1. Economics 173 Business Statistics Lecture 11 Fall, 2001 Professor J. Petry http://www.cba.uiuc.edu/jpetry/Econ_173_fa01/

2. 2 Linear Regression & Review Exam is Thursday, October 4 th, 7-9 in Lincoln Theatre. There is no class Thursday. Office hours will be extended prior to the exam. Petry office hours: Tues: 2-4, Wed: 11:30-12:30 TA’s will post hours on web-board. We’ll get as far as possible through two topics of importance for Thursday’s exam: 1.Simple Linear Regression 2.Identifying the proper technique

3. 3 To calculate the estimates of the coefficients that minimize the differences between the data points and the line, use the formulas: The regression equation that estimates the equation of the first order linear model is:

4. 4 Example – Armani’s Pizza –Armani’s Pizza is considering locating at the U of I campus. To do their financial analysis, they first need to estimate sales for their product. –They have data from their existing 10 locations on other college campuses. –Estimate sales for the University of Illinois, with a college population of 35,000.

5. 5 Example – Armani’s Pizza –Begin by plotting the data –Followed by calculating the statistics of your regression

6. 6

7. 7 Example – Armani’s Pizza –Solve for b 1, then b 0 using the second formula –After obtaining values for your regression line, interpret its meaning. –Finally, plug in the value for your independent variable (35, not 35,000) into the formula, and predict sales!

8. 8 Example – Armani’s Pizza Excel Output

9. 9 17.4 Error Variable: Required Conditions The error  is a critical part of the regression model. Four requirements involving the distribution of  must be satisfied. –The probability distribution of  is normal. –The mean of  is zero: E(  ) = 0. –The standard deviation of  is   for all values of x. –The set of errors associated with different values of y are all independent.

10. 10 Simple Linear Regression-Ex 2 A dog trainer has noticed that his dog Chip seems to perform better in dog shows if he has been given “speedy biscuits—the biscuit with a zip!” prior to the show. To examine this possible relationship, he records the number of biscuits Chip consumed prior to each show, and the score (1-10, with 10 being the highest) from each show. Find b 0 Find b 1 Interpret the slope coefficient.

11. 11 Linear Regression—Dog Show Ex.

12. 12 Identifying the correct Technique Describe a single population: Using the same data, you could use all the single population tests we have discussed, depending upon what information you have, and what you are after. In this case, you have the alphabetical listing of race times from last year’s race to work from. Your roommate thinks the average time to complete the Chicago Marathon >4 hours? Your roommate thinks the percentage of racers finishing the race under 3 hours is less than 5%. Your roommate is also a male chauvenist pig, and believes that male runners are superior. This is demonstrated by the fact that their race times are more spread out than women’s. All women are mediocre, and hence are clumped in the middle of the pack, while some men are at the front of the pack—they have achieved their superior status; while many are also at the back—they are on their way to realizing their superior status.

13. 13 Identifying the correct Technique Compare two populations: He is from the Chicago area, and naturally knows that all people from the Chicago area are also superior. This can be easily verified by categorizing his sample by race time, and demonstrating that Chicagoans have a better race time than non-Chicagoans. To do further analysis, he obtains the results from two years ago as well. Part of being superior is being consistent, he therefore plans to use this data to show that Chicagoans race times are more consistent in their race times than are non-Chicagoans. A critical component to being a male chauvenist pig, is eating like one. He eats pigs feet for breakfast and believes this is one of his keys to success. He wants to verify that eating pigs feet improves performance, so he obtains data from each year: those that eat pigs feet and those that don’t and compares scores. He does the same thing, but this time he takes those that have “seen the light” since the race two years ago, and began eating pigs feet before the last race, but hadn’t yet started before the race two years ago.

14. 14 Identifying the correct Technique Compare two populations: Unfortunately, he believes the Chicago Marathon is going down hill. To test this claim, all he believes he has to do is show that the number of male Chicagoans running the race is less as a percentage of total racers than it was two years ago.