GU5205 p41-p49.pdf - 2.7 General Linear Test The analysis...

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2.7 General Linear Test The analysis of variance test of H 0 : β 1 = 0 versus H A : β 1 6 = 0 is an example of the general test for a linear statistical model . General linear test Let SSE R be the sum of squares error for the reduced model with degrees of freedom df R and let SSE F be the sum of squares error for the full model with degrees of freedom df F . Then the general F-test uses the following statistic: f calc = SSE R - SSE F df R - df F ÷ SSE F df F . (2.14) Note: The F-statistic can be derived through a likelihood ratio test. Likelihood ratio test D EFINITION 2.4 Consider a realized dataset y 1 , y 2 , . . . , y n . The likelihood ratio test statistic for testing H 0 : 2 0 versus H A : 2 C 0 is λ ( y 1 , y 2 , . . . , y n ) = max 0 L ( ; y 1 , y 2 , . . . , y n ) max L ( ; y 1 , y 2 , . . . , y n ) . Notes: 41
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General F-test statistic f calc = SSE R - SSE F df R - df F ÷ SSE F df F Same statistic defined in Equation (2.14). Rejection rule Rejection region for a level test Reject H 0 if f calc f ,df R - df F ,df F General F-test for simple linear regression

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