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.

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.

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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