Regression Load The Boston Housing Price Dataset And Improve

Regression Load The Boston Housing Price Dataset and Improve Results

Load the Boston housing price dataset and analyze it to identify missing values. Display a correlation matrix to examine the relationships between features. Select the features RM and LSTAT for modeling, providing an explanation for their suitability. Visualize these features against the target variable MEDV. Split the data into training and testing sets, train a linear regression model, and evaluate its performance using RMSE and R² scores. To enhance the model, create and apply a polynomial regressor of degree 2 and compare the results.

Paper For Above instruction

The Boston Housing dataset is a widely used dataset in machine learning, particularly for regression tasks. It contains various features related to housing in Boston suburbs, with the goal of predicting the median value of owner-occupied homes (MEDV). Initially, loading the dataset and thoroughly examining the data, especially for missing values, is essential to ensure data quality. Missing values can significantly distort analyses and model performance, so confirming their absence assures the reliability of subsequent steps (Hastie, Tibshirani, & Friedman, 2009).

Once data integrity is established, calculating the correlation matrix helps to understand the linear relationships between features. Correlation coefficients indicate which variables tend to change together and can inform feature selection processes (Liu, 2018). In this context, features RM (average number of rooms per dwelling) and LSTAT (% lower status of the population) are known to have strong correlations with MEDV, making them prime candidates for training a model. RM generally shows a positive relationship with housing prices, while LSTAT is negatively correlated, indicating that larger rooms and higher socioeconomic status are associated with higher property values (Belsley, Kuh, & Welsch, 1980).

Plotting these features against the target variable MEDV provides visual insights into their relationships. Typically, RM demonstrates a positive trend as homes with more rooms tend to be more expensive, while LSTAT exhibits a negative trend, consistent with socioeconomic impacts on housing prices. Visual assessment supports the choice of these features for regression analysis, confirming their predictive relevance (LeSage & Pace, 2009).

Next, the dataset should be split into training and testing subsets, commonly with an 80/20 ratio, to evaluate the model's generalization capabilities (James, Witten, Hastie, & Tibshirani, 2013). A linear regression model is fitted to the training data to establish a baseline prediction. Model performance is then assessed on the test data using metrics such as the Root Mean Square Error (RMSE) and R-squared (R²). RMSE provides an estimate of the average prediction error magnitude, while R² indicates the proportion of variance explained by the model (Seber & Lee, 2012).

To improve the predictive performance, polynomial regression of degree 2 is introduced. Polynomial regression captures non-linear relationships between features and the target variable, potentially leading to more accurate predictions (Hastie et al., 2009). This involves transforming the original features into polynomial features and re-fitting the regression model. Comparing the performance metrics of the linear and polynomial models demonstrates the extent of improvement achieved through non-linear modeling methodologies.

In conclusion, the process of analyzing the Boston Housing dataset involves ensuring data integrity, selecting meaningful features based on correlations and visualizations, and employing regression techniques to predict housing prices. The transition from simple linear models to polynomial regressors exemplifies how feature transformations can enhance predictive accuracy. Such analyses foster a deeper understanding of the housing market dynamics and demonstrate key principles in supervised learning and model optimization.

References

  • Belsley, D. A., Kuh, E., & Welsch, R. E. (1980). Regression diagnostics: Identifying influential data and sources of collinearity. John Wiley & Sons.
  • Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning. Springer.
  • James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning. Springer.
  • LeSage, J. P., & Pace, R. K. (2009). Introduction to Spatial Econometrics. CRC Press.
  • Liu, H. (2018). Data analysis with Python: a modern approach. O'Reilly Media.
  • Seber, G. A. F., & Lee, A. J. (2012). Linear Regression Analysis. Wiley-Interscience.
  • Automated analysis of the Boston housing data, available at UCI Machine Learning Repository. (n.d.). Retrieved from https://archive.ics.uci.edu/ml/datasets/Housing
  • Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data. MIT Press.
  • Pedregosa, F., Varoquaux, G., Gramfort, A., et al. (2011). Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research, 12, 2825-2830.
  • Murphy, K. P. (2012). Machine Learning: A Probabilistic Perspective. MIT Press.

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