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Multilinear Regression

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Multilinear Regression


Multiple linear regression is an extension of simple linear regression that allows for the modeling of the relationship between multiple independent variables and a single dependent variable. In other words, it enables us to predict a continuous outcome based on two or more predictor variables.

Here's how it works and how to implement it:

How it works:

  1. Model Representation

In multiple linear regression, the relationship between the independent variables X1​,X2​,...,Xn​ and the dependent variable y is represented by the equation:


  • y is the dependent variable (the variable we want to predict).
  • X1​,X2​,...,Xn​ are the independent variables (features).
  • β0​ is the intercept .
  • β1​,β2​,...,βn​ are the coefficients .
  • ϵ is the error term .
  1. Objective

The objective is to estimate the coefficients β0​,β1​,...,βn​ that minimize the difference between the observed and predicted values of the dependent variable.

  1. Model Training

We use a dataset with observations for both the independent variables and the dependent variable. The model is trained using techniques like ordinary least squares (OLS) to find the best-fitting line through the data.

  1. Model Evaluation

After training, the model's performance is evaluated using metrics such as mean squared error (MSE), R-squared, or others, to assess how well the model fits the data and how much variance it explains.


Here's how to implement multiple linear regression in Python using scikit-learn:

Import Libraries

import numpy as np

import pandas as pd

from sklearn.model_selection import train_test_split

from sklearn.linear_model import LinearRegression

from sklearn.metrics import mean_squared_error, r2_score

# Step 1: Collect Data

data = pd.read_csv('energy_efficiency.csv')

# Step 2: Explore the Data (omitted for brevity)

# Step 3: Data Preprocessing

X = data[['Relative_Compactness', 'Surface_Area', 'Wall_Area', 'Roof_Area', 'Overall_Height',

          'Orientation', 'Glazing_Area', 'Glazing_Area_Distribution']]  # Independent variables

y = data[['Heating_Load', 'Cooling_Load']]                            # Dependent variables

# Step 4: Split Data

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Step 5: Create and Fit the Model

model = LinearRegression()

model.fit(X_train, y_train)

# Step 6: Make Predictions

y_pred = model.predict(X_test)

# Step 7: Evaluate the Model

mse = mean_squared_error(y_test, y_pred)

r_squared = r2_score(y_test, y_pred)

print("Mean Squared Error:", mse)

print("R-squared:", r_squared)

# Step 8: Interpret the Coefficients

coefficients = pd.DataFrame({'Variable': X.columns, 'Heating_Load_Coefficient': model.coef_[0],


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