The Table Below Shows Data for N = 20 Observations

question 33

Essay

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.

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