1. Randomly divide the data in half, 132 training observations, 131 testing

set.seed(77)
baseball_split <- initial_split(baseball, prop = 0.5)
baseball_train <- training(baseball_split)

2. Create cross-validation object for 6-fold cross validation

baseball_cv <- vfold_cv(baseball_train, v = 6)

3. Create a model specification that tunes based on complexity, $\alpha$

tree_spec <- decision_tree(
  cost_complexity = tune(), 
  tree_depth = 10,
  mode = "regression") %>%
  set_engine("rpart")

4. Fit the model on the cross validation set

grid <- expand_grid(cost_complexity = seq(0.01, 0.05, by = 0.01))
model <- tune_grid(tree_spec,
                   Salary ~ Hits + Years + PutOuts + RBI + Walks + Runs,
                   grid = grid,
                   resamples = baseball_cv)

5. Choose $\alpha$ that minimizes the RMSE

model %>%
  collect_metrics() %>%
  filter(.metric == "rmse") %>%
  arrange(mean)

## # A tibble: 5 x 6
##   cost_complexity .metric .estimator  mean     n std_err
##             <dbl> <chr>   <chr>      <dbl> <int>   <dbl>
## 1            0.03 rmse    standard    391.     6    38.5
## 2            0.05 rmse    standard    399.     6    38.8
## 3            0.01 rmse    standard    399.     6    34.9
## 4            0.02 rmse    standard    402.     6    36.2
## 5            0.04 rmse    standard    404.     6    36.6

5. Choose $\alpha$ that minimizes the RMSE

model %>%
  collect_metrics() %>%
  filter(.metric == "rmse") %>%
  arrange(mean)

model %>%
  select_best(metric = "rmse")

## # A tibble: 1 x 1
##   cost_complexity
##             <dbl>
## 1            0.03

5. Choose $\alpha$ that minimizes the RMSE

model %>%
  collect_metrics() %>%
  filter(.metric == "rmse") %>%
  arrange(mean)

final_complexity <- model %>%
  select_best(metric = "rmse") %>%
  pull()

6. Fit the final model

final_spec <- decision_tree(
  cost_complexity = final_complexity,
  tree_depth = 10,
  mode = "regression") %>%
  set_engine("rpart")
final_model <- fit(final_spec,
                   Salary ~ Hits + Years + PutOuts + RBI + Walks + Runs,
                   data = baseball_train)

Final tree

Calculate RMSE on the test data

baseball_test <- testing(baseball_split)
final_model %>%
  predict(new_data = baseball_test) %>%
  bind_cols(baseball_test) %>%
  metrics(truth = Salary, estimate = .pred)

## # A tibble: 3 x 3
##   .metric .estimator .estimate
##   <chr>   <chr>          <dbl>
## 1 rmse    standard     363.   
## 2 rsq     standard       0.356
## 3 mae     standard     267.