The table below shows data for n = 20 observations. $$\begin{array} { c c c }
\hline \mathrm { y } & \mathrm { x } 1 & \mathrm { x } 2 \
\hline 18 & 3 & 8 \
23 & 5 & 10 \
15 & 2 & 7 \
31 & 6 & 12 \
24 & 4 & 9 \
28 & 5 & 11 \
17 & 2 & 7 \
19 & 3 & 8 \
30 & 7 & 10 \
28 & 5 & 8 \
14 & 3 & 6 \
32 & 7 & 11 \
17 & 2 & 8 \
24 & 5 & 10 \
26 & 6 & 11 \
27 & 6 & 11 \
21 & 3 & 6 \
31 & 7 & 13 \
19 & 2 & 8 \
25 & 5 & 10 \
\hline
\end{array}$$ a. Use a first-order regression model to find a least squares prediction equation for the model.
b. Find a $95 \%$ confidence interval for the coefficient of $x _ { 1 }$ in your model. Interpret the result.
c. Find a $95 \%$ confidence interval for the coefficient of $x _ { 2 }$ in your model. Interpret the result.
d. Find $R ^ { 2 }$ and $R _ { a ^ { 2 } } ^ { 2 }$ and interpret these values.
e. Test the null hypothesis $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = 0$ against the alternative hypothesis $H _ { \mathrm { a } }$ : at least one $\beta _ { i } \neq 0$. Use $\alpha = .05$. Interpret the restilt.

Question

The table below shows data for n = 20 observations. $$\begin{array} { c c c } 
\hline \mathrm { y } & \mathrm { x } 1 & \mathrm { x } 2 \
\hline 18 & 3 & 8 \
23 & 5 & 10 \
15 & 2 & 7 \
31 & 6 & 12 \
24 & 4 & 9 \
28 & 5 & 11 \
17 & 2 & 7 \
19 & 3 & 8 \
30 & 7 & 10 \
28 & 5 & 8 \
14 & 3 & 6 \
32 & 7 & 11 \
17 & 2 & 8 \
24 & 5 & 10 \
26 & 6 & 11 \
27 & 6 & 11 \
21 & 3 & 6 \
31 & 7 & 13 \
19 & 2 & 8 \
25 & 5 & 10 \
\hline
\end{array}$$ a. Use a first-order regression model to find a least squares prediction equation for the model.
b. Find a $95 \%$ confidence interval for the coefficient of $x _ { 1 }$ in your model. Interpret the result.
c. Find a $95 \%$ confidence interval for the coefficient of $x _ { 2 }$ in your model. Interpret the result.
d. Find $R ^ { 2 }$ and $R _ { a ^ { 2 } } ^ { 2 }$ and interpret these values.
e. Test the null hypothesis $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = 0$ against the alternative hypothesis $H _ { \mathrm { a } }$ : at least one $\beta _ { i } \neq 0$. Use $\alpha = .05$. Interpret the restilt.

Quizplus · Accepted Answer

The Answer of The table below shows data for n = 20 observations. $$\begin{array} { c c c } 
\hline \mathrm { y } & \mathrm { x } 1 & \mathrm { x } 2 \
\hline 18 & 3 & 8 \
23 & 5 & 10 \
15 & 2 & 7 \
31 & 6 & 12 \
24 & 4 & 9 \
28 & 5 & 11 \
17 & 2 & 7 \
19 & 3 & 8 \
30 & 7 & 10 \
28 & 5 & 8 \
14 & 3 & 6 \
32 & 7 & 11 \
17 & 2 & 8 \
24 & 5 & 10 \
26 & 6 & 11 \
27 & 6 & 11 \
21 & 3 & 6 \
31 & 7 & 13 \
19 & 2 & 8 \
25 & 5 & 10 \
\hline
\end{array}$$ a. Use a first-order regression model to find a least squares prediction equation for the model.
b. Find a $95 \%$ confidence interval for the coefficient of $x _ { 1 }$ in your model. Interpret the result.
c. Find a $95 \%$ confidence interval for the coefficient of $x _ { 2 }$ in your model. Interpret the result.
d. Find $R ^ { 2 }$ and $R _ { a ^ { 2 } } ^ { 2 }$ and interpret these values.
e. Test the null hypothesis $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = 0$ against the alternative hypothesis $H _ { \mathrm { a } }$ : at least one $\beta _ { i } \neq 0$. Use $\alpha = .05$. Interpret the restilt.

The Table Below Shows Data for N = 20 Observations