README for Property Price Prediction Using Linear Regression

Overview

This project develops a linear regression model to predict property sale prices using characteristics like the number of rooms, property taxes, and square footage.

Contents

• Writeup: A report detailing the data, variable selection, model diagnostics, and results.
• Codebase: Python scripts for data analysis, model building, and evaluation.

Features

• Predictors: Property attributes such as size, taxes, and rooms.
• Methodology: Exploratory data analysis, variable selection, and model diagnostics.
• Framework: Based on strategies from Montgomery et al. (2021, p. 367).

Tools

• Python Libraries: pandas, numpy, matplotlib, seaborn, statsmodels, and sklearn.

Key Findings

1. Final Model:

   • Key predictors include property taxes, living space, number of garage stalls, and number of fireplaces.
   • Interaction terms (e.g., taxes × living space) capture nuanced relationships and enhance predictive power.
   • Excluded variables were found redundant or insignificant.

2. Model Performance:

   • Adjusted ( R^2 ): 93%, explaining a significant portion of variance in property prices.
   • AIC and BIC values improved significantly after variable selection, reducing overfitting risks.
   • PRESS statistic indicates better generalization to new data compared to the initial model.

3. Validation:

   • Residual analysis confirms assumptions of linearity and constant variance, with minor deviations in the tails.
   • K-fold cross-validation (mean ( R^2 ): 89.3%) highlights strong generalization, though one fold showed reduced performance (( R^2 ): 58.8%).

4. Multicollinearity:

   • High multicollinearity detected in some variables (e.g., number of rooms vs. bedrooms). Addressed through interaction terms and variable elimination.

Conclusion

The model effectively predicts property prices by focusing on key variables and accounting for interaction effects. While robust, minor deviations in residuals and cross-validation results suggest further refinements, such as addressing outliers and exploring non-linear models.

Future Recommendations

• Address variability in cross-validation results by examining data quality in weaker folds.
• Explore Ridge or Lasso regression to reduce multicollinearity and improve generalization.
• Investigate advanced non-linear techniques or transformations to capture complex relationships.
• Expand the dataset for better validation in diverse market conditions.

Reference

Montgomery, D. C., Peck, E. A., & Vining, G. G. (2021). Introduction to Linear Regression Analysis.