Statistic
9.18 a) Using forward stepwise regression to find the best subset of predictor variables to predict job proficiency.
The Alpha-to-Enter significance level was set at 0.05 and the Alpha-to-Leave significance level was set at 0.10. The first predictor entered into the stepwise model is X3. SAS tells us that the estimated intercept is -106.13 and the estimated slope for X3 is 1.968. The R2-value is 0.8047, mean square error is 76.87. The second predictor entered into the stepwise model is X1. The estimated intercept is -127.596, the estimated slope for X1 is 0.3485 and the slope for X3 is 1.8232. The R2-value is 0.933 and the mean square error is 27.575. The final predictor entered is X4. The estimated intercept is -124.20, the estimated slope for X4 is 0.5174, the slope for X1 adjusts to 0.2963 and the slope for X3 adjusts to 1.357. The R2-value is 0.9615 and the mean square error is 16.581. Predictor X2 is not eligible for entry into the stepwise model because its t-test P-value doesn’t meet the 0.05 significance level. We prefer the model containing the three predictors X3, X1 and X4, because its R2-value is 0.9615, which is higher than 0.9330 (the model containing just two predictors X3 and X1) and 0.8047(the model containing just one predictor X3). Checking the mean square error of the three models we find that the model we selected as best model has the smallest mean square error 16.581, which is good. To sum up, using forward stepwise regression, the best model to predict the job proficiency is Y= -124.20 + 0.2963X1 + 1.357X3 + 0.5174X4, a model containing predictor variables X1, X3 and X4.
b) Compare the best subset obtained from forward stepwise regression with that obtained from the adjusted R-square value criterion.
Above is the SAS output of the Adjusted R-Square Selection Method.
According to the adjusted R-square value criterion, the best model should be the model with
The Alpha-to-Enter significance level was set at 0.05 and the Alpha-to-Leave significance level was set at 0.10. The first predictor entered into the stepwise model is X3. SAS tells us that the estimated intercept is -106.13 and the estimated slope for X3 is 1.968. The R2-value is 0.8047, mean square error is 76.87. The second predictor entered into the stepwise model is X1. The estimated intercept is -127.596, the estimated slope for X1 is 0.3485 and the slope for X3 is 1.8232. The R2-value is 0.933 and the mean square error is 27.575. The final predictor entered is X4. The estimated intercept is -124.20, the estimated slope for X4 is 0.5174, the slope for X1 adjusts to 0.2963 and the slope for X3 adjusts to 1.357. The R2-value is 0.9615 and the mean square error is 16.581. Predictor X2 is not eligible for entry into the stepwise model because its t-test P-value doesn’t meet the 0.05 significance level. We prefer the model containing the three predictors X3, X1 and X4, because its R2-value is 0.9615, which is higher than 0.9330 (the model containing just two predictors X3 and X1) and 0.8047(the model containing just one predictor X3). Checking the mean square error of the three models we find that the model we selected as best model has the smallest mean square error 16.581, which is good. To sum up, using forward stepwise regression, the best model to predict the job proficiency is Y= -124.20 + 0.2963X1 + 1.357X3 + 0.5174X4, a model containing predictor variables X1, X3 and X4.
b) Compare the best subset obtained from forward stepwise regression with that obtained from the adjusted R-square value criterion.
Above is the SAS output of the Adjusted R-Square Selection Method.
According to the adjusted R-square value criterion, the best model should be the model with