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# How to build regression trees in R?

# How to build regression trees in R?

This recipe helps you build regression trees in R

Decision Tree is a supervised machine learning algorithm which can be used to perform both classification and regression on complex datasets. They are also known as Classification and Regression Trees (CART). Hence, it works for both continuous and categorical variables.

Important basic tree Terminology is as follows:

- Root node: represents an entire popuplation or dataset which gets divided into two or more pure sets (also known as homogeneuos steps). It always contains a single input variable (x).
- Leaf or terminal node: These nodes do not split further and contains the output variable

In this recipe, we will only focus on Regression Trees where the target variable is continuous in nature. The splits in these trees are based on minimising the Residual sum of squares of each groups formed. RSS is calculated by the predicted values is the mean response for the training observations within the jth group.

This recipe demonstrates the modelling of a Regression Tree, we use a famous dataset by National institute of Diabetes and Digestive and Kidney Diseases.

```
# For data manipulation
library(tidyverse)
# For Decision Tree algorithm
library(rpart)
# for plotting the decision Tree
install.packages("rpart.plot")
library(rpart.plot)
# Install readxl R package for reading excel sheets
install.packages("readxl")
library("readxl")
```

Loading the test and train dataset sepearately. Here Train and test are split in 80/20 proportion respectively.

Dataset description: The company wants to predict the cost they should set for a new variant of the kinds of bags based on the attributes mentioned below using the following variables:

- Height – The height of the bag
- Width – The width of the bag
- Length – The length of the bag
- Weight – The weight the bag can carry
- Weight1 – Weight the bag can carry after expansion

```
# calling the function read_excel from the readxl library
train = read_excel('R_255_df_train_regression.xlsx')
test = read_excel('R_255_df_test_regression.xlsx')
# gives the number of observations and variables involved with its brief description
glimpse(train)
```

Rows: 127 Columns: 6 $ Cost242, 290, 340, 363, 430, 450, 500, 390, 450, 500, 475, 500,... $ Weight 23.2, 24.0, 23.9, 26.3, 26.5, 26.8, 26.8, 27.6, 27.6, 28.5,... $ Weight1 25.4, 26.3, 26.5, 29.0, 29.0, 29.7, 29.7, 30.0, 30.0, 30.7,... $ Length 30.0, 31.2, 31.1, 33.5, 34.0, 34.7, 34.5, 35.0, 35.1, 36.2,... $ Height 11.5200, 12.4800, 12.3778, 12.7300, 12.4440, 13.6024, 14.17... $ Width 4.0200, 4.3056, 4.6961, 4.4555, 5.1340, 4.9274, 5.2785, 4.6...

```
# gives the number of observations and variables involved with its brief description
glimpse(test)
```

Rows: 32 Columns: 6 $ Cost1000.0, 200.0, 300.0, 300.0, 300.0, 430.0, 345.0, 456.0, 51... $ Weight 41.1, 30.0, 31.7, 32.7, 34.8, 35.5, 36.0, 40.0, 40.0, 40.1,... $ Weight1 44.0, 32.3, 34.0, 35.0, 37.3, 38.0, 38.5, 42.5, 42.5, 43.0,... $ Length 46.6, 34.8, 37.8, 38.8, 39.8, 40.5, 41.0, 45.5, 45.5, 45.8,... $ Height 12.4888, 5.5680, 5.7078, 5.9364, 6.2884, 7.2900, 6.3960, 7.... $ Width 7.5958, 3.3756, 4.1580, 4.3844, 4.0198, 4.5765, 3.9770, 4.3...

This is a pre-modelling step. In this step, the data must be scaled or standardised so that different attributes can be comparable. Standardised data has mean zero and standard deviation one. we do thiis using scale() function.

Note: Scaling is an important pre-modelling step which has to be mandatory

```
# scaling the independent variables in train dataset
train_scaled = scale(train[2:6])
# using cbind() function to add a new column Outcome to the scaled independent values
train_scaled = data.frame(cbind(train_scaled, Outcome = train$Cost))
train_scaled %>% head()
```

Weight Weight1 Length Height Width Outcome -0.33379271 -0.3132781 -0.08858827 0.4095324 -0.42466337 242 -0.22300101 -0.1970948 0.04945726 0.6459374 -0.22972408 290 -0.23684997 -0.1712763 0.03795346 0.6207701 0.03681581 340 0.09552513 0.1514550 0.31404453 0.7075012 -0.12740825 363 0.12322305 0.1514550 0.37156350 0.6370722 0.33570907 430 0.16476994 0.2418198 0.45209006 0.9223343 0.19469206 450

```
# scaling the independent variables in train dataset
test_scaled = scale(test[2:6])
# using cbind() function to add a new column Outcome to the scaled independent values
test_scaled = data.frame(cbind(test_scaled, Outcome = test$Cost))
test_scaled %>% head()
```

Weight Weight1 Length Height Width Outcome 0.72483012 0.72445274 0.69959684 2.15715925 1.87080937 1000 0.07204194 0.08459639 0.09077507 0.03471101 -0.06904068 200 0.17201851 0.17756697 0.24556027 0.07758442 0.29059599 300 0.23082825 0.23225555 0.29715533 0.14769072 0.39466263 300 0.35432872 0.35803927 0.34875040 0.25564092 0.22707121 300 0.39549554 0.39632128 0.38486694 0.56280832 0.48296300 430

We use rpart() function to fit the model.

Syntax: rpart(formula, data = , method = '')

Where:

- Formula of the Decision Trees: Outcome ~. where Outcome is dependent variable and . represents all other independent variables
- data = train_scaled
- method = 'anova' (to Fit a regression model)

```
# creation of an object 'model' using rpart function
model = rpart(Outcome~., data = train_scaled, method = 'anova')
```

Using rpart.plot() function to plot the decision tree model

```
rpart.plot(model)
```

We use Predict() function to do the same.

Syntax: predict(fitted_model, df, type = '')

where:

- fitted_model = model fitted by train dataset
- df = test dataset

```
predict_test = predict(model, test_scaled)
predict_test %>% head()
```

1 700.909090909091 2 316.625 3 316.625 4 316.625 5 495.9 6 495.9

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