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4-24-09 - Economic Statistics Class Notes 11 An F Test on a...

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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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…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 chi-square distribution, thus we know it is an F-Test (because there are only 4 distributions) ….because as we add extra variables, SSE tends to
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