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Hypothesis testing of multiple predictors. Another way to test whether predictors have reliable effects on the outcome is to test whether they explain more variability than would be expected by chance. This can be done with multiple predictors, by comparing how much variability the regression explains with those predictors to how much it explains with those predictors left out. We’ll focus on the most common situation, where we want to test whether the full set of predictors, X1 through Xm, collectively tell us anything meaningful about the outcome, Y. As explained above, SSregression represents the amount of variability in Y explained by all of the predictors. We want to test whether SSregression is larger than would be expected by chance. Our null hypothesis is that none of the predictors has any effect on the outcome, meaning that the true values of the regression coefficients (except perhaps the intercept, b0) are all zero. Notice that this is the same null hypothesis used above for testing predictors one at a time, except that now we’re testing them all at once, to see whether any predictor gives reliable information about the outcome. Even if all the bis are zero in the population, the regression coefficients we get from our sample will deviate from zero because of sampling variability. This leads the variability explained by the regression, SSregression, to be greater than zero, even though this “explained” variability is meaningless random error. Therefore, SSregression has a sampling distribution that, as usual, tells us how large it can be expected to be just by chance. Comparing the actual value of SSregression obtained from the sample to the amount expected by chance allows us to test whether chance is a good ex...
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This document was uploaded on 02/25/2014 for the course PSYC 3101 at Colorado.
 Spring '08
 MARTICHUSKI
 Psychology

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