# APPENDIX B

# Regression Analysis^{1}

**T**he purpose of this appendix is to provide a quick and informative review of ordinary least squares (OLS) regression. OLS regression is used in almost every field imaginable, from anthropology to zoology. In the field of finance, the most common application of OLS regression is estimating betas for individual stocks. In the finance subfield of derivatives risk management, OLS regression is frequently used in identifying risk-minimizing hedge ratios. In this appendix, we review OLS regression by discussing topics such as regression estimation, testing, and prediction using both simple and multiple regression models. To avoid unnecessary repetition, the content of Appendix A, “Elementary Statistics,” is assumed to be background knowledge.

## OBJECTIVES

After reviewing this appendix, you should be able to:

- State and understand the four OLS regression assumptions.
- Estimate a simple OLS regression model from summary statistics.
- Interpret OLS regression and ANOVA results from a statistical software package.
- Perform hypothesis tests and construct confidence intervals for individual regression coefficients.
- Perform hypothesis tests on an entire model.
- Calculate and interpret the
*R*-squared and adjusted *R*-squared for a model.
- Choose from among a collection of models based on explanatory power and parsimony.
- Recognize when model assumptions are violated and understand the consequences.

## SIMPLE LINEAR REGRESSION

The goal of regression is to learn about a relation ...