Solution Found!
Minitab was used to fit the complete second-order model to
Chapter 12, Problem 53E(choose chapter or problem)
Minitab was used to fit the complete second-order model
\(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2}+\beta_{4} x_{1}^{2}+\beta_{5} x_{2}^{2}\)
to n = 39 data points. The printout is shown below.
a. Is there sufficient evidence to indicate that at least one of the parameters \(-\beta_1, \beta_2, \beta_3, \beta_4\), and \(\beta_5\)-is nonzero? Test using \(\alpha=.05\).
b. Test \(H_0: \beta_4=0\) against \(H_{\mathrm{a}}: \beta_4 \neq 0\). Use \(\alpha=.01\).
c. Test \(H_0: \beta_5=0\) against \(H_{\mathrm{a}}: \beta_5 \neq 0\). Use \(\alpha=.01\).
d. Use graphs to explain the consequences of the tests in parts b and c.
Questions & Answers
QUESTION:
Minitab was used to fit the complete second-order model
\(E(y)=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{1} x_{2}+\beta_{4} x_{1}^{2}+\beta_{5} x_{2}^{2}\)
to n = 39 data points. The printout is shown below.
a. Is there sufficient evidence to indicate that at least one of the parameters \(-\beta_1, \beta_2, \beta_3, \beta_4\), and \(\beta_5\)-is nonzero? Test using \(\alpha=.05\).
b. Test \(H_0: \beta_4=0\) against \(H_{\mathrm{a}}: \beta_4 \neq 0\). Use \(\alpha=.01\).
c. Test \(H_0: \beta_5=0\) against \(H_{\mathrm{a}}: \beta_5 \neq 0\). Use \(\alpha=.01\).
d. Use graphs to explain the consequences of the tests in parts b and c.
ANSWER:Step 1 of 5
a) A better method is to conduct a test of hypothesis involving all the 
(except 
The elements of the global test of the model follow:
