Predict the number of applications received using all other variables in the College data set.

The dataset, available in the ISLR2 library, contains statistics for a large number of US Colleges. It has 777 observations and 18 variables.

dim(College)
[1] 777  18

Questions

• Create a 70-30 train-test split of the College data set. Use a seed value of 1. Store the numeric vector with training data indices in train.idx.
• Fit a regression tree on the training data with Apps as dependent variable and all other variables as independent variables. Store the model in the variable tree.college.
• Perform cross-validation to determine the optimal level of tree complexity. Use a seed value of 1. Store the model in the variable cv.college.
• Interpret the results and store the optimal number of nodes in the variable size.cv.
  (note: try to avoid hardcoding and use e.g. the which.min() function to find the index of the tree size with the lowest value for the dev attribute)
• Prune the tree to obtain the desired number of nodes size.cv. Store the model in the variable prune.college.
• Use the pruned tree to make predictions on the test set. Store the predictions in the variable yhat.
• Finally, calculate the test set MSE. Store the result in the variable mse.

Assume that:

• The ISLR2 library has been loaded
• The College dataset has been loaded and attached