Regression

1. Regression Marketing Analytics

2. Conservatism in Major League BB • Batting Average = Hits/(Opportunities– Walks) • OnBase% = (Hits+Walks)/Opportunities • OVERUSED: “small ball” • Sacrifice Bunt • Give up an out to advance the runner • Stealing Bases • Risk an Out to advance the runner. • UNDERUSED • Don’t risk making outs and runswill take care of themselves.

3. Diagnosing Market Response: Regression Analysis $ SPENT BY A CUSTOMER NUMBER OF PROMOTIONS Marketing Analytics

4. Example: Shopper Card Program Units purchased = a+b1*price paid + b2*feature ad + b3*display Data Marketing Analytics

5. Example: Regression Output From Excel Marketing Analytics

6. Price Elasticity Price elasticity can be derived as the ratio of change in quantity demanded (%∆Q) and percentage change in price (%∆P). PED = [Change in Sales/Change in Price] × [Price/Sales] = (∆Q/∆P)×(P/Q) Marketing Analytics

7. Belvedere Vodka Marketing Analytics

8. Belvedere Price Elasticity Marketing Analytics

9. Belvedere Advertising Elasticity Marketing Analytics

10. Marketing Analytics

11. Customer Retention: Logistic Regression 0 • Linear regression assumes the dependent variable (DV) to be continuous (and normally distributed) • Often we have variables where there are only 2 different values • Buy (1) vs no buy (0) • Retain (1) vs lose customer (0) Profits - + Marketing Analytics

12. Customer Retention: Logistic Regression • With categorical (1/0) dependent variables, linear regression can result in nonsensical estimated probabilities (e.g. probability of retention > 100%) • A model that allows us to do this is the so-called “logistic regression” • Predictions are bound between [0,1] Marketing Analytics

13. Marketing Analytics

14. Logistic Regression: The connection to Bookies This is called  the “odds” Chance of retention to chance of churn Marketing Analytics

15. SuperBowl 2012 Odds Marketing Analytics

16. What is Odds? • If you chose a random day of the week (7 days), then the odds that you would choose a Sunday would be: • (1/7)/[1-(1/7)] = 1/6, but not  1/7. • The odds against you choosing Sunday are 6/1 = 6 , meaning that it's 6 times more likely that you don't choose Sunday. • Generally, 'odds' are not quoted to the general public in this format because of the natural confusion with the chance of an event occurring being expressed fractionally as a probability. • A bookmaker may (for his own purposes) use 'odds' of 'one-sixth', the overwhelming everyday use by most people is odds of the form 6 to 1, 6-1, or 6/1 (all read as 'six-to-one') where the first figure represents the number of ways of failing to achieve the outcome and the second figure is the number of ways of achieving a favorable outcome: thus these are "odds against". • An event with m to n "odds against" would have probability n/(m + n), while an event with m to n "odds on" would have probability m/(m + n). Source: http://en.wikipedia.org/wiki/Odds Marketing Analytics

17. Example: Will a Physician Prescribe a Drug? Data Model Marketing Analytics

18. Example: XLStat Output Marketing Analytics

19. Logistic Regression: Coefficients • Key difference: coefficients are not interpreted as such • Need to calculate “odds ratio” • For example, if the logit regression coefficent b = 2.303, then the odds ratio is: eb =e2.303 = 10 •  when the IV increases one unit, the odds that the DV = 1 increases by a factor of 10, when other variables are controlled. Marketing Analytics

20. Example: XLStat Output What is the Odds Ratio for Sales Calls? • Caution: odds ratios that are close to one, do NOT suggest that the coefficients are insignificant – it just means there is 50/50 chance of outcome Marketing Analytics

21. Example: Physicians Prescriptions For each additional sales call, the odds of a physician prescribing a drug increases by 43% (holding everything else constant). Prob (prescription) when sales calls is zero = exp(-0575)/[1+exp(-0.575)] Prob (prescription) when sales calls is one = exp(-0.575+0.361)/[1+exp(-0.575+0.361)] 0.36/(1-0.36) Marketing Analytics

22. Reaction to econometric analysis?

23. Combined Effect of Age and Online Average Profit Marketing Analytics

24. Diagnosing Customer Profits and Retention: Common Drivers Behavioral characteristics • purchase volume/quantity • Frequency of buying • length of relationship • number of product categories purchased • selling costs • customer satisfaction Demographic/firmographic characteristics • Age, income, gender • Loyalty program membership • Firm size Psychographic characteristics • Attitudes, values • Interests • Activities Goal: To identify key lever(s) that “drive” customer value Marketing Analytics

25. Model Building • Determine properties of dependent variable • Linear, + ve values, Dummy Variable • Select model that reflects dependent variable properties • Logistic regression for dummy variables Marketing Analytics

26. Model Building • Include the decision variable of interest among the independent variable set • Price, advertising, online • Include common control variables • Quality, Distribution, Demographics, Tenure, Competition etc. Marketing Analytics

27. Model Building • Does including lagged dependent variable lead to UNIT ROOT? • If UNIT ROOT, use difference as the dependent variable • Are some independent variables correlated more than 0.8. If so, can we eliminate one of the correlated variables or combine them. Marketing Analytics

28. Model Building • Are some variables Missing at Random (MAR) or are they missing systematically? • If variables are missing systematically, are there proxies that can replace the missing variables Marketing Analytics

29. Model Building • Does the model hint @ causality or is it a correlational model? • Are dependent and independent variables measured at the same time? • Are there sufficient controls or confounding variables included • Can a reverse causation reasonably exist • Do we need to recommend an experiment? Marketing Analytics