2. A sociologist is interested in the historical relationships between characteristics of var- ious occupations. In particular, they wish to model the Pineo-Porter prestige score (a measure of the prestige of an occupation with higher values indicating higher prestige) as the response (y) variable. The researcher has access to data on each of a range of occupations, including: - y - Pineo-Porter prestige score education - Average duration of education of those in the occupation, in years income - Average income of those in the occupation, in Canadian dollars women - Percentage of those in the occupation who were women type - Type of occupation. A factor with levels: bc (Blue Collar); prof (Profes- sional, Managerial, and Technical); wc (White Collar). The sociologist ran a forward selection algorithm to decide on the variables to be included in their final model. The output of the algorithm is printed on the next two pages. Forward Selection Method Step 0: AIC = 837.5078 y 1 Variable DF AIC Sum Sa RSS R-Sq Adj. R-S. 1 1 education type income women 703.342 724.290 772.624 838.312 21282.471 19775.594 14021.617 343.887 7064.405 8571.281 14325.259 28002.988 0.751 0.698 0.495 0.012 0.74 0.69 0.48 0.00 1 1 Step 1 : AIC = 703.3419 education Variable DF AIC Sum Sa RSS R-Sq Adj. R-Sq 1 income type women 1 676.669 686.997 694.133 1791.966 1324.358 763.477 5272.439 5740.047 6300.927 0.814 0.798 0.778 0.810 0.791 0.773 1 Step 2 : AIC = 676.6695 education + income Variable DF AIC Sum Sa RSS R-Sq Adj. R-Sq 1 type women 669.015 678.477 591.163 10.371 4681.276 5262.068 0.835 0.814 0.828 0.808 1 Step 3: AIC = 669.0151 education + income + type Variable DF AIC Sum Sa RSS R-Sq Adj. R-Sq women 1 670.967 2.288 4678.988 0.835 0.826 CONTINUED OVERLEAF/ 5 Final Model Output Model Summary R R-Squared Adj. R-Squared Pred R-Squared 0.914 0.835 0.828 0.816 RMSE Coef. Var MSE MAE 7.095 14.991 50.336 5.527 RMSE: Root Mean Square Error MSE: Mean Square Error MAE: Mean Absolute Error Sum of Squares DF Mean Square F Sig. 4 117.537 0.0000 Regression Residual Total 23665.599 4681.276 28346.876 5916.400 50.336 93 97 Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) type 2 19775.6 9887.8 196.435 1t) (Intercept) -0.6229292 5.2275255 -0.119 0.905 typeprof 6.0389707 3.8668551 1.562 0.122 typewc -2.7372307 2.5139324 -1.089 0.279 education 3.6731661 0.6405016 5.735 1.21e-07 *** income 0.0010132 0.0002209 4.586 1.40e-05 *** Residual standard error: 7.095 on 93 degrees of freedom (4 observations deleted due to missingness) Multiple R-squared: 0.8349, Adjusted R-squared: 0.8278 F-statistic: 117.5 on 4 and 93 DF, p-value: F) type 2 19775.6 9887.8 196.435 1t) (Intercept) -0.6229292 5.2275255 -0.119 0.905 typeprof 6.0389707 3.8668551 1.562 0.122 typewc -2.7372307 2.5139324 -1.089 0.279 education 3.6731661 0.6405016 5.735 1.21e-07 *** income 0.0010132 0.0002209 4.586 1.40e-05 *** Residual standard error: 7.095 on 93 degrees of freedom (4 observations deleted due to missingness) Multiple R-squared: 0.8349, Adjusted R-squared: 0.8278 F-statistic: 117.5 on 4 and 93 DF, p-value:
