Question

The following MS Excel outputs were generated for a multiple linear regression analysis. (Use the exact values found in the MS Excel output.) ANOVA egin{tabular}{|l|c|c|c|c|c|} hline & df & SS & MS & ( F ) & Significance ( F ) \ hline Regression & 2 & ( star star ) & ( 177.607 ) & ( star star ) & ( 0.002 ) \ hline Residual & ( star star ) & ( 76.433 ) & ( star star ) & & \ hline Total & 9 & ( 431.647 ) & & & \ hline end{tabular} egin{tabular}{|l|l|l|c|c|} hline & Coefficients & Standard Error & ( mathbf{t} ) Stat & P-Value \ hline Intercept & ( -8.175 ) & ( 4.206 ) & ( -1.944 ) & ( 0.093 ) \ hline ( mathbf{x 1} ) & ( 0.296 ) & ( 0.136 ) & ( 2.176 ) & ( 0.066 ) \ hline ( mathbf{x} mathbf{2} ) & ( 4.438 ) & ( 0.800 ) & ( 5.548 ) & ( 0.001 ) \ hline end{tabular} What model has been fitted to the data. [ egin{array}{l} E(y)=eta_{0}+eta_{1} x_{1}+eta_{2} sqrt{x_{1}} \ E(y)=eta_{0}+eta_{1} x_{1}+eta_{2} x_{1}^{2} \ E(y)=eta_{0}+eta_{1} x_{1}+eta_{2} 3 x_{1} \ E(y)=eta_{0}+eta_{1} x_{1}+eta_{2} 2 x_{1} \ E(y)=eta_{0}+eta_{1} x_{1}+eta_{2} x_{2} end{array} ] What is the least-squares prediction equation? [ dot{y}= ] Fill in the blanks in the ANOVA table. (Round your ( F ) statistic to two decimal places.) ANOVA Use the ANOVA table to test for a significant regression using ( alpha=0.05 ). State the null and alternative hypotheses. [ egin{array}{l} H_{0}: ext { At least one of } eta_{1}, eta_{2} ext { is not } 0 . \ H_{a}: eta_{1}=eta_{2}=0 \ H_{0}: eta_{1}=eta_{2}=0 \ H_{a}: ext { At least one of } eta_{1}, eta_{2} ext { is not } 0 ext {. } \ H_{0}: ext { At least one of } eta_{1}, eta_{2} ext { is not } 0 \ H_{a}: eta_{1}>eta_{2}>0 \ H_{0}: eta_{1}=eta_{2} \ H_{a}: eta_{1} eq eta_{2} \ H_{0}: eta_{1}<eta_{2} \ H_{a}: eta_{1} eq eta_{2} end{array} ] Find the test statistic. (Round your answer to two decimal places.) ( F= ) Find the approximate p-value for the test. ( p )-value ( <0.005 ) ( 0.005<p )-value ( <0.010 ) ( 0.010<p )-value ( <0.025 ) ( 0.025<p )-value ( <0.050 ) ( 0.050<p )-value ( <0.100 ) ( p )-value ( >0.100 ) State your conclusion. ( mathrm{H}_{0} ) is rejected. There is insufficient evidence to indicate that the regression is significant. ( mathrm{H}_{0} ) is rejected. There is sufficient evidence to indicate that the regression is significant. ( mathrm{H}_{0} ) is not rejected. There is insufficient evidence to indicate that the regression is significant. ( mathrm{H}_{0} ) is not rejected. There is sufficient evidence to indicate that the regression is significant. You may need to use the appropriate appendix table or technology to answer this question.

          The following MS Excel outputs were generated for a multiple linear regression analysis. (Use the exact values found in the MS Excel output.)
ANOVA
egin{tabular}{|l|c|c|c|c|c|}
hline & df & SS & MS & ( F ) & Significance ( F ) \
hline Regression & 2 & ( star star ) & ( 177.607 ) & ( star star ) & ( 0.002 ) \
hline Residual & ( star star ) & ( 76.433 ) & ( star star ) & & \
hline Total & 9 & ( 431.647 ) & & & \
hline
end{tabular}
egin{tabular}{|l|l|l|c|c|}
hline & Coefficients & Standard Error & ( mathbf{t} ) Stat & P-Value \
hline Intercept & ( -8.175 ) & ( 4.206 ) & ( -1.944 ) & ( 0.093 ) \
hline ( mathbf{x 1} ) & ( 0.296 ) & ( 0.136 ) & ( 2.176 ) & ( 0.066 ) \
hline ( mathbf{x} mathbf{2} ) & ( 4.438 ) & ( 0.800 ) & ( 5.548 ) & ( 0.001 ) \
hline
end{tabular}
What model has been fitted to the data.
[
egin{array}{l}
E(y)=eta_{0}+eta_{1} x_{1}+eta_{2} sqrt{x_{1}} \
E(y)=eta_{0}+eta_{1} x_{1}+eta_{2} x_{1}^{2} \
E(y)=eta_{0}+eta_{1} x_{1}+eta_{2} 3 x_{1} \
E(y)=eta_{0}+eta_{1} x_{1}+eta_{2} 2 x_{1} \
E(y)=eta_{0}+eta_{1} x_{1}+eta_{2} x_{2}
end{array}
]
What is the least-squares prediction equation?
[
dot{y}=
]
Fill in the blanks in the ANOVA table. (Round your ( F ) statistic to two decimal places.)
ANOVA
Use the ANOVA table to test for a significant regression using ( alpha=0.05 ).
State the null and alternative hypotheses.
[
egin{array}{l}
H_{0}: 	ext { At least one of } eta_{1}, eta_{2} 	ext { is not } 0 . \
H_{a}: eta_{1}=eta_{2}=0 \
H_{0}: eta_{1}=eta_{2}=0 \
H_{a}: 	ext { At least one of } eta_{1}, eta_{2} 	ext { is not } 0 	ext {. } \
H_{0}: 	ext { At least one of } eta_{1}, eta_{2} 	ext { is not } 0 \
H_{a}: eta_{1}>eta_{2}>0 \
H_{0}: eta_{1}=eta_{2} \
H_{a}: eta_{1} 
eq eta_{2} \
H_{0}: eta_{1}<eta_{2} \
H_{a}: eta_{1} 
eq eta_{2}
end{array}
]
Find the test statistic. (Round your answer to two decimal places.)
( F= )
Find the approximate p-value for the test.
( p )-value ( <0.005 )
( 0.005<p )-value ( <0.010 )
( 0.010<p )-value ( <0.025 )
( 0.025<p )-value ( <0.050 )
( 0.050<p )-value ( <0.100 )
( p )-value ( >0.100 )
State your conclusion.
( mathrm{H}_{0} ) is rejected. There is insufficient evidence to indicate that the regression is significant.
( mathrm{H}_{0} ) is rejected. There is sufficient evidence to indicate that the regression is significant.
( mathrm{H}_{0} ) is not rejected. There is insufficient evidence to indicate that the regression is significant.
( mathrm{H}_{0} ) is not rejected. There is sufficient evidence to indicate that the regression is significant.
You may need to use the appropriate appendix table or technology to answer this question.

The following MS Excel outputs were generated for a multiple linear regression analysis. (Use the exact values found in the MS Excel output.)
ANOVA
egintabular|l|c|c|c|c|c|
hline df SS MS ( F ) Significance ( F ) hline Regression 2 ( star star ) ( 177.607 ) ( star star ) ( 0.002 ) hline Residual ( star star ) ( 76.433 ) ( star star ) hline Total 9 ( 431.647 ) hline
endtabular
egintabular|l|l|l|c|c|
hline Coefficients Standard Error ( mathbft ) Stat P-Value hline Intercept ( -8.175 ) ( 4.206 ) ( -1.944 ) ( 0.093 ) hline ( mathbfx 1 ) ( 0.296 ) ( 0.136 ) ( 2.176 ) ( 0.066 ) hline ( mathbfx mathbf2 ) ( 4.438 ) ( 0.800 ) ( 5.548 ) ( 0.001 ) hline
endtabular
What model has been fitted to the data.
[
eginarrayl
E(y)=eta0+eta1 x1+eta2 sqrtx1 E(y)=eta0+eta1 x1+eta2 x1^2 E(y)=eta0+eta1 x1+eta2 3 x1 E(y)=eta0+eta1 x1+eta2 2 x1 E(y)=eta0+eta1 x1+eta2 x2
endarray
]
What is the least-squares prediction equation?
[
doty=
]
Fill in the blanks in the ANOVA table. (Round your ( F ) statistic to two decimal places.)
ANOVA
Use the ANOVA table to test for a significant regression using ( alpha=0.05 ).
State the null and alternative hypotheses.
[
eginarrayl
H0: ext At least one of eta1, eta2 ext is not 0 . Ha: eta1=eta2=0 H0: eta1=eta2=0 Ha: ext At least one of eta1, eta2 ext is not 0 ext . H0: ext At least one of eta1, eta2 ext is not 0 Ha: eta1>eta2>0 H0: eta1=eta2 Ha: eta1
eq eta2 H0: eta1<eta2 Ha: eta1
eq eta2
endarray
]
Find the test statistic. (Round your answer to two decimal places.)
( F= )
Find the approximate p-value for the test.
( p )-value ( <0.005 )
( 0.005<p )-value ( <0.010 )
( 0.010<p )-value ( <0.025 )
( 0.025<p )-value ( <0.050 )
( 0.050<p )-value ( <0.100 )
( p )-value ( >0.100 )
State your conclusion.
( mathrmH0 ) is rejected. There is insufficient evidence to indicate that the regression is significant.
( mathrmH0 ) is rejected. There is sufficient evidence to indicate that the regression is significant.
( mathrmH0 ) is not rejected. There is insufficient evidence to indicate that the regression is significant.
( mathrmH0 ) is not rejected. There is sufficient evidence to indicate that the regression is significant.
You may need to use the appropriate appendix table or technology to answer this question.

Added by Wade D.

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