1. Psychology 202b Advanced Psychological Statistics, II February 1, 2011

2. Overview Multiple regression (review) Inference for multiple regression Added variable plots (review) Partial correlation

3. 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.

4. 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.

5. 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.

6. 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.”