11-06 math

Therefore we want to know the probability of an f

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Unformatted text preview: planation for the results (H0) or the predictors are explaining something real about the outcome (H1). To test whether SSregression is larger that would be expected by chance, we first divide it by its degrees of freedom to get the mean square, MSregression. SSregression (7) MSregression = df regression According to the null hypothesis that the regression doesn’t explain anything real, 2 MSregression has a (modified) chi ­square distribution, multiplied by &quot;Y , the variance of Y in ! 2 the population. If we knew &quot;Y then we would know the likelihood function for MSregression exactly. This is the same situation that came up with t ­tests, where we knew the likelihood 2 function for M except for not knowing σ2. Once again, we divide by an estimate of &quot;Y to get ! 2 our final test statistic, and once again, we estimate &quot;Y using the residual mean square. In ! this case, the residual mean square is the residual sum of squares divided by its degrees of freedom (see Eq. 3). ! ! SS MSresidual = residual (8) df residual 2 When we divide MSregression by MSresidual, &quot;Y cancels out, and we end up with a test statistic that doesn’t depend on any population par...
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