MultRegTests - 1 Hypothesis Tests in Multiple Regression...

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1 Hypothesis Tests in Multiple Regression Analysis Multiple regression model: ε β β β β + + + + + = 1 1 2 2 1 1 0 ... p p X X X Y where p represents the total number of variables in the model. I. Testing for significance of the overall regression model. Question of interest: Is the regression relation significant? Are one or more of the independent variables in the model useful in explaining variability in Y and/or predicting future values of Y ? Null Hypothesis: The initial assumption is that there is no relation, which is expressed as: H 0 : β 1 = β 2 = … = β p-1 =0. Alternative Hypothesis: At least one of the independent variables IS useful in explaining/predicting Y, expressed as: H 1 : At least one β i is 0. Test Statistic: MSE MSR p n SSE p SSR F = = ) /( ) 1 /( which is found on any regression printout Sampling Distribution: Under the null hypothesis the statistic follows an F -distribution with p – 1 and n - p degrees of freedom. Reject in the upper tail of this distribution. Interpreting Results: If we reject H 0 we conclude that the relation is significant/does have explanatory or predictive power. If we fail to reject, we conclude that there isn't any evidence of explanatory power, which suggests that there is no point in using this model.
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