Decision trees can be implemented by using the 'rpart' package in R. The 'rpart' package extends to Recursive Partitioning and Regression Trees which applies the tree-based model for regression and classification problems.

In this tutorial, we'll briefly learn how to fit and predict regression data by using 'rpart' function in R. The
tutorial covers:

- Preparing the data
- Fitting the model and prediction
- Accuracy checking
- Source code listing

We'll start by loading the required libraries.

`library(rpart)`

library(caret)

**Preparing the data**

We use Boston house-price dataset as a target regression data in this
tutorial. After loading the dataset, first, we'll split them into the
train and test parts, and extract x-input and y-label parts. Here, I'll
extract 15 percent of the dataset as test data. It is better to scale x part of data to improve the accuracy.

`boston = MASS::Boston`

str(boston)

set.seed(12)

indexes = createDataPartition(boston$medv, p = .85, list = F)

train = boston[indexes, ]

test = boston[-indexes, ]

train_x = train[, -14]

train_x = scale(train_x)[,]

train_y = train[,14]

test_x = test[, -14]

test_x = scale(test[,-14])[,]

test_y = test[,14]

` `

**Fitting the model and prediction**

We'll define the model by using the rpart() function of the rpart package and fit on train data. Here, we'll set 'control' parameters as shown below. The
calling the function is enough to train the model with included data.
You can check the summary of the model by using the print() or printcp() function.

`fit = rpart(train_y~., data = data.frame(train_x, train_y), `

control = rpart.control(cp = 0.00001))

` `

`printcp(fit)`

` `

`Regression tree:`

rpart(formula = train_y ~ ., data = data.frame(train_x, train_y),

control = rpart.control(cp = 1e-05))

Variables actually used in tree construction:

[1] age black crim dis lstat nox ptratio rad rm tax zn

Root node error: 38319/458 = 83.667

n= 458

CP nsplit rel error xerror xstd

1 0.45252258 0 1.00000 1.00371 0.087768

2 0.17808779 1 0.54748 0.62144 0.061139

3 0.06372523 2 0.36939 0.41766 0.049265

4 0.04001076 3 0.30566 0.34812 0.045449

5 0.03530233 4 0.26565 0.34948 0.046059

6 0.02585806 5 0.23035 0.31908 0.044292

7 0.00855071 6 0.20449 0.27123 0.039490

`....`

Next, we'll apply prune function for fitted data. Then we can plot the trees.

`fit.pruned = prune(fit, cp = 0.0001)`

plot(fit.pruned)

text(fit.pruned, cex = 0.9, xpd = TRUE)

Now, we can predict the x test data with the trained model.

`pred_y = predict(fit.pruned, data.frame(test_x))`

**Accuracy checking**

Next, we'll check the prediction accuracy with MSE, MAE, and RMSE metrics.

`print(data.frame(test_y, pred_y))`

mse = mean((test_y - pred_y)^2)

mae = caret::MAE(test_y, pred_y)

rmse = caret::RMSE(test_y, pred_y)

cat("MSE: ", mse, "MAE: ", mae, " RMSE: ", rmse)

`MSE: 20.28907 MAE: 2.979355 RMSE: 4.504339`

MSE: 11.99942 MAE: 2.503739 RMSE: 3.464018

Finally, we'll visualize original test and predicted data in a plot.

`x = 1:length(test_y)`

plot(x, test_y, col = "red", type = "l", lwd=2,

main = "Boston housing test data prediction")

lines(x, pred_y, col = "blue", lwd=2)

legend("topright", legend = c("original-medv", "predicted-medv"),

fill = c("red", "blue"), col = 2:3, adj = c(0, 0.6))

grid()

` `

In this tutorial, we've learned how to fit and predict regression data
with rpart function in R. The full source code is listed below.

**Source code listing**

`library(rpart)`

library(caret)

boston = MASS::Boston

str(boston)

set.seed(12)

indexes = createDataPartition(boston$medv, p = .9, list = F)

train = boston[indexes, ]

test = boston[-indexes, ]

train_x = train[, -14]

train_x = scale(train_x)[,]

train_y = train[,14]

test_x = test[, -14]

test_x = scale(test[,-14])[,]

test_y = test[,14]

fit = rpart(train_y~., data = data.frame(train_x, train_y),

control = rpart.control(cp = 0.00001))

printcp(fit)

fit.pruned = prune(fit, cp = 0.0001)

plot(fit.pruned)

text(fit.pruned, cex = 0.9, xpd = TRUE)

pred_y = predict(fit.pruned, data.frame(test_x))

print(data.frame(test_y, pred_y))

mse = mean((test_y - pred_y)^2)

mae = caret::MAE(test_y, pred_y)

rmse = caret::RMSE(test_y, pred_y)

cat("MSE: ", mse, "MAE: ", mae, " RMSE: ", rmse)

x = 1:length(test_y)

plot(x, test_y, col = "red", type = "l", lwd=2,

main = "Boston housing test data prediction")

lines(x, pred_y, col = "blue", lwd=2)

legend("topright", legend = c("original-medv", "predicted-medv"),

fill = c("red", "blue"), col = 2:3, adj = c(0, 0.6))

grid()

**Reference:**
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