Chapter 2 Exercises

1. Load the Boston housing data set from the pdp package. These data come from a classic paper that analyzed the relationship between several characteristics (e.g., crime rate, average rooms per dwelling, property tax value) and the median value of homes within a census tract (cmedv). See ?pdp::boston for details and further references.

   • What are the dimensions of this data set?
   • Perform some exploratory data analysis on this data set (be sure to assess the distribution of the target variable cmedv).

2. Split the Boston housing data into a training set and test set using a 70-30% split.

   • How many observations are in the training set and test set?
   • Compare the distribution of cmedv between the training set and test set.

3. Load the spam data set from the kernlab package.

   • What is the distribution of the target variable (type) across the entire data set?
   • Create a 70/30 training/test split stratified by the target variable.
   • Compare the distribution of the target variable between the training set and test set.

4. Using the Boston housing training data created in 2), fit a linear regression model that use all available features to predict cmedv.

   • Create a model with lm(), glm(), and caret::train().
   • How do the coefficients compare across these models?
   • How does the MSE/RMSE compare across these models?
   • Which method is caret::train() using to fit a linear regression model?

5. Using the Boston housing training data created in exercise 2), perform a 10-fold cross-validated linear regression model, repeated 5 times, that uses all available features to predict cmedv.

   • What is the average RMSE across all 50 model iterations?
   • Plot the distribution of the RMSE across all 50 model iterations.
   • Describe the results.
   • Repeat this exercise for the spam data from exercise 3); since the target (type) is binary, be sure to use a more appropriate metric (e.g., AUC or misclassification error).

6. Repeat exercise 5) on the Boston housing data; however, instead of a linear regression model, use a k-nearest neighbor model that executes a hyperparameter grid search where k ranges from 2–20. How does this model’s results compare to the linear regression results?