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Psychology 202b Advanced Psychological Statistics, II February 1, 2011
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Overview Multiple regression (review) Inference for multiple regression Added variable plots (review) Partial correlation
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Inference for regression Comparing variance that we understand to variance that we don’t understand. The decomposition of the sum of squares. The F statistic. Inference through the t statistic. Standard errors are available from the estimated error variance and (X’X) -1.
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Standard errors Specifically, the matrix of squared standard errors and the covariance between the intercept and the slope is given by. But where do we get that from? Using the /inverse statement in SAS. Implication: estimates of the intercept and the slope are negatively correlated.
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Uses of standard errors The t test is equivalent to the F test in simple regression, but in multiple regression, gives an easier way to focus on single predictors. Confidence intervals. Confidence intervals for the conditional mean. Confidence intervals for individual scores.
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While we are on the subject of confidence intervals… Your book’s explanations of how to interpret them would earn a grade of F in my class. First bad interpretation: “There is a 95% chance that the true (but unknown) regression coefficient is somewhere within the range.809 to 3.171” Second bad interpretation: “If we were to conduct this study 100 times, 95 times out of 100 the b would be within the range.809 to 3.171.”
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