1. Statistics 350 Lecture 17

2. Today Last Day: Introduction to Multiple Linear Regression Model Today: More Chapter 6

3. Inference for the General Linear Model As before, can construct confidence intervals for the regression parameters: Know estimates are unbiased and also have an estimate of the variance for each parameter Formula for standard error:

4. Inference for the General Linear Model Confidence interval: Confidence interval interpretation

5. Inference for the General Linear Model Hypotheses: Tests for parameters:

6. Inference for the General Linear Model Often interested in inference about the mean response for a set of explanatory variables X h Estimate of E(Y h )= This is a random variable with mean and variance:

7. Inference for the General Linear Model Estimate of variance: T-stat: Confidence interval: How would you make a prediction interval for a new value?

8. Diagnostics The model assumptions for the multiple regression model are the same as the simple linear regression model Assessment of assumptions done via residual plots New property to note:

9. Diagnostics Possible violations for the model:

10. Diagnostics Use plots to verify model assumptions: 1. 2. 3. 4. 5. 6.