Evaluate a modeling procedure using n-fold cross-validation

In this exercise you will use splitPlan, the 3-fold cross validation plan from the previous exercise, to make predictions from a model that predicts mpg$cty from mpg$hwy.

If dframe is the training data, then one way to add a column of cross-validation predictions to the frame is as follows:

# Initialize a column of the appropriate length
dframe$pred.cv <- 0 

# k is the number of folds
# splitPlan is the cross validation plan

for(i in 1:k) {
  # Get the ith split
  split <- splitPlan[[i]]

  # Build a model on the training data 
  # from this split 
  # (lm, in this case)
  model <- lm(fmla, data = dframe[split$train,])

  # make predictions on the 
  # application data from this split
  dframe$pred.cv[split$app] <- predict(model, newdata = dframe[split$app,])
}

Cross-validation predicts how well a model built from all the data will perform on new data. As with the test/train split, for a good modeling procedure, cross-validation performance and training performance should be close.

Instructions

The data frame mpg, the cross validation plan splitPlan, and the function to calculate RMSE (rmse()) from one of the previous exercises is available in your workspace.

Run the 3-fold cross validation plan from splitPlan and put the predictions in the column mpg$pred.cv.
- Use lm() and the formula cty ~ hwy.
Create a linear regression model on all the mpg data (formula cty ~ hwy) and assign the predictions to mpg$pred.
Use rmse() to get the root mean squared error of the predictions from the full model (mpg$pred). Recall that rmse() takes two arguments, the predicted values, and the actual outcome.
Get the root mean squared error of the cross-validation predictions. Are the two values about the same?

Take Hint (-30xp)