1. 1 Multiple Regression A single numerical response variable, Y. Multiple numerical explanatory variables, X 1, X 2,…, X k

2. 2 Simple Linear Regression

3. 3

4. 4 Multiple Regression

5. 5

6. 6 Conditions The random error term,, is Independent Identically distributed Normally distributed with standard deviation,.

7. 7 Example Y, Response – Effectiveness score based on experienced teachers’ evaluations. Explanatory – Test 1, Test 2, Test 3, Test 4.

8. 8

9. 9

10. 10

11. 11

12. 12 Individual Tests None of the individual tests (explanatory variables) appears to be strongly related to the evaluation (response variable).

13. 13 Method of Least Squares Choose estimates of the various parameters in the multiple regression model so that the sum of squared residuals, (SS Error ), is the smallest it can be.

14. 14 Method of Least Squares Finding the estimates involves solving k+1 simultaneous equations with k+1 unknowns (the estimates of the parameters). Do this with a statistical analysis computer package, like JMP.

15. 15 JMP Analyze – Fit Model Pick Role Variables Y – EVAL Construct Model Effects Add – Test1, Test2, Test3, Test4

16. 16 JMP Analyze – Fit Model Personality – Standard Least Squares Emphasis – Minimal Report

17. 17

18. 18 Prediction Equation Predicted Evaluation = –193.50 + 1.116*Test1 + 2.243*Test2 – 1.367*Test3 + 6.048*Test4