1. Buy!!! What’s best for me? Which brand to buy? What Style? Color? Sell!!! What matters to customers? Where are we positioned relative to competitors? BusinessCustomer Complex products, such as a cars, have dozens of criteria to consider.

2. Perceptual Map: Automobile Understand Customers Survey Attribute Ratings Factor Analysis Perceptual Map R Analytic Approach Research Objectives Get Data Analysis Software Reporting Project Plan

3. Surveys

4. Exploratory: no guiding hypotheses Confirmatory: set of hypotheses that form the conceptual basis Factor Analysis

5. QRate on a scale of 1-Low to 9-High (randomized list) Shopper#1New BMW 1971 Olds 442 Conv. 1Initial Price934 2Style789 3# of Miles on Car794 4Reliability762 5Color579 6Comfort675 7Horsepower269 8Safety671 9Financing Terms752 10Country Origin177 11Drive Type (Front, 4WD)446 12Miles Per Gallon (MPG)675 13Warranty Coverage452 Survey: Attribute Ratings Many more features, options….

6. QRate on a sale of 1- 9 1Initial Price 2Style 3# of Miles on Car 4Reliability 5Color 6Comfort 7Horsepower 8Safety 9Financing Terms 10Country Origin 11Drive Type (Front, 4WD) 12Miles Per Gallon (MPG) 13Warranty Coverage Survey: Attribute Ratings 12345678910101 1212 1313

7. cor(data, digits=2) Correlation Matrix

9. install.packages("corrgram") library(corrgram) corrgram(data)

10. Factor Analysis / Variable Reduction Correlation Matrix Correlated variables are grouped together and separated from other variables with low or no correlation Factor Analysis

11. F1 Factor Analysis F2FN …. F3

12. F1 b’s  Factor Loadings Factor Analysis F2FN …. F3

13. Psych Package – includes FA

14. Psych Package – fa library(psych) rmodel <- fa(r = corMat, nfactors = 3, rotate = “none", fm = "pa")

15. Psych Package

16. Each variable (circle) loads on both factors and there is no clarity about separating the variables into different factors, to give the factors useful names. Factor 2 Factor 1 Rotation Rotations Courtesy of Professor Paul Berger

17. 17 “CLASSIC CASE” After rotation of ~45 0 NOW, all variables are loading on one factor and not at all the other; This is an overly “dramatic” case. Not Correlated  Orthogonal Varimax = Orthogonal Rotation Rotation Rotations Courtesy of Professor Paul Berger

18. Psych Package – fa library(psych) rmodel <- fa(r = corMat, nfactors = 3, rotate = "oblimin", fm = "pa")

19. Principal Components Analysis

20. Psych Package – principal library(psych) fit <- principal(ratings6, nfactors=4, rotate=“null")

21. Model model <- princomp(data, cor=TRUE) summary(model) biplot(model)

22. Psych Package – principal library(psych) fit <- principal(ratings6, nfactors=4, rotate="varimax“) corrgram(ratings6[,(1,2,9,12,3,4,6,8,10,5,11,7,13)]) Orthogonal / No Correlation

23. Psych Package – principal plot(fit)

24. Output # scree plot plot(fit,type="lines")

25. 3 Factor vs. 4 Factor

26. Style Comfort Color Upgrade Packages Reliability Safety Country Origin Horsepower Nice Dash Miles Per Gallon Initial Price # of Miles on Car Financing Options Aaahh!!! Factor Money

27. Perceptual Map Factor Loadings Brand Ratings Weights Average Variance

28. Which One? Which Car? Price $$$ $ Sweet!!!BORING Aaaah factor…

29. Factor Analysis Recap