HW 8

2. Model building: Using Minitab using the Ford data: Response is HwyMPG Vars R-Sq R-Sq (adj) R-Sq (pred) Mallows Cp S W e i g h t H o r s e p o w e r C y l i n d e r s D i s p l a c e m e n t M a n T r a n s G e a r s F W D 1 78.9 78.4 75.8 23.0 2.2294 X 1 74.6 74.0 71.7 35.7 2.4418 X 2 85.2 84.5 82.2 5.9 1.8890 X X 2 83.8 83.1 80.5 9.9 1.9730 X X 3 86.7 85.8 83.2 3.1 1.8076 X X X 3 85.5 84.5 82.0 6.8 1.8896 X X X 4 87.5 86.3 83.5 2.8 1.7769 X X X X 4 86.8 85.5 82.7 4.8 1.8235 X X X X 5 87.7 86.2 83.1 4.1 1.7832 X X X X X 5 87.6 86.0 82.5 4.6 1.7949 X X X X X 6 87.8 85.8 82.2 6.0 1.8037 X X X X X X 6 87.7 85.8 82.4 6.1 1.8056 X X X X X X 7 87.8 85.5 81.8 8.0 1.8279 X X X X X X X Adjusted R squared: Here, on the basis of the adjusted R squared value, we can see that highest adjusted R-squared value is 86.3 and if we select that model then the best subset model will have independent variables of weight, horsepower, cylinder and displacement. Mallows Cp: On the basis of Mallows Cp, Best MALO cp is the one closest to P (Number of IV+Slope). From the list of Mallows Cp values, we can see that 4.8 is the best Mallows Cp in terms of being closest to P (in this case 5) . If we use this model, it is using the following four variables to predict the highway mileage of the car: Weight, Horsepower, Cylinder, and FWD. So, combining both, we now have two models as the best predictors of highway mileage. We may now use these two models to further test our hypothesis and decide the fittest between the two. Step-wise regression using SPSS: