Multiple Linear Regression (MLR) with Python: A Hands-on Guide

Multiple Linear Regression

In our previous discussion, we learned about Simple Linear Regression, where a single independent variable (X) is used to predict a dependent variable (). But what happens when the outcome depends on more than one factor? That’s where Multiple Linear Regression (MLR) comes into play.

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🔍 What is Multiple Linear Regression?

Multiple Linear Regression is a variant of Simple Linear Regression. It models the linear relationship between a single continuous dependent variable and two or more independent variables (which can be either continuous or categorical).

✅ Real-Life Example:

Let’s say you want to predict CO₂ emissions of a car. It’s not enough to look only at the engine size. Other factors, like the number of cylinders, also affect emissions. That’s a classic case for Multiple Linear Regression.

📌 Key Points About MLR

• The dependent variable (Y) must be continuous.
• The independent variables (X) can be continuous or categorical.
• Each independent variable should have a linear relationship with the dependent variable.
• The regression line is fitted through a multidimensional space.

📐 MLR Mathematical Equation

The MLR model can be represented as:

Y = b₀ + b₁x₁ + b₂x₂ + b₃x₃ + … + bₙxₙ

Where:

• Y = Target variable
• b₀ = Intercept
• b₁, b₂, …, bₙ = Coefficients
• x₁, x₂, …, xₙ = Independent variables

🧠 Assumptions in MLR

1. Linear relationship between dependent and independent variables.
2. Residuals (errors) are normally distributed.
3. No or minimal multicollinearity between independent variables.

🛠 Implementing Multiple Linear Regression in Python

Let’s explore a practical example to predict company profits using Python.

🎯 Problem Statement:

We have a dataset of 50 startup companies. It includes:

• R&D Spend
• Administration Spend
• Marketing Spend
• State
• Profit (Target Variable)

🔎 Step 1: Data Pre-processing

# Importing necessary libraries
import numpy as np  
import matplotlib.pyplot as plt  
import pandas as pd  

# Importing dataset
dataset = pd.read_csv('50_CompList.csv')

# Extracting independent (X) and dependent (Y) variables
x = dataset.iloc[:, :-1].values  
y = dataset.iloc[:, 4].values

📦 Step 2: Encoding Categorical Data

The “State” column is categorical, so we encode it using LabelEncoder and OneHotEncoder.

from sklearn.preprocessing import LabelEncoder, OneHotEncoder
from sklearn.compose import ColumnTransformer

labelencoder = LabelEncoder()
x[:, 3] = labelencoder.fit_transform(x[:, 3])

# Creating dummy variables
ct = ColumnTransformer([("State", OneHotEncoder(), [3])], remainder='passthrough')
x = ct.fit_transform(x)

# Avoiding the Dummy Variable Trap
x = x[:, 1:]

✂ Step 3: Splitting the Dataset

from sklearn.model_selection import train_test_split
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.2, random_state=0)

Note: Feature Scaling is not required here as the library handles it internally.

⚙ Step 4: Fitting the MLR Model

from sklearn.linear_model import LinearRegression
regressor = LinearRegression()
regressor.fit(x_train, y_train)

🔮 Step 5: Predicting the Results

y_pred = regressor.predict(x_test)

# Comparing predictions with actual results
comparison = pd.DataFrame({'Actual': y_test, 'Predicted': y_pred})
print(comparison)

✅ Output:

You’ll get a table comparing the predicted profits to the actual ones from the test set, helping you see how well the model performs.

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💡 Final Thoughts

Multiple Linear Regression is one of the most widely used techniques in machine learning and statistics. It’s simple yet powerful when multiple factors are involved in making a prediction.

By mastering MLR:

• You can make better business predictions.
• Understand how different features affect the output.
• Develop more accurate forecasting models.

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