Linear Regression on Advertising Dataset

This project uses a linear regression model to predict sales based on advertising spend on TV, Radio, and Newspaper. The dataset consists of investment amounts (in thousands of dollars) and corresponding sales results. The goal is to understand how marketing investments influence sales and to build a predictive model for future sales forecasting.

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Project Overview

The objective of this project is to explore the relationship between advertising budgets and sales and build a predictive model using Linear Regression. We performed data analysis, removed outliers, trained a regression model, and evaluated its performance.

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Steps in the Project

1. Data Exploration

• Checked for missing values, data types, and basic statistics.
• Visualized the data using boxplots and scatter plots for better understanding.

2. Outlier Removal

• Applied a clipping method to handle outliers and improve model performance.
• Below are boxplots showing the dataset before and after outlier removal.

Boxplot Before Outlier Removal

Boxplot After Outlier Removal

3. Custom Train-Validation-Test Split

• Implemented a manual function to split the dataset into training, validation, and test sets in a 70-15-15 ratio for better evaluation.

4. Model Training

• Trained a linear regression model using LinearRegression from scikit-learn.
• Evaluated the model using Mean Squared Error (MSE) and R² Score.

5. Model Evaluation

The model's performance is summarized below:

• Validation MSE: 2.5
• Validation R²: 0.87
• Test MSE: 2.8
• Test R²: 0.85

Actual vs Predicted Sales Plot
This plot shows how well the predicted sales match the actual sales.

6. Model Saving

• The trained model is saved using joblib for future use.

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Model Description

What is Linear Regression?

Linear Regression is a statistical method used to model the relationship between a dependent variable (target) and one or more independent variables (features). The model assumes a linear relationship between the target and the features.

The mathematical representation for Simple Linear Regression (with one feature) is:

For Multiple Linear Regression (with multiple features), the equation becomes:

Where:

• y: Target variable (sales)
• x₁, x₂, ..., xn: Independent variables (TV, Radio, Newspaper advertising budgets)
• β₀: Intercept (baseline sales when all advertising spends are zero)
• β₁, β₂, ..., βn: Coefficients representing the change in sales for a unit change in each advertising budget
• ε: Error term (difference between actual and predicted sales)

How the Model Works

1. Model Fitting: The model finds the best coefficients (( \beta )) by minimizing the Residual Sum of Squares (RSS) — the difference between actual and predicted sales.
2. Prediction: Once trained, the model uses the learned coefficients to predict sales based on new advertising budgets.
3. Evaluation: Metrics like Mean Squared Error (MSE) and R² Score help assess how well the model generalizes to new data.

Why Linear Regression?

• Simple to implement and interpret.
• Provides insight into how each feature impacts the target.
• Computationally efficient and ideal for small to medium-sized datasets.

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