Decision Tree Exercises in R: 18 Real-World Practice Problems

Explanation: rpart() infers the task from the response: a factor Species triggers classification (Gini by default), a numeric response would trigger regression. The formula Species ~ . says "use every other column as a predictor." Each printed line is a node: n is the count, loss the misclassified count at that node, yval the majority class, and the parenthesized vector is per-class probability. Asterisks mark terminal leaves.

Explanation: Because mpg is numeric, rpart() fits an anova (regression) tree by default and minimises within-node sum of squares. The printed deviance is the residual sum of squares at that node, and yval is the mean response. The first split on cyl mirrors what you would expect from EDA: heavier engines run lower mpg. You can force regression explicitly with method = "anova" if your response could be misinterpreted.

Explanation: rpart() does not natively handle NA in the response: those rows would be silently dropped from the model frame anyway, so cleaning first makes the row count explicit (111 of 153 retained). Predictor NAs could be handled via surrogate splits (covered later), but na.omit() is the simplest baseline. The first split on Temp is a strong signal that ozone formation is photochemical and temperature-driven.

Explanation: Even on 20 rows, rpart() finds a clean single-split rule on tenure: customers under 10 months are mostly churners, and longer-tenured customers are not. Notice monthly_charges and contract did not enter the tree because tenure dominated the impurity reduction at the root. The default cp = 0.01 and minsplit = 20 are gentle enough that tiny datasets often stop after one split. We will tune these in the next section.

Explanation: maxdepth counts edges from the root, so maxdepth = 2 permits at most one further split below each child of the root. The deeper Solar.R split present in the unconstrained tree is dropped here. maxdepth is a hard ceiling that bypasses cross-validation; it is useful when a stakeholder has a fixed display budget (a slide, a report) rather than a statistical motivation.

Explanation: Two parameters interact here. minsplit is the structural floor: a node with fewer than 5 observations is never considered for splitting. cp is the statistical floor: a candidate split is kept only if it reduces overall lack of fit by at least cp times the root deviance. Lowering both lets the tree grow until either floor is hit. This is the standard approach for "grow then prune": grow large with low cp, then prune back to the cross-validated optimum (Section 5).

Explanation: cp = 0.5 is unusually aggressive: only a split that cuts at least half of the root impurity survives. On iris, that single survivor is the textbook Petal.Length < 2.45 rule, which perfectly isolates setosa. Auditors and regulators often prefer this kind of one-line rule because it is trivially explainable and trivially testable, even if it groups versicolor and virginica together. Tune cp upward whenever interpretability outranks accuracy.

Explanation: fit$frame is the internal node table; each row is one node (internal or terminal), so nrow() is a clean size proxy. The default tree has 5 nodes (3 leaves), the deep tree balloons to 17 because the lower cp and minsplit = 2 permit splits that fit individual misclassified flowers. Most of those extra splits will fail cross-validation, which motivates the printcp / prune workflow in Section 5. Always grow then prune; never trust a tree fit at very low cp directly.

Explanation: rpart.plot() is purpose-built for rpart objects and is far more readable than the base plot.rpart() plus text.rpart() combination. By default it shows the predicted class, the per-class probability vector, and the percentage of training rows that land in each leaf, which is everything a non-technical reader needs to follow the tree. Tweak type (0-5), extra (0-104), and box.palette to control verbosity and colour. For high-stakes communication, extra = 104 adds the loss count to leaves.

Explanation: variable.importance is an unnormalised numeric vector indexed by predictor name, summing across both primary and surrogate splits. A predictor can score high even if it never won a primary split, because rpart credits surrogates that mimic the chosen split. To convert to a percentage, divide by the sum: round(100 * fit_mt$variable.importance / sum(fit_mt$variable.importance), 1). Cross-check against the printed tree: predictors that win primary splits should sit at the top.

Explanation: rpart.rules() walks every leaf and emits the conjunction of conditions that route a row there, alongside the predicted value. It is far easier to drop into a campaign brief than the indented printout of the fitted object. For multi-class problems it returns one column per class probability. If you want plain English output, post-process the data frame with glue::glue() or paste rules into a templated email. Keep in mind: every rpart.rules() row is mutually exclusive and collectively exhaustive over the training space.

Explanation: For a classification rpart, type = "class" returns the majority class at the leaf each row falls into, as a factor with the same levels as the training response. Without type, you would get the per-class probability matrix (the next exercise). Always pass newdata explicitly even when you want training predictions; relying on the default fitted values from the model object is a frequent source of leakage in larger pipelines.

Explanation: Probabilities from a single rpart tree are the per-class proportions inside the leaf the row lands in, so within one leaf every row gets identical probabilities. This is why ROC and lift curves built on a single tree look "stair-stepped." Bagged or random forest ensembles smooth these out by averaging across many trees. For threshold tuning or calibration work, prefer probabilities to hard labels.

Explanation: table() with named arguments produces a labelled contingency. The 6 misclassifications (5 versicolor predicted as virginica, 1 virginica predicted as versicolor) match what the printed tree's leaf loss counts foreshadowed. Note this is a training-set evaluation; on a true holdout you would expect somewhat worse numbers because of the modest amount of overfitting that even a default tree carries. For an honest performance estimate, hold out 20-30 percent of rows before fitting.

Explanation: RMSE is in the same units as the response (mpg here), so a 3.18 mpg average deviation is interpretable directly: the tree is roughly within 3 mpg of the truth on cars it has not seen. Compare this to the standard deviation of mpg in the holdout to gauge whether the model beats a "predict the mean" baseline. With only 32 rows total, a single split like this is noisy: in production you would prefer k-fold cross-validation or a bootstrap to stabilise the estimate.

Explanation: The cp table summarises every candidate subtree from a one-node stump up to the fully grown tree. rel error is training error relative to the root; xerror is the cross-validated equivalent (rpart runs 10-fold CV internally during fitting). xstd is the standard error of the cross-validated estimate. Pick cp by reading down the table for the row with smallest xerror (the next exercise) or the most parsimonious row within one xstd of that minimum (the exercise after).

Explanation: which.min() on the xerror column finds the cp index that minimises cross-validated error; passing that CP value into prune() returns the corresponding subtree. Because xerror is an estimate, the minimum can shift between runs unless you fix the seed before calling rpart() (rpart uses its own internal CV folds). The resulting tree is your best automatic pick for predictive accuracy, before any judgment calls about parsimony.

Explanation: The 1-SE rule (Breiman et al.) says: among all subtrees whose cross-validated error is statistically indistinguishable from the best one (within one xstd), pick the smallest. This guards against overfitting when the cv estimate is noisy. which(cpt[, "xerror"] <= threshold)[1] returns the first qualifying row, which because the cp table is ordered by descending CP corresponds to the most parsimonious qualifier. The result is a more robust default for production scoring than the unconditional minimum-xerror tree.