Multiple Linear Regression and Ordinary Least Squares in Quantitative Finance

Summary

The document introduces multiple linear regression as a model relating one dependent variable to several explanatory variables, contrasting it with simple regression. It connects the method’s broad use in quantitative finance with the progression from the Capital Asset Pricing Model toward Arbitrage Pricing Theory, where multiple factors can be considered together.

It explains that ordinary least squares chooses the intercept and factor coefficients to minimize the sum of squared differences between observed and fitted outcomes. Squaring residuals makes positive and negative errors both contribute positively and gives larger errors more weight. The text presents the basic concept but omits the displayed equations and provides no worked market example, dataset, or empirical findings. It does not discuss assumptions such as linearity, multicollinearity, or residual behavior, so readers should treat it as an introductory outline rather than a complete guide to model use or validation.

Key ideas

• Multiple regression models one outcome using several explanatory variables.
• Ordinary least squares estimates coefficients by minimizing the sum of squared residuals.
• Squaring errors prevents positive and negative residuals from canceling and penalizes larger errors more heavily.
• The article relates multiple-factor regression to asset pricing frameworks including CAPM and APT.
• The overview provides no empirical example or discussion of regression assumptions and diagnostics.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.