Stat 112: Lecture 18 Notes

1. Stat 112: Lecture 18 Notes • Chapter 7.1: Using and Interpreting Indicator Variables. • Visualizing polynomial regressions in multiple regression • Review Problem for Quiz

2. Comparing Toy Factory Managers • An analysis has shown that the time required to complete a production run in a toy factory increases with the number of toys produced. Data were collected for the time required to process 20 randomly selected production runs as supervised by three managers (A, B and C). Data in toyfactorymanager.JMP. • How do the managers compare?

3. Including Categorical Variable in Multiple Regression: Right Approach • Create an indicator (dummy) variable for each category. • Manager[a] = 1 if Manager is A 0 if Manager is not A • Manager[b] = 1 if Manager is B 0 if Manager is not B • Manager[c] = 1 if Manager is C 0 if Manager is not C

4. For a run size of length 100, the estimated time for run of Managers A, B and C ar • For the same run size, Manager A is estimated to be on average 38.41-(-14.65)=53.06 minutes slower than Manager B and 38.41-(-23.76)=62.17 minutes slower than Manager C.

5. Effect Tests • Effect test for manager: vs. Ha: not all manager[a],manager[b],manager[c] equal. Null hypothesis is that all managers are the same (in terms of mean run time) when run size is held fixed, alternative hypothesis is that not all managers are the same (in terms of mean run time) when run size is held fixed. This is a partial F test. • p-value for Effect Test <.0001. Strong evidence that not all managers are the same when run size is held fixed. • Note: equivalent to because JMP has constraint that manager[a]+manager[b]+manager[c]=0. • Effect test for Run size tests null hypothesis that Run Size coefficient is 0 versus alternative hypothesis that Run size coefficient isn’t zero. Same p-value as t-test.

6. Effect tests shows that managers are not equal. • For the same run size, Manager C is best (lowest mean run time), followed by Manager B and then Manager C. • The above model assumes no interaction between Manager and run size – the difference between the mean run time of the managers is the same for all run sizes.

7. Testing for Differences Between Specific Managers

8. Inference for Differences of Coefficients in JMP

11. Visualizing Polynomial Effects in Multiple Regression • Fit Special provides a good plot of the effect of X on Y when using simple regression. • When we use polynomials in multiple regression, how can we see the changes in the mean that are associated with changes in one variable. • Solution: Use the Prediction Profiler. After Fit Model, click the red triangle next to Response, click Factor Profiling and then Profiler.

12. Polynomials in Multiple Regression Example- • Fast Food Locations. An analyst working for a fast food chain is asked to construct a multiple regression model to identify new locations that are likely to be profitable. The analyst has for a sample of 25 locations the annual gross revenue of the restaurant (y), the mean annual household income and the mean age of children in the area. Data in fastfoodchain.jmp

13. Polynomial Regression for Fast Food Chain Data

15. Prediction Profiler