The General Linear Model: The Basics

7.1 Introduction

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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