. Use \(\alpha\ =\ .05\).
ANSWER:Step 1 of 4
In least square prediction equation method, 
Hence here we have