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# week6 - Econ 508 Multiple Regression t and F tests Juan...

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Econ 508: Multiple Regression: t and F tests Juan Fung MSPE March 18, 2011 Juan Fung (MSPE) Econ 508: Multiple Regression: t and F tests March 18, 2011 1 / 10

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General tests of the parameters Recall the multiple regression model Y i = β 0 + β 1 X 1 + ··· + β k X k + ± i You should be comfortable computing t statistics for tests about individual parameters. We also reviewed how to conduct tests of joint signiﬁcance, H 0 : β 1 = ··· = β k = 0 H 0 : R 2 = 0 , via the F statistic, F ( k , n - k - 1) = SSR / k SSE / ( n - k - 1) . Juan Fung (MSPE) Econ 508: Multiple Regression: t and F tests March 18, 2011 2 / 10
More general tests To test hypotheses involving more general restrictions on the parameters, use the F statistic, F ( m , n - k - 1) = ( SSE * - SSE ) / m SSE / ( n - k - 1) , where SSE * obtained by imposing the restrictions, SSE is obtained from the full model, and m is the number of restrictions. By deﬁnition of R 2 , the statistic is equivalent to (verify) F ( m , n - k - 1) = ( R 2 - R * 2 ) / m (1 - R 2 ) / ( n - k - 1) , where R * 2 corresponds to the restricted model. Also, recall that if

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