Palanquin Auto is a national pre-owned car retailer that offers an online marketplace for customers interested in purchasing a preowned automobile. In an effort to reduce price negotiation, Palanquin collects data on automobile sales in an effort to set fair, competitive prices. The file palanquin contains data for the variables listed in the following table.

Predict the pre-owned car prices using an individual regression tree. Set aside 50%
of the data as a test set and use 50% of the data for training and validation. Categorical input variables with many possible categories can pose computational difficulties for regression trees, so exclude any categorical variable with more than 16 categorical values from consideration as an input variable.

a. Train a full regression tree and report its RMSE from a validation experiment.

b. Train a pruned regression tree and report its RMSE from a validation experiment.

c. Compare the RMSE from the full regression tree in part (a) to the RMSE from the pruned regression tree in part (b). Explain the difference.

d. Compute the RMSE of the pruned regression tree from part (b) on the test set.

e. Using the pruned tree settings from part (b), predict the sales price of a vehicle with the following variable values:

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Variable Price Year Manufacturer Model Condition Cylinders Fuel Odometer Drive Type Paint State Description Sales price of vehicle Model year of vehicle Name of company manufacturing vehicle (categorical) Model name of vehicle (categorical) Categorical variable describing condition of vehicle (fair, good, excellent, like new, new) Number of cylinders in engine Type of fuel used by vehicle (diesel, electric, gas, hybrid) Number of miles on vehicle's odometer Categorical variable indicating drivetrain (four wheel drive, front wheel drive, rear wheel drive) Categorical variable indicating Color of vehicle's paint State of the United States in which vehicle was sold