We can also use the regsubsets() function to perform forward stepwise or backward stepwise selection, using the argument method="forward" or method="backward".

regfit.fwd <- regsubsets(Salary ~ ., data = Hitters, nvmax = 19, method = "forward")
summary(regfit.fwd)
regfit.bwd <- regsubsets(Salary ~ ., data = Hitters, nvmax = 19, method = "backward")
summary(regfit.bwd)

For instance, we see that using forward stepwise selection, the best one variable model contains only CRBI, and the best two-variable model additionally includes Hits. For this data, the best one-variable through six variable models are each identical for best subset and forward selection. However, the best seven-variable models identified by forward stepwise selection, backward stepwise selection, and best subset selection are different.

> coef(regfit.full, 7)
 (Intercept)         Hits        Walks       CAtBat 
  79.4509472    1.2833513    3.2274264   -0.3752350 
       CHits       CHmRun    DivisionW      PutOuts 
   1.4957073    1.4420538 -129.9866432    0.2366813 
> coef(regfit.fwd, 7)
 (Intercept)        AtBat         Hits        Walks 
 109.7873062   -1.9588851    7.4498772    4.9131401 
        CRBI       CWalks    DivisionW      PutOuts 
   0.8537622   -0.3053070 -127.1223928    0.2533404 
> coef(regfit.bwd, 7)
 (Intercept)        AtBat         Hits        Walks 
 105.6487488   -1.9762838    6.7574914    6.0558691 
       CRuns       CWalks    DivisionW      PutOuts 
   1.1293095   -0.7163346 -116.1692169    0.3028847 

Try applying forward and backward selection to the Boston dataset with medv as the response. Store the output in regfit.fwd and regfit.bwd respectively. Set the nvmax parameter to 13.

Assume that:

• The MASS and leaps libraries have been loaded
• The Boston dataset has been loaded and attached