Credit Scores (regression tree). A consumer advocacy agency, Equitable Ernest, is interested in providing a service that allows an individual to estimate his or her own credit score (a continuous measure used by banks, insurance companies, and other businesses when granting loans, quoting premiums, and issuing credit). Data from several individuals has been collected. The variables in these data are listed in the following table.

Variable	Description
BureauInquiries	number of inquiries about an individuals credit
CreditUsage	percent of an individuals credit used
TotalCredit	total amount of credit available to individual
CollectedReports	number of times an unpaid bill was reported to collection agency
MissedPayments	number of missed payments
HomeOwner	1 if individual is homeowner. 0 if not
CreditAge	average age of individuals credit
TimeOnJob	how long the individual has been continuously employed
CreditScore	score between 300 and 850 with larger number representing increased credit worthiness

Predict the individuals credit scores using an individual regression tree. Use CreditScore as the target (or response) variable and all the other relevant variables as input variables.

1. In the construction parameters of the tree, set the minimum number of records in a terminal node to be 244. What is the RMSE of the best-pruned tree on the validation data (a static validation set or through a 10-fold cross-validation procedure) and on the test set? Discuss the implication of these calculations.

2. Consider an individual with 5 credit bureau inquiries, has used 10% of her available credit, has $14,500 of total available credit, has no collection reports or missed payments, is a homeowner, has an average credit age of 6.5 years, and has worked continuously for the past 5 years. Using the best-pruned tree from part (a), what is the predicted credit score for this individual?

3. Repeat the construction of an individual regression tree, but now set the minimum number of records in a terminal node to be 1. How does the RMSE of the best-pruned tree on the test set compare to the analogous measure from part (a)? In terms of number of decision nodes, how does the size of the best-pruned tree compare to the size of the best-pruned tree from part (a)?