Comparative Analysis of Linear Regression, Gaussian Elimination, and LU
  Decomposition for CT Real Estate Purchase Decisions
Xilin Cheng
This paper presents a comprehensive evaluation of three distinct
computational algorithms applied to the decision-making process of real estate
purchases. Specifically, we analyze the efficacy of Linear Regression from
Scikit-learn library, Gaussian Elimination with partial pivoting, and LU
Decomposition in predicting the advisability of buying a house in the State of
Connecticut based on a set of financial and market-related parameters. The
algorithms' performances were compared using a dataset encompassing
town-specific details, yearly data, interest rates, and median sale ratios. Our
results demonstrate significant differences in predictive accuracy, with Linear
Regression and LU Decomposition providing the most reliable recommendations and
Gaussian Elimination showing limitations in stability and performance. The
study's findings emphasize the importance of algorithm selection in predictive
analytic and offer insights into the practical applications of computational
methods in real estate investment strategies. By evaluating model efficacy
through metrics such as R-squared scores and Mean Squared Error, we provide a
nuanced understanding of each method's strengths and weaknesses, contributing
valuable knowledge to the fields of real estate analysis and predictive
modeling.