Regression Analysis for Financial Relationships › Summary

This chapter developed regression analysis as the primary tool for understanding relationships between financial variables. We covered:

• The OLS framework provides closed-form estimates for linear relationships. The slope coefficient measures the change in the dependent variable for a unit change in the explanatory variable, while the intercept captures the baseline level.

• Factor exposures and beta quantify systematic risk. In the market model, beta measures an asset's sensitivity to market movements, which is the foundation for the CAPM that we'll explore in Part IV.

• Hypothesis testing assesses whether relationships are statistically significant. T-tests evaluate individual coefficients, F-tests assess overall model significance, and R-squared measures explanatory power.

• Diagnostic tests reveal violations of OLS assumptions. The Durbin-Watson test detects autocorrelation, the Breusch-Pagan test identifies heteroskedasticity, and VIF measures multicollinearity.

• Robust standard errors (HAC/Newey-West) provide valid inference when classical assumptions fail. These are essential for financial time series data where volatility clusters and returns may be serially correlated.

• Multiple regression extends the framework to multiple factors, decomposing returns into exposures to market, size, value, and other systematic factors.

The techniques developed here will serve as building blocks for the upcoming chapters. In Chapter 20, we'll use Principal Component Analysis to extract factors from return data rather than specifying them a priori. Part IV will apply these regression tools extensively to estimate and test asset pricing models, measure portfolio performance, and attribute returns to different sources.