1. Statistics 350 Lecture 16

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

3. General Linear Model Have model with one response variable, Y, and (p-1) explanatory variables, X 1, …, X p-1 For the i th observation, have recorded (Y i, X 1, …, X p-1 ) General Linear Model:

4. General Linear Model The mean of Y i : Variance: Simple linear regression model is a special case

5. General Linear Model Interpretation of  0 Interpretation of  1

6. General Linear Model Examples:

7. ANOVA Least Squares minimizes: Total Variability: Variability partitioned same as before, only change now is that we have p-1 explanatory (predictor) variables

8. ANOVA ANOVA Table Compare to simple linear regression

9. ANOVA Hypothesis test from ANOVA table: Interpretation