UNIT7 - MULTIPLE REGRESSION MODELS
Gujarati & Porter (Basic Econometrics): Chapter 6 (not functional form) & 7 & 8 /
Gujarati & Porter: Chapt 4 and 7/
7/ Stock & Watson, Chapt 6&7
6&7
How do we specify a multiple regression?
Example:
|
,
,
=
+
+
+
+
This is still a linear regression model, WHY??
,
& are all partial regression/slope coefficients, WHY?
Goodness of Fit of the regression model:
The adjusted take into account the d.f. Therefore, adding another
explanatory variable and an increase in , does not mean this new variable
improves the fit of the model. Therefore, we must look at the
=
=
=
=
Testing the joint hypothesis that
t-value look at individually stat significance.
The F-test, tests joint significance: Look whether the explanatory variables
together have an influence on the dependent variable.
&
=
!" #.%
'
&
(! #.%
where k=number of explanatory variables incl intercept.
RELATIONSHIP between F &
=
)
)
'*
+
!" #.%
"!'*
+
(! #.%
:
where k=number of explanatory variables incl intercept.
Therefore, a large F-value Evidence against,- , OR, if
./01
> .3 4 56 789 :;<;7= ,(EVIEWS gives you the F value, as well as P-value.
NB: In some cases (especially with multicollinearity), the individual statistics
are not stat sign, but jointly they still are.)
How do we conclude whether to include another explanatory variable or not?
As long as the increase, you may include the variable in the model.
ASSUMPTIONS:
HYPOTHESIS & CI TESTING: (NB, d.f. = n-(number of b’s, including intercept)
For 2sided, if level of sign = 5%, you need to look at t value for a 5%/2
= 2.5% level of sign!!!
EXAMPLES:
Chapter 6: p150; 156; 161; 163; 165; 167; 170; And end of chapter 6 examples.
Chapter 7: p198; 204; 208; 211; 213; And end of chapter 7 examples.
Chapter 8: p234; 248; 250; 253; 261; And end of chapter 8 examples.