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Economic Statistics – Class Notes – 4/24/09
11.
An F Test on a Subset of Variables
Purpose – To evaluate the impact of a subset of
independent variables
on the
multiple
regression model
•
The two models are naturally
related
Effects of excluded variables are picked up by the variables that are included
Big Model
(Officially known as the
Unrestricted Model
)
•
Y = a + b1X1 + b2X2 + b3X3 + b4X4 + ei
o
Only 4 explanatory models
Small Model
(Officially known as the
Restricted Model
)
•
Yi = a + b1X1 + b2X2 + ei
Idea
:
I think the small model can do just as good of job as the big model at modeling the
relationship
•
Restricting the value of the coefficients b3 and b4 to
ZERO
Q:
Do X3 and X4 play a role in explaining “y” ?
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View Full Document …where
SSE(s) is
the sum of squares errors
from the
small model
.
SSE(b) is
the sum of squares errors
from the
big model.
This does not look like a Z, T, or single chisquare distribution, thus we know it is an FTest
(because there are only 4 distributions)
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This note was uploaded on 06/03/2009 for the course ECON 203 taught by Professor Casler during the Spring '09 term at Allegheny.
 Spring '09
 Casler

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