Rajkumar VenkatesanMarketing Analytics Regression

Rajkumar Venkatesan 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 runs will take care of themselves.

Rajkumar VenkatesanMarketing Analytics Diagnosing Market Response: Regression Analysis NUMBER OF PROMOTIONS $ SPENT BY A CUSTOMER

Rajkumar VenkatesanMarketing Analytics Example: Shopper Card Program Units purchased = a+b 1 *price paid + b 2 *feature ad + b 3 *display Data

Rajkumar VenkatesanMarketing Analytics Example: Regression Output From Excel

Rajkumar Venkatesan Price Elasticity Marketing Analytics 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)

Rajkumar Venkatesan Belvedere Vodka Year Sales (units)Ln(Sales) Price (dollars )Ln(Price) Advertising (dollars)Ln (Advertising) Marketing Analytics

Rajkumar Venkatesan Belvedere Price Elasticity Regression Statistics Multiple R R Square Adjusted R Square Observations7 Coefficients Standard Errort StatP-value Intercept Ln (Price)− − Marketing Analytics

Rajkumar Venkatesan Belvedere Advertising Elasticity Regression Statistics Multiple R R Square Adjusted R Square− Standard Error Observations7 Coefficients Standard Errort StatP-value Intercept Ln (advertising)− − Marketing Analytics

Rajkumar VenkatesanMarketing Analytics

Rajkumar VenkatesanMarketing Analytics Customer Retention: Logistic Regression 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

Rajkumar VenkatesanMarketing Analytics 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]

Rajkumar VenkatesanMarketing Analytics

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

Rajkumar Venkatesan SuperBowl 2012 Odds Green Bay Packers3.45 to 1 New England Patriots4.4 to 1 New Orleans Saints8.5 to 1 Baltimore Ravens9.5 to 1 San Deigo Chargers10.5 to 1 Detroit Lions13 to 1 Houston Texans17.5 to 1 Pittsburg Steelers20 to 1 Marketing Analytics

Rajkumar VenkatesanMarketing Analytics 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:

Rajkumar VenkatesanMarketing Analytics Example: Will a Physician Prescribe a Drug? Data Model

Rajkumar VenkatesanMarketing Analytics Example: XLStat Output

Rajkumar VenkatesanMarketing Analytics 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: e b =e = 10 –  when the IV increases one unit, the odds that the DV = 1 increases by a factor of 10, when other variables are controlled.

Rajkumar VenkatesanMarketing Analytics 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

Rajkumar VenkatesanMarketing Analytics 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( )/[1+exp( )] 0.36/(1-0.36)

Rajkumar Venkatesan Reaction to econometric analysis?

Rajkumar VenkatesanMarketing Analytics Combined Effect of Age and Online Average Profit

Rajkumar VenkatesanMarketing Analytics 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

Rajkumar Venkatesan 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

Rajkumar Venkatesan 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

Rajkumar Venkatesan 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

Rajkumar Venkatesan 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

Rajkumar Venkatesan Model Building Does the model 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