SCENARIO 15-6 Given Below Are Results from the Regression Analysis $( Y )$

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff $( Y )$ and the independent variables are the age of the worker $\left( X _ { 1 } \right)$ , the number of years of education received $\left( X _ { 2 } \right)$ , the number of years at the previous job $\left( X _ { 3 } \right)$ , a dummy variable for marital status ( $X _ { 4 } : 1 =$ married, $0 =$ otherwise), a dummy variable for head of household $\left( X _ { 5 } : 1 = \right.$ yes, $0 =$ no) and a dummy variable for management position $\left( X _ { 6 } : 1 = \right.$ yes, $0 =$ no $)$ .

The coefficient of multiple determination $\left( R _ { j } ^ { 2 } \right)$ for the regression model using each of the 6 variables $X _ { j }$ as the dependent variable and all other $X$ variables as independent variables are, respectively, $0.2628,0.1240,0.2404,0.3510,0.3342$ and $0.0993$ .

The partial results from best-subset regression are given below:
$\begin{array}{|l|r|r|r|}\hline {\text { Model }} & \text { R Square } & \text { Adj. R Square } & \text { Std. Error } \\\hline \text { X1X5X6 } & 0.4568 & 0.4116 & 18.3534 \\\hline \text { X1X2X5X6 } & 0.4697 & 0.4091 & 18.3919 \\\hline \text { X1X3X5X6 } & 0.4691 & 0.4084 & 18.4023 \\\hline \text { X1X2X3X5X6 } & 0.4877 & 0.4123 & 18.3416 \\\hline \text { X1X2X3X4X5X6 } & 0.4949 & 0.4030 & 18.4861 \\\hline\end{array}$

-Referring to Scenario 15-6, the model that includes $X _ { 1 } , X _ { 5 } \text { and } X _ { 6 }$ should be selected using the
adjusted $r ^ { 2 }$ statistic.