1. Statistics 350 Lecture 22

2. Today Last Day: Multicollinearity Today: Example

3. Example Investigators studied physical characteristics and ability in 13 football punters Each volunteer punted a football ten times The investigators recorded the average distance for the ten punts, in feet In addition, the investigators recorded five measures of strength and flexibility for each punter: right leg strength (pounds), left leg strength (pounds), right hamstring muscle flexibility (degrees), left hamstring muscle flexibility (degrees), and overall leg strength (foot-pounds) From the study "The relationship between selected physical performance variables and football punting ability" by the Department of Health, Physical Education and Recreation at the Virginia Polytechnic Institute and State University, 1983

4. Example Variables: Y: Distance traveled in feet X 1 : Right leg strength in pounds X 2 : Left leg strength in pounds X 3 : Right leg flexibility in degrees X 4 : Left leg flexibility in degrees X 5 : Overall leg strength in pounds

5. Example

6. What do you notice from this output? Hypothesis Test:

7. Example Why do you suppose that this phenomenon has occurred?

8. Example What do you notice from this output? Hypothesis Test:

9. Example

10. What do you notice from this output? Hypothesis Test:

11. Example What should we have done before hypothesis tests?

12. Example

14. Other plots:

15. Example Could also look at extra sums of squares:

16. Example

17. 95% Confidence interval for  1 : 95% confidence region for the estimated coefficients:

18. Example Other stuff of possible interest: