1. Getting Down to Business: Engaging Business Majors in Statistics Class Heather Smith and John Walker Cal Poly, San Luis Obispo E-mail: jwalker@calpoly.edu Downloads: statweb.calpoly.edu/jwalker

2. CORS-INFORMS, Banff 20042 Topics for Today Background on our students and program A few examples of how we utilize – Demonstrations – Activities – Assignments to engage business students

3. CORS-INFORMS, Banff 20043 Our Business Students & Classes Statistics requirements for all business majors First quarter: 4 hrs./week for 10 weeks -Up to hypothesis testing for large samples Second quarter: 5 hrs./week for 10 weeks -Small sample inference, Chi-square tests, Quality, ANOVA, Regression, Time Series. Most students have limited business knowledge Class size ranges from 35 to 50 Emphasis on design, interpretation, computing

4. CORS-INFORMS, Banff 20044 Business Majors with Statistics Minors Currently about 40 minors, most from business Four additional statistical content courses -Two of the following: Regression, DOE, or SAS software -Two of the following: Time Series, Categorical Data Analysis, Survey Research, S-Plus, Multivariate Analysis To attract new statistics minors, we invite current statistics minors to speak in introductory classes

5. CORS-INFORMS, Banff 20045 Activities and Assignments 1.The Cal Poly Alphabet Company (Quality) 2.Market Beta (Time Series Simple Regression) 3.The Long Jump Activity (Multiple Regression) 4.The Helicopter Experiment (DOE) 5.The Sampling SIM Program (Simulations) Introduction to sampling distributions Introduction to the t-distribution The activities above take class time, and will reduce the time available for lecture, but it’s worth it.

6. CORS-INFORMS, Banff 20046 #1: The Cal Poly Alphabet Company THE NECESSITY OF TRAINING HANDS FOR FIRST-CLASS FARMS IN THE FATHERLY HANDLING OF FRIENDLY FARM LIVESTOCK IS FOREMOST IN THE MINDS OF FARM OWNERS. SINCE THE FOREFATHERS OF THE FARM OWNERS TRAINED THE FARM HANDS FOR FIRST-CLASS FARMS IN THE FATHERLY HANDLING OF FARM LIVESTOCK, THE OWNERS OF THE FARMS FEEL THEY SHOULD CARRY ON WITH THE FAMILY TRADITION OF TRAINING FARM HANDS OF FIRST- CLASS FARMS IN THE FATHERLY HANDLING OF FARM LIVESTOCK BECAUSE THEY BELIEVE IT IS THE BASIS OF GOOD FUNDAMENTAL FARM EQUIPMENT. “The Cal Poly Alphabet Company doesn’t like F’s. Inspect this passage; find and count the F’s.”

7. CORS-INFORMS, Banff 20047 Lessons from the Alphabet Company Activity Introduction to Six-Sigma and SPC Opens the discussion about quality How can it be measured? Quality by inspection vs. Focus on process and variation Students are surprised by the amount of variation

8. CORS-INFORMS, Banff 20048 #2: A Time Series Regression Project: Computing the Market Beta of a Stock Each group picks a stock. (No duplicates.) Collect stock price and market index from Web. Regress Stock Price vs. Market Index –Check model assumptions. –Transform the data. Regress “Return on Stock” vs. “Return on Index” –Check model assumptions and influential observations. –Interpret the Market Beta. Test whether  = 1.

9. CORS-INFORMS, Banff 20049 Model 1: Dell Stock Price vs. S&P Index The regression equation is DELL = - 55.2 + 0.0667 SPX Predictor Coef SE Coef T P Constant -55.20 15.01 -3.68 0.001 SPX 0.06674 0.01125 5.93 0.000 S = 7.412 R-Sq = 60.5% R-Sq(adj) = 58.8% Durbin-Watson statistic = 0.38

10. CORS-INFORMS, Banff 200410 Transformed Model 2: Return vs. Return The regression equation is DELL-r = 2.16 + 2.58 SPX-r 24 cases used 1 cases contain missing values Predictor Coef SE Coef T P Constant 2.157 3.253 0.66 0.514 SPX-r 2.5775 0.6351 4.06 0.001 S = 15.68 R-Sq = 42.8% R-Sq(adj) = 40.2% Durbin-Watson statistic = 1.86

11. CORS-INFORMS, Banff 200411 Lessons from the Market Beta Activity Statistics really is used in business! (Business students love looking at stock data.) It’s important to check the data against the assumptions of the statistical model Time series data must be analyzed differently than cross-sectional data Data transformation is useful, not scary or wrong The most important hypothesis to test in a regression isn’t always  = 0

12. CORS-INFORMS, Banff 200412 #3: The Long Jump Activity Divide the class into teams and pick team leaders Equipment: a yardstick and a data collection form Teams go outside, and each person jumps For each person, record: Name Jumping distance (in.) Height (in.) Foot-to-waist height (in.) Gender (M/F) Age (years) Shoe type (Good/Bad/None)

13. CORS-INFORMS, Banff 200413 Sample Long Jump Data Jumping distance HeightFoot-to- waist Gender (m=1) AgeGood shoes Bad shoes 81.074.042.012201 78.065.041.002000 78.075.042.012001 77.068.041.002100 77.069.040.011910 76.067.041.001910 76.067.036.012110 75.562.035.502100 75.067.042.002200 75.066.037.012210

14. CORS-INFORMS, Banff 200414 Scatterplot: Distance vs. Height

15. CORS-INFORMS, Banff 200415 What about gender?

16. CORS-INFORMS, Banff 200416 A Typical Analysis The regression equation is: Distance = 24.7 - 0.067 Height + 1.03 Foot-to-waist + 21.6 Gender + 0.407 Age + 0.08 Goodshoes - 3.68 Badshoes Predictor Coef SE Coef t pvalue Constant 24.65 30.81 0.80 0.427 Height -0.0673 0.6041 -0.11 0.912 Foot-to-waist 1.0291 0.5747 1.79 0.078 Gender 21.641 3.710 5.83 0.000 Age 0.4065 0.3295 1.23 0.222 Goodshoes 0.076 2.176 0.03 0.972 Badshoes -3.680 3.093 -1.19 0.239 s = 7.876 R-Sq = 70.0% R-Sq(adj) = 67.1%

17. CORS-INFORMS, Banff 200417 Benefits of the Long Jump Activity Physically involves the students No need for business knowledge, in fact, students have good intuition about the relationships that likely exist Easy introduction to a complex area of statistics Outside activity, easily managed, requires about 15 minutes to collect the data Can illustrate many important issues in multiple regression

18. CORS-INFORMS, Banff 200418 Lessons from the Long Jump Activity Simple regression doesn’t tell the whole story Predictors may be quantitative (e.g. height, age) or categorical (e.g. gender, type of shoes) How to create and interpret indicator variables Interactions may be present (height*gender) Multicollinearity may cause problems (Height is highly correlated with foot-to-waist ht.)

19. CORS-INFORMS, Banff 200419 #4: The Helicopter Experiment Demonstrates DOE and ANOVA Divide the class into teams Equipment: 1.paper helicopters of various designs 2.a stop watch 3.data collection form 4.a high location to drop from (window, stairs, etc.) Each team gets two different helicopters Roles within the team: randomizer, pilot, timer, and data recorder. Teams turn in data to be analyzed at next class.

20. CORS-INFORMS, Banff 200420 Common Variables Common Variables Response Flight Time (quantitative) What factors lead to increased flight time? Factors Wing Length (2 levels or many levels) Body Length (2 levels or many levels) Type of Paper (2 levels or many levels) Paper Clip (Y/N) or (number of clips)

21. CORS-INFORMS, Banff 200421 Benefits of the Helicopter Experiment Another physical activity Introduces principles of DOE Control, Randomization, Replication, and Blocking Great for demonstrating randomization and data collection! No need for business knowledge, but easily relates to business processes Can be an outside activity, easily managed As simple or as complex as your time, course content, or interest allows

22. CORS-INFORMS, Banff 200422 Helicopter Experiment Variations Helicopter Experiment Variations Two sample t-test Paired t-test One-way ANOVA Multi-factor ANOVA with or without interactions Fractional factorial design and analysis Quadratic terms Gloria Barrett and Floyd Bullard North Carolina School of Science and Mathematics http://courses.ncssm.edu/math/Stat_inst01/PDFS/theme_var.pdf

23. CORS-INFORMS, Banff 200423 #5: The Sampling SIM Program Garfield, delMas, and Chance (NSF project) FREE! www.gen.umn.edu/faculty_staff/delmas/stat_tools Possible simulation exercises 1.What is a Sampling Distribution? 2.Sampling from Non-Normal Populations Where does the “magic” n = 30 come from? 3.What does “confidence” mean? “Good” intervals vs. “Bad” intervals 4.Why bother with the t-distribution? Coverage probabilities

24. CORS-INFORMS, Banff 200424 Files Available for Download http://statweb.calpoly.edu/jwalker 1.This Presentation 2.The Cal Poly Alphabet Company handout 3.Market Beta Lab Assignment 4.Sampling SIM Lab: Sampling Distributions 5.Sampling SIM Lab: t-distribution 6.Helicopter Lab 7.Helicopter Blueprint 8.Helicopter Experiment Variations 9.Link to the Sampling SIM Software