THREE. Reformulating Ordinary Regression Analysis in Matrix Notation

  1. Mari Palta

Published Online: 11 AUG 2003

DOI: 10.1002/0471467979.ch3

Quantitative Methods in Population Health: Extensions of Ordinary Regression

Quantitative Methods in Population Health: Extensions of Ordinary Regression

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

Author Information

  1. Madison, Wisconsin, USA

Publication History

  1. Published Online: 11 AUG 2003
  2. Published Print: 15 AUG 2003

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780471455059

Online ISBN: 9780471467977

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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.