1. Statistics 350 Lecture 24

2. Today Last Day: Exam Today: Start Chapter 9

3. Model Building Process Read 9.1-9.2…important ideas Four Steps to Model Building: 1.Data collection and preparation: What sort of data is being collect…source of data? What sort of study has been conducted? Response and explanatory variables? Much of the work Masters statisticians do involves data preparation…look for proablems

4. Model Building Process 2.Reduction of number of explanatory variables: Researchers are wise to gather all they can, since any unmeasured phenomena get lumped into random error. Key things are: Need number of variables in final model to be large enough so that your model provides an adequate approximation to reality, but small enough to be practical for use Do not omit anything that the researcher considers vital just because it is highly correlated with another variable

5. Model Building Process 3.Model refinement and selection: Once step 2 is done, then it is time to use techniques learned in Chapters 2-7 (transformations, interactions, plots, tests, …) Try to develop one or more plausible models that could potentially be considered as final answers

6. Model Building Process 4.Model validation: Not always possible, but it's best not to claim to have discovered a new scientific principle before you try it out on an independent data set

7. 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

8. 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

9. Example

10. When we looked at this example in lecture 22, we saw that the regression equation was significant, but that the individual t-tests identified none of the variables as important Why? We then went through a process of selecting variable to include in the model…seemed a bit ad-hoc Chapter 9 deals with the problem of model selection

11. Criteria for Model Selection So how do we deal with Step 2 of our procedure? Would like tests that identify some variables as unimportant Suppose have P-1 potential explanatory variables and fir all possible sub-sets of variables There are such models So, in the football example, there are possible subsets

12. Criteria for Model Selection Goal is to choose a “good” set from these variables that explain the data well So, may wish to choose a few possible models that appear “good” What is good? There exist criteria that assess the relative goodness of models

13. Criteria for Model Selection Criteria: R 2 p Is the coefficient of determination (SSR/SSTO) p represents Good models have What happens if you add more variables? How to use?

14. Criteria for Model Selection Criteria: R 2 a

15. Criteria for Model Selection Mallows C p

16. Criteria for Model Selection AIC

17. Criteria for Model Selection PRESS: