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Statistics for Health Care Management and Administration by David A. Rosenthal, John F. Kros

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Appendix A

Multiple Regression and Matrices

In order to understand how the computer carries out regression analysis—which automatically leads to a better understanding of regression—it is necessary to understand something about matrix math. This section provides a brief introduction to matrix math.

Matrices are used to describe linear equations by tracking the coefficients of linear transformations and to record data that depend on multiple parameters.

An Introduction to Matrix Math

A matrix is a set of numbers in a two-dimensional space. Matrices are almost always designated with capital letters in boldface type. In general, a matrix X has n rows and m columns, as shown in Equation A.1, where the first subscript denotes the row and the second denotes the column.

A matrix is said to have dimensions equal to n and m so that the matrix X has dimensions n × m (rows first, columns second). The following is a typical example of a 2 × 3 matrix.

equation

A vector is a matrix with dimensions n × 1 or 1 × m, as shown in Equation A.2.

The following are typical examples of a 3 × 1 vector and a 1 × 3 vector.

A scalar can be considered a matrix of dimensions 1 × 1. The individual entries of ...

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