Thus, all relevant explanatory variables should be included in the regression model, as
otherwise the OLS estimators of the parameters of interest may be biased, and will then stay
away from the true values even if the sample size
n
grows to infinity.
2.
The multiple regression model
,
and least squares estimation
The multiple regression model with an intercept takes the form
Y
j
'
β
1
X
1,
j
%
β
2
X
2,
j
%
...
%
β
k
&
1
X
k
&
1,
j
%
β
k
%
U
j
,
j
'
1,2,...,
n
,
(7)
where
are the explanatory variables,
is the error term, and
is the
X
i
,
j
,
i
'
1,2,...,
k
&
1,
U
j
β
k
intercept. We can write this model more compactly as
Y
j
'
'
k
i
'
1
β
i
X
i
,
j
%
U
j
,
j
'
1,2,...,
n
,
(8)
where
X
k
,
j
/
1.