Regression Analysis and Multivariate Regression.pptx

Regression Analysis

1. Objectives 2

2. Overview 3 Continuous Variable Continuous Variable Correlation

3. Example of Two Continuous Variables 4 ? Weight Height in. lb.

4. Relationships between Continuous Variables 5

5. Correlation 6

6. Extreme Data Values 7 Y X 13 12 11 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 Correlation with One Extreme Value

7. Simple Linear Regression

8. Objectives 9

9. Simple Linear Regression Analysis 10

10. Simple Linear Regression Model 11 1 unit units Response (Y) Predictor (X)

11. Simple Linear Regression Model 12 Predictor (X) Response (Y) Unknown Population Relationship Y Y -

12. Explained versus Unexplained Variability 13 Predictor (X) Response (Y) Unexplained Variability Explained Variability Total Variability Y _

13. Model Hypothesis Test 14

14. Concepts of Multiple Regression

15. Objectives 16

16. Multiple Linear Regression with Two Variables 17

17. Picturing the Model: No Relationship 18 * * * * * * * * * * b X 1 Y X 2

18. Picturing the Model: A Relationship 19 X X * * * * * * * * * * * * * Y * * * * 2 1

19. The Multiple Linear Regression Model 20

20. Model Hypothesis Test 21

21. Assumptions for Linear Regression 22

22. Multiple Linear Regression versus Simple Linear Regression Main Advantage Multiple linear regression enables you to investigate the relationship among Y and several independent variables simultaneously. Main Disadvantages Increased complexity makes it more difficult to ascertain which model is “best” interpret the models. 23

23. Common Applications 24

24. Prediction The terms in the model, the values of their coefficients, and their statistical significance are of secondary importance. The focus is on producing a model that is the best at predicting future values of Y as a function of the Xs . The predicted value of Y is given by 25