getting down to business: engaging business majors in statistics class heather smith and john walker...

Getting Down to Business:Getting Down to Business:Engaging Business MajorsEngaging Business Majors

in Statistics Classin Statistics Class

Heather Smith and John WalkerHeather Smith and John WalkerCal Poly, San Luis ObispoCal Poly, San Luis Obispo

E-mail: [email protected]: [email protected]: statweb.calpoly.edu/jwalkerDownloads: statweb.calpoly.edu/jwalker

CORS-INFORMS, Banff 2004CORS-INFORMS, Banff 2004 22

Topics for TodayTopics for Today

• Background on our students and program

• A few examples of how we utilize – Demonstrations– Activities – Assignments

to engage business students


Our Business Students & ClassesOur 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


Business Majors with Statistics MinorsBusiness 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


Activities and AssignmentsActivities 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.


#1:#1: The Cal Poly Alphabet CompanyThe 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.”


Lessons from the AlphabetLessons from the Alphabet Company ActivityCompany Activity

• Introduction to Six-Sigma and SPCOpens the discussion about qualityHow can it be measured?

• Quality by inspection vs. Focus on process and variation

• Students are surprised by the amount of variation


#2: A Time Series Regression Project:#2: A Time Series Regression Project:Computing the Market Beta of a StockComputing 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.


Model 1: Dell Stock Price vs. S&P IndexModel 1: Dell Stock Price vs. S&P IndexThe regression equation is DELL = - 55.2 + 0.0667 SPX

Predictor Coef SE Coef T PConstant -55.20 15.01 -3.68 0.001SPX 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


Transformed Model 2: Return vs. ReturnTransformed Model 2: Return vs. ReturnThe regression equation is DELL-r = 2.16 + 2.58 SPX-r24 cases used 1 cases contain missing valuesPredictor Coef SE Coef T PConstant 2.157 3.253 0.66 0.514SPX-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


Lessons from the Market Beta ActivityLessons 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


#3: The Long Jump Activity#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:

NameJumping distance (in.)Height (in.)Foot-to-waist height (in.)Gender (M/F)Age (years)Shoe type (Good/Bad/None)


Sample Long Jump DataSample Long Jump Data

Jumping

distance

Height Foot-to-waist

Gender (m=1)

Age Good

shoes

Bad

shoes

81.0 74.0 42.0 1 22 0 1

78.0 65.0 41.0 0 20 0 0

78.0 75.0 42.0 1 20 0 1

77.0 68.0 41.0 0 21 0 0

77.0 69.0 40.0 1 19 1 0

76.0 67.0 41.0 0 19 1 0

76.0 67.0 36.0 1 21 1 0

75.5 62.0 35.5 0 21 0 0

75.0 67.0 42.0 0 22 0 0

75.0 66.0 37.0 1 22 1 0


Scatterplot: Distance vs. HeightScatterplot: Distance vs. Height

75706560

110

100

90

80

70

60

height

jum

ping

dis

tanc

eScatterplot of jumping data


What about gender?What about gender?

womenmen

75706560

110

100

90

80

70

60

height

jum

ping

dis

tanc

eScatterplot of jumping data


A Typical AnalysisA Typical AnalysisThe 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 pvalueConstant 24.65 30.81 0.80 0.427Height -0.0673 0.6041 -0.11 0.912Foot-to-waist 1.0291 0.5747 1.79 0.078Gender 21.641 3.710 5.83 0.000Age 0.4065 0.3295 1.23 0.222Goodshoes 0.076 2.176 0.03 0.972Badshoes -3.680 3.093 -1.19 0.239

s = 7.876 R-Sq = 70.0% R-Sq(adj) = 67.1%


Benefits of the Long Jump ActivityBenefits 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


Lessons from the Long Jump ActivityLessons 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.)


#4: The Helicopter Experiment#4: The Helicopter Experiment

• Demonstrates DOE and ANOVA• Divide the class into teams• Equipment:

1. paper helicopters of various designs2. a stop watch3. data collection form4. 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.


Common VariablesCommon Variables

ResponseFlight 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)


Benefits of the Helicopter ExperimentBenefits 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


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 Mathematicshttp://courses.ncssm.edu/math/Stat_inst01/PDFS/theme_var.pdf


#5: The Sampling SIM Program#5: The Sampling SIM Program

• Garfield, delMas, and Chance (NSF project)

• FREE!

• www.gen.umn.edu/faculty_staff/delmas/stat_tools

Possible simulation exercises1. What is a Sampling Distribution?

2. Sampling from Non-Normal PopulationsWhere 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


Files Available for DownloadFiles Available for Download

http://statweb.calpoly.edu/jwalker1. 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

getting down to business: engaging business majors in statistics class heather smith and john walker...

Documents

variation slide

computing slide

class time

edujwalker slide

time series regression

engaging business majors

minds of farm owners

dell stock price