# The General Linear Model: The Basics

Consider the following regression equation

y = Хв + u (7.1)

where

‘ Yi " |
‘ Xu |
X12 • |
• Xik ■ |
‘ в i " |
u1 |
||||

y = |
Yf |
; X = |
X21 |
X22 • |
• X2k |
; в = |
в 2 |
; u = |
u2 |

_ Yra _ |
Xni |
Xn2 |
Xnk |
. вk _ |
un |

with n denoting the number of observations and k the number of variables in the regression, with n > k. In this case, y is a column vector of dimension (n x 1) and X is a matrix of dimension (n x k). Each column of X denotes a variable and each row of X denotes an observation on these variables. If y is log(wage) as in the empirical example in Chapter 4, see Table 4.1 then the columns of X contain a column of ones for the constant (usually the first column), weeks worked, years of full time experience, years of education, sex, race, marital status, etc.

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