Classwork 8

Decision Trees

Author

Byeong-Hak Choe

Published

March 25, 2026

Modified

March 30, 2026

Setup

library(tidyverse)
library(janitor)
library(rpart)
library(rpart.plot)
library(broom)

library(DT)
library(rmarkdown)
library(hrbrthemes)
library(ggthemes)

theme_set(
  theme_ipsum()
)

scale_colour_discrete <- function(...) scale_color_colorblind(...)
scale_fill_discrete <- function(...) scale_fill_colorblind(...)

Packages

library(tidyverse)
library(janitor)
library(rpart)
library(rpart.plot)
library(broom)
library(skimr)

Part 1. Regression Tree with MLB Batting Data

MLB Batting Data

mlb_data <- read_csv(
  "http://bcdanl.github.io/data/mlb_fg_batting_2022.csv"
) |>
  clean_names() |>
  mutate(across(bb_percent:k_percent, readr::parse_number))

mlb_data |> 
  paged_table()

Variable Description

  • w_oba: weighted on-base average, a summary measure of offensive performance
  • bb_percent: walk percentage
  • k_percent: strikeout percentage
  • iso: isolated power
  • avg: batting average
  • obp: on-base percentage
  • slg: slugging percentage
  • war: wins above replacement


Explore the variables

mlb_data |>
  select(w_oba, bb_percent, k_percent, iso) |>
  skimr::skim()
Data summary
Name select(mlb_data, w_oba, b…
Number of rows 157
Number of columns 4
_______________________
Column type frequency:
numeric 4
________________________
Group variables None

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
w_oba 0 1 0.33 0.04 0.25 0.31 0.33 0.35 0.44 ▃▇▇▃▁
bb_percent 0 1 8.80 2.97 3.50 6.50 8.60 11.00 20.30 ▆▇▆▁▁
k_percent 0 1 20.47 5.89 8.10 16.10 19.90 24.80 36.10 ▃▇▇▅▁
iso 0 1 0.17 0.06 0.05 0.12 0.17 0.20 0.35 ▃▇▇▂▁ 
mlb_data |>
  ggplot(aes(x = iso, y = w_oba)) +
  geom_point(alpha = 0.6) +
  geom_smooth(method = lm,
              color = 'steelblue',
              fill = 'steelblue') +
  geom_smooth(color = 'red4',
              fill = 'red4') +
  labs(
    title = "wOBA and ISO",
    x = "ISO",
    y = "wOBA"
  )

Question 1. Fit an initial regression tree

Fit a simple regression tree using three predictors, bb_percent, k_percent, and iso.

  • Do not specify any control options in rpart().
# CODE HERE

Answer the following in complete sentences:

  1. Which variable appears at the first split?
  2. What does that suggest about the predictor’s importance in this tree?
  3. Choose one terminal node and explain what its predicted value means.


Question 2. Grow a larger tree

Now let the algorithm grow a much more flexible tree.

# CODE HERE

Answer the following:

  1. Compared with the first tree, is this tree more or less complex?
  2. Why might a very large tree be a problem for out-of-sample prediction?
  3. Looking at plotcp(), what kind of tree are we usually trying to choose: the biggest tree, the smallest tree, or a tree that balances fit and complexity?


Question 3. Fine-tune tree growth before pruning

Before pruning, try a few different tree-growth settings. This is a simple form of hyperparameter tuning. The goal is to see how choices like minsplit and maxdepth affect the size of the tree and the cross-validated error.

reg_tuning_grid <- tribble(
  ~minsplit, ~maxdepth,
  20,        4,
  20,        6,
  40,        4,
  40,        6
)
# CODE HERE

Answer the following:

  1. Which combination of minsplit and maxdepth gives the smallest cross-validated error?
  2. What does the xerror column represent? Why do we often use it when choosing the pruning parameter?
  3. Does a deeper tree always give the best xerror?
  4. Based on this table, which setting would you carry forward to pruning, and why?


Question 4. Prune the tuned tree

  • Fit a decision tree using the hyperparameter setting you prefer from Question 3.

  • Then prune the tuned tree.

# CODE HERE

Compare the tuned unpruned tree and the pruned tree.

  • What became simpler after pruning?
  • Why can a pruned tree sometimes predict better on new data even if it fits the training data less closely?
  • Did your earlier hyperparameter choices seem to matter for the final pruned result?



Part 2. Classification Tree with MLB Batted-Ball Data

MLB batted-ball data

batted_ball_data <- read_csv(
  "http://bcdanl.github.io/data/mlb_batted_balls_2022.csv"
) |>
  mutate(is_hr = as.factor(events == "home_run")) |>
  filter(
    !is.na(launch_angle),
    !is.na(launch_speed),
    !is.na(is_hr)
  )

batted_ball_data |> 
  paged_table()
batted_ball_data |> 
  count(is_hr) 
# A tibble: 2 × 2
  is_hr     n
  <fct> <int>
1 FALSE  6702
2 TRUE    333

Question 5. Visualize the classification problem

batted_ball_data |>
  ggplot(aes(x = launch_speed, y = launch_angle, color = is_hr)) +
  geom_point(alpha = 0.35) +
  labs(
    title = "Home Runs vs. Other Batted Balls",
    x = "Launch speed",
    y = "Launch angle",
    color = "Home run?"
  )

Based on the scatterplot, where do home runs seem more likely to happen? Describe the rough region using launch speed and launch angle.


Question 6. Train-test split

  • Divide the batted_ball_data data.frame into training and test data.frames.
    • Use dtrain and dtest for training and test data.frames, respectively.
    • 70% of observations in the batted_ball_data are assigned to dtrain; the rest is assigned to dtest.
# CODE HERE


Question 7. Fit a classification tree

Fit a simple classification tree using three predictors, launch_speed, launch_angle, and iso.

  • Do not specify any control options in rpart().

  • Which predictor appears to play a larger role near the top of the tree?

# CODE HERE


Question 8. Tuning

Tune a classfication tree with the following hyperparameter settings:

  • cp = 0.0005
  • minsplit = 30
  • maxdepth = 5

Is the tuned tree more complex?

# CODE HERE


Question 9. Classification

  • Build two classifiers using the original classification tree and tuned classification trees.

  • Compare the original classification tree and the tuned classification tree.

# CODE HERE



Discussion

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