A multiple regression model is a linear model with many predictors. In general, we write the model as
^y = B0 + B1x1 + B2x2 + · · · + Bkxk
The adjusted R-squared is a modified version of R-squared that has been adjusted for the number of predictors in the model. The adjusted R-squared increases only if the new term improves the model more than would be expected by chance. It decreases when a predictor improves the model by less than expected by chance.
Baby weights, Part IV. Exercise 8.3 considers a model that predicts a newborn’s weight using several predictors (gestation length, parity, age of mother, height of mother, weight of mother, smoking status of mother). The table below shows the adjusted R-squared for the full model as well as adjusted R-squared values for all models we evaluate in the first step of the backwards elimination process.
| N | Model | Adjusted R2 |
|---|---|---|
| 1 | Fullmodel | 0.2541 |
| 2 | No gestation | 0.1031 |
| 3 | No parity | 0.2492 |
| 4 | No age | 0.2547 |
| 5 | No height | 0.2311 |
| 6 | No weight | 0.2536 |
| 7 | No smokingstatus | 0.2072 |
Which, if any, variable should be removed from the model first?
Since age has R2 higher then full model, it can be eliminated.