In the following regression, which are the three best predictors? $$\begin{array} { l r r r r }
\hline \text { Variables } & \text { Coefficients } & \text { Std. Error } & t ( d f = 81 ) & p \text {-value } \
\hline \text { Intercept } & 9.8080 & 16.9900 & 0.577 & .5654 \
\text { NumCyl } & - 1.6804 & 0.5757 & - 2.919 & .0045 \
\text { HPMax } & - 0.0369 & 0.0140 & - 2.630 & .0102 \
\text { ManTran } & 0.2868 & 1.2802 & 0.224 & .8233 \
\text { Length } & 0.1109 & 0.0601 & 1.845 & .0686 \
\text { Wheelbase } & - 0.0701 & 0.1714 & - 0.409 & .6836 \
\text { Width } & 0.4079 & 0.2922 & 1.396 & 1665 \
\text { RearStRm } & - 0.0085 & 0.2018 & - 0.042 & .9666 \
\text { Weight } & - 0.0025 & 0.0020 & - 1.266 & .2090 \
\text { Domestic } & - 1.2291 & 1.1391 & - 1.079 & .2838 \
\hline
\end{array}$$
A)ManTran, Wheelbase, RearStRm
B)ManTran, Length, Width
C)NumCyl, HPMax, Length
D)Cannot be ascertained from given information

Question

In the following regression, which are the three best predictors? $$\begin{array} { l r r r r } 
\hline \text { Variables } & \text { Coefficients } & \text { Std. Error } & t ( d f = 81 ) & p \text {-value } \
\hline \text { Intercept } & 9.8080 & 16.9900 & 0.577 & .5654 \
\text { NumCyl } & - 1.6804 & 0.5757 & - 2.919 & .0045 \
\text { HPMax } & - 0.0369 & 0.0140 & - 2.630 & .0102 \
\text { ManTran } & 0.2868 & 1.2802 & 0.224 & .8233 \
\text { Length } & 0.1109 & 0.0601 & 1.845 & .0686 \
\text { Wheelbase } & - 0.0701 & 0.1714 & - 0.409 & .6836 \
\text { Width } & 0.4079 & 0.2922 & 1.396 & 1665 \
\text { RearStRm } & - 0.0085 & 0.2018 & - 0.042 & .9666 \
\text { Weight } & - 0.0025 & 0.0020 & - 1.266 & .2090 \
\text { Domestic } & - 1.2291 & 1.1391 & - 1.079 & .2838 \
\hline
\end{array}$$
A)ManTran, Wheelbase, RearStRm
B)ManTran, Length, Width
C)NumCyl, HPMax, Length
D)Cannot be ascertained from given information

Quizplus · Accepted Answer

In order to determine the best predictors, we should look for the variables with the highest values of t-statistics since higher t-statistics mean lower p-values and more significant predictors. Based on that, NumCyl and HPMax have the highest t-statistics of -2.919 and -2.630 respectively, both of which have p-values less than 0.05. Length also has a relatively high t-statistic of 1.845, although its p-value is 0.0686, which is slightly above 0.05. Therefore, the three best predictors are NumCyl, HPMax, and Length.

In the Following Regression, Which Are the Three Best Predictors