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Show that under the normality assumption, the F test is equivalent to the likelihood ratio test.

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Basic Math

Show that under the normality assumption, the F test isequivalent to the likelihood ratio test.

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The ratio s 2 Y 2 is of course the Fstatistic up to constants not depending on the data Since for this problem the likelihood ratio test and the F test use equivalent test statistics if we fix the same size or level for the two tests they will have exactly the same power In fact even for more complicated linear models    See Answer
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