Editing Design matrix (section)

==Definition==
The design matrix is defined to be a matrix <math>X</math> such that <math>X_{ij}</math> (the ''j''<sup>th</sup> column of the ''i''<sup>th</sup> row of <math>X</math>) represents the value of the ''j''<sup>th</sup> variable associated with the ''i''<sup>th</sup> object.

A regression model may be represented via matrix multiplication as
:<math>y=X\beta+e,</math>
where ''X'' is the design matrix, <math>\beta</math> is a vector of the model's coefficients (one for each variable), <math>e</math> is a vector of random errors with mean zero, and ''y'' is the vector of predicted outputs for each object.