1. Psychology 202a Advanced Psychological Statistics November 3, 2015

2. The plan for today An example of probabilistic reasoning The t test as regression (continued) Restriction of range Introducing multiple regression

3. The t test as regression Recall that regression is a model for the conditional mean. Sometimes, the variable on which we condition can be artificially constructed for a special purpose. Long digression in SAS.

4. The unity of assumptions Initially, the assumptions underlying regression and the t test appear different. However, when they are all satisfied, they become the same.

5. Restriction of range When the range is restricted, the estimate of the correlation is biased toward zero. Regression estimates are unbiased, but are estimated with less precision. Illustration in R.

6. Introducing multiple linear regression Multiple regression has more than one predictor on the right hand side of the equation. Example:

7. When is multiple regression like simple regression? Illustration with artificial data (digression in SAS) The simple regression slope is identical to the multiple regression slope only when the predictors are perfectly uncorrelated. That won’t happen except by design.