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

question 53

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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)( Y ) and the independent variables are the age of the worker (X1)\left( X _ { 1 } \right) , the number of years of education received (X2)\left( X _ { 2 } \right) , the number of years at the previous job (X3)\left( X _ { 3 } \right) , a dummy variable for marital status ( X4:1=X _ { 4 } : 1 = married, 0=0 = otherwise), a dummy variable for head of household (X5:1=\left( X _ { 5 } : 1 = \right. yes, 0=0 = no) and a dummy variable for management position (X6:1=\left( X _ { 6 } : 1 = \right. yes, 0=0 = no )) .

The coefficient of multiple determination (Rj2)\left( R _ { j } ^ { 2 } \right) for the regression model using each of the 6 variables XjX _ { j } as the dependent variable and all other XX variables as independent variables are, respectively, 0.2628,0.1240,0.2404,0.3510,0.33420.2628,0.1240,0.2404,0.3510,0.3342 and 0.09930.0993 .

The partial results from best-subset regression are given below:
 Model  R Square  Adj. R Square  Std. Error  X1X5X6 0.45680.411618.3534 X1X2X5X6 0.46970.409118.3919 X1X3X5X6 0.46910.408418.4023 X1X2X3X5X6 0.48770.412318.3416 X1X2X3X4X5X6 0.49490.403018.4861\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 all six independent variables
should be selected using the adjusted r2 statistic.

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