We could change the number of trees grown by randomForest() using the ntree argument:

bag.boston <- randomForest(medv ~ ., data = Boston, subset = train, mtry = 13, ntree = 25)
yhat.bag <- predict(bag.boston, newdata = Boston[-train,])
mean((yhat.bag - boston.test)^2)
[1] 23.66716

Growing a random forest proceeds in exactly the same way, except that we use a smaller value of the mtry argument. By default, randomForest() uses \(p/3\) variables when building a random forest of regression trees, and \(\sqrt p\) variables when building a random forest of classification trees. Here we use mtry = 6.

set.seed(1)
rf.boston <- randomForest(medv ~ ., data = Boston, subset = train, mtry = 6, importance = TRUE)
yhat.rf <- predict(rf.boston, newdata = Boston[-train,])
mean((yhat.rf - boston.test)^2)
[1] 19.62021

The test set MSE is 19.62; this indicates that random forests yielded an improvement over bagging in this case.

Questions

• With the mtcars data set, sample the indices for the training set and store them in train (70-30 split).
• Train a random forest model on the training set with mpg as the independent variable and all other variables as dependent variables.
  • Set the number of trees on 100.
  • Set the number of variables per tree on 4
  • Set the argument importance to TRUE
  • Store the model in fit.
• Calculate the MSE on the test set and store the result in test.mse.

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Assume that:

• The randomForest library has been loaded
• The mtcars data set has been loaded and attached