INTRODUCTION TO ECONOMETRICS II
ECO 306
NOUN
76 From [3.57] and working through [3.55] to [3.56], the following expression for b
2
is obtained
(
) (
) (
) (
)
(
) (
) , (
)-
,∑(
)(
)- ,∑(
)(
)-
,∑(
)∑(
) ∑,(
)-
…[2.58] Similarly, theexpressionofb
3
can be obtained by switching X
2
and X
3
in [2.58]. Clearly, the principles behind the derivation of the regression coefficients have been shown to be the same for multiple regression as that of the simple regression. But, it should also be observed that the expressions are however different and so should not try to use expressions derived for simple regression in a multiple regression situations. A generalized framework for the multiple regression model is
1 2
2
i
i
k
ki
i
Y
X
X
…[2.59] We may write [2.59] for three variables as,
1 2
2 3
3
i
i
i
i
Y
X
X
…[2.60] whereY is the dependent variable,
2
and
k
X
X
(kth term) the regressors,
the stochastic disturbance term and i the ith (tth, if in time series) observation. Also
1 2
,
and
k
are the partial regression coefficients but is the intercept term which gives the mean effect on Y of all the variables excluded from the model. That is, in the case of [2.50], when
2
and
k
X
X
are set equal to zero. Zero mean value of
i
in [2.60] is
2 3
(
|
,
)
0
i
i
i
E
X
X
…[2.61]
Share with your friends: |
