Exploring Non-linear Regression through Decision Trees in R: A Step-by-Step Coding Guide

Exploring Non-linear Regression through Decision Trees in R: A Step-by-Step Coding Guide


The domain of machine learning presents a variety of algorithms for dealing with diverse data patterns. Among these, decision trees are renowned for their capability to handle both categorical and continuous data, making them suitable for both classification and regression tasks. In this comprehensive guide, we explore the use of decision trees for non-linear regression tasks in R, providing detailed coding examples.

Theoretical Background: Non-linear Regression and Decision Trees

Non-linear regression is a type of regression analysis that models relationships between a dependent variable and one or more independent variables when the relationship is complex and can’t be accurately described by a linear equation.

On the other hand, decision trees are a type of machine learning algorithm that segments the dataset by asking a series of questions, aiming to minimize the variance of the dependent variable in each subset of data for regression tasks.

Setting Up Decision Trees for Non-linear Regression in R

R language offers the `rpart` package, a user-friendly library for creating decision tree models. We’ll use this package to perform non-linear regression.

Start by installing and loading the `rpart` package:


Suppose your dataset is already loaded into a dataframe `df`. A decision tree model can be fitted using `rpart`:


model <- rpart(dependent_variable ~ ., data = df, method = "anova")


Here, `method = “anova”` specifies that the task is regression (not classification).

To predict using the trained model, use the `predict()` function:

predictions <- predict(model, newdata = df)

Plotting the Decision Tree

A visual representation of the decision tree can aid in understanding the model’s decision-making process. For this, we use the `rpart.plot` package:



Pruning the Tree

Overfitting is a common issue in machine learning, including decision trees. Pruning the tree, i.e., trimming some branches, helps to create a simpler model and prevent overfitting.

pruned_model <- prune(model, cp = model$cptable[which.min(model$cptable[,"xerror"]),"CP"])

This code prunes the tree at the complexity parameter (CP) level that minimizes the cross-validation error.

Evaluating the Model

The model’s performance can be evaluated by calculating the Mean Absolute Error (MAE) or Mean Squared Error (MSE):

MAE <- mean(abs(df$dependent_variable - predictions))
MSE <- mean((df$dependent_variable - predictions)^2)


In the realm of non-linear regression, decision trees offer a robust tool for modeling complex relationships. With R and the `rpart` package, we can effectively create, visualize, prune, and assess decision tree models, making this complex task more approachable and intuitive.

Coding Prompts for Further Study

1. Write R code to perform non-linear regression with decision trees.
2. Visualize a decision tree in R using the `rpart.plot` package.
3. Perform tree pruning in R to combat overfitting.
4. Evaluate the performance of a decision tree regression model in R.
5. Tune a decision tree model in R for optimal performance.
6. Write R code to compare the performance of pruned and unpruned decision tree models.
7. Implement cross-validation in R to select the optimal pruning level for a decision tree model.
8. Use a decision tree model to predict values for new data in R.
9. Implement feature importance analysis for a decision tree model in R.
10. Write R code to plot the learning curve of a decision tree model.
11. Implement a bagged decision tree model in R for non-linear regression.
12. Implement a Random Forest model in R for non-linear regression and compare it with a single decision tree.
13. Write R code to implement a Gradient Boosting Machine (GBM) for non-linear regression.
14. Implement non-linear regression with decision trees in R using a real-world dataset.
15. Write R code to visualize the residuals of a decision tree regression model.

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