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 ( ), the number of years of education received ( ), the number of years at the previous job ( ), a dummy variable for marital status ( 1 = married, 0 = otherwise), a dummy variable for head of household ( 1 = yes, 0 = no)and a dummy variable for management position ( 1 = yes, 0 = no). The coefficient of multiple determination ( )for the regression model using each of the 6 variables 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:
-Referring to Scenario 15-6, the variable X3 should be dropped to remove collinearity?

Question

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 (  ), the number of years of education received (  ), the number of years at the previous job (  ), a dummy variable for marital status (  1 = married, 0 = otherwise), a dummy variable for head of household (  1 = yes, 0 = no)and a dummy variable for management position (  1 = yes, 0 = no). The coefficient of multiple determination (  )for the regression model using each of the 6 variables  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: 
-Referring to Scenario 15-6, the variable X3 should be dropped to remove collinearity?

Quizplus · Accepted Answer

The presence of collinearity cannot be determined solely based on the coefficient of multiple determination or the R-squared value. The best-subset regression analysis may provide more information on which variables to include in the final model, but it does not necessarily indicate the presence of collinearity. Therefore, there is not enough information to determine whether or not variable X3 should be dropped to remove collinearity. The question does not provide information regarding collinearity among variables. The given information only includes the coefficient of multiple determination and results from best-subset regression. Therefore, it is not possible to determine if X3 should be dropped to address collinearity.

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