Linear Regression on the Boston Housing Dataset

This repository demonstrates an end-to-end Linear Regression project built in Python using the Boston Housing dataset. The objective is to predict the median value of owner-occupied homes (MEDV) given various socio-economic, demographic, and housing-related features. The project includes dataset exploration, regression modeling, evaluation, and visualization to understand how these features influence housing prices.

Dataset

The Boston Housing dataset is a well-known dataset in machine learning, often used as a benchmark for regression tasks. It contains 506 observations and 14 variables (13 input features and 1 target variable).

• Target variable:

  • MEDV: Median value of owner-occupied homes (in $1000s).

• Input features:

Feature	Description
CRIM	Per capita crime rate by town
ZN	Proportion of residential land zoned for lots over 25,000 sq.ft.
INDUS	Proportion of non-retail business acres per town
CHAS	Charles River dummy variable (1 if tract bounds river; 0 otherwise)
NOX	Nitric oxide concentration (parts per 10 million)
RM	Average number of rooms per dwelling
AGE	Proportion of owner-occupied units built before 1940
DIS	Weighted distance to employment centers
RAD	Index of accessibility to radial highways
TAX	Full-value property-tax rate per $10,000
PTRATIO	Pupil-teacher ratio by town
B	1000(Bk - 0.63)² where Bk is the proportion of Black residents
LSTAT	% lower status of the population

Workflow

1. Data Loading
   Loaded the dataset using pandas and inspected its structure with .head(), .info(), and .describe().

2. Exploratory Data Analysis (EDA)

   • Checked for missing values.
   • Visualized feature distributions and relationships with MEDV.
   • Built a correlation heatmap to identify the most significant predictors.

3. Data Preprocessing

   • Defined features (X) as the 13 independent variables and target (y) as MEDV.
   • Split dataset into training (80%) and testing (20%) sets.

4. Model Training

   • Applied LinearRegression from scikit-learn.
   • Trained the model on the training set and extracted intercepts and coefficients.

5. Evaluation

   • Predictions were made on the test set.
   • Model performance was measured with:
     • Mean Absolute Error (MAE)
     • Mean Squared Error (MSE)
     • Root Mean Squared Error (RMSE)
     • R² Score

6. Visualization

   • Predicted vs actual plot to show model accuracy.
   • Residual plots to analyze model errors.

Results

• Mean Absolute Error (MAE): ~3.1
• Mean Squared Error (MSE): ~21.5
• Root Mean Squared Error (RMSE): ~4.6
• R² Score: ~0.72

The model explains about 72% of the variance in housing prices. While results are reasonable, there is scope for improvement with more advanced techniques.

Tools and Libraries

• Python
• pandas, numpy
• matplotlib, seaborn
• scikit-learn