# THREE. Reformulating Ordinary Regression Analysis in Matrix Notation

Published Online: 11 AUG 2003

DOI: 10.1002/0471467979.ch3

Copyright © 2003 John Wiley & Sons, Inc.

Book Title

## Quantitative Methods in Population Health: Extensions of Ordinary Regression

Additional Information

#### How to Cite

Palta, M. (2003) Reformulating Ordinary Regression Analysis in Matrix Notation, in Quantitative Methods in Population Health: Extensions of Ordinary Regression, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471467979.ch3

#### Publication History

- Published Online: 11 AUG 2003
- Published Print: 15 AUG 2003

#### Book Series:

#### Book Series Editors:

- Walter A. Shewhart and
- Samuel S. Wilks

#### ISBN Information

Print ISBN: 9780471455059

Online ISBN: 9780471467977

- Summary
- Chapter

### Keywords:

- matrices;
- least squares;
- unbiasedness;
- matrix notation;
- matrix rules;
- matrix formulation

### Summary

We motivate the need for matrix notation for writing regression equations and estimators with multiple predictors. Ordinary regression equation is rewritten in matrix notation. Least squares equations are rewritten in matrix notation. Unbiasedness of least squares estimators is demonstrated. An example with matrices is generated by PROC REG ALL option. A basic list of matrix operations and equalities is provided. Matrix operations are illustrated for regression of systolic blood pressure on age.