Palanquin Auto is a national used 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 Problem 25.

Predict the pre-owned car prices using k-nearest neighbors. Set aside 50% of the data as a test set and use 50% of the data for training and validation.

a. Based on all the input variables, determine the value of k that minimizes the RMSE in a validation procedure.

b. Experiment with different subsets of variables as input features and re-calibrate the value of k to minimize the RMSE. How does this k-nearest neighbors model compare to the model obtained in part (a)?

c. For the best-performing k-nearest neighbors model in the validation procedure, what is the RMSE on the test set?

Problem 25

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.

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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