Linear Regression for Quantitative Finance

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Summary

This introductory tutorial explains machine learning concepts before focusing on linear regression. It defines features and labels, distinguishes supervised from unsupervised learning, and outlines classification, regression, clustering, and parameterized versus non-parameterized approaches. It also describes separating data into training, validation, and test sets, though it gives general split proportions rather than a finance-specific validation design.

The regression section presents the model as a relationship between input features, a continuous target, learned coefficients, and an error term. It explains that least squares estimates coefficients by minimizing mean squared error, with training and test performance assessed using MSE or R-squared. For quantitative finance, it says simple linear regression is often too limited as a standalone return-prediction strategy, but can help construct factors using coefficients, fitted values, or residuals, including a residual-based example associated with the Fama–French three-factor model. The examples are illustrative; the document supplies no detailed empirical results, and its links point to platform demonstrations rather than reproducible analysis.

Key ideas

Features are model inputs, while labels are the quantities a supervised model aims to predict.
Training, validation, and test data serve different purposes and should remain separate.
Linear regression models a continuous target as a function of features and learned coefficients, with an error term.
Least squares estimates coefficients by minimizing training-sample squared error.
Regression coefficients, fitted values, and residuals can each be used to construct quantitative factors.
The tutorial characterizes basic linear regression as limited for direct return-prediction strategies and gives no robust performance evidence.

Linear Regression Basics and Quantitative Finance Applications

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