1. Business Intelligence and Decision Modeling Week 11 Predictive Modeling (2) Logistic Regression

2. Outline Logistic Regression Purpose Odds and Logit Interpretation

3. Logistic Regression Models Logistic regression (binary target) Understand risk factors Assumptions same as linear regression Forecasting Split Samples

4. Logistic Regression: Odds and Probabilities Dichotomised Response (Y/N) Response Probability p Non Response Probability (1-p) Odds = p /(1-p) P = odds/(1+odds) O = p / (1-p)  (O – O p) = p O =p + Op  O = p (1+O) p = O /(1+O)

5. Probabilities and Odss Probability.10.20.30.40.50.60.70.80.90 Odds.11.25.43.67 1.00 1.50 2.33 4.00 9.00 Odds = (p / 1-p) P = odds/(1+odds)

6. Logistic Regression: Logit Logit Calculation Logit  ln(odds) or ln(p/1-p) Inverse Process e (Logit)  Odds If P = odds/(1+odds) Then p = e (Logit) /1+e (Logit) Orp = 1 / 1+e -Logit

7. Logistic Regression: Logit From p = e (Logit) /1+e (Logit) To p = 1 / 1+e -(Logit) Divide all members of the right proportion by e (Logit) P = 1 _  __1____ 1+ _1__ 1+ e- (Logit) e (Logit)

8. Logistic Regression and Function p = 1 / 1+e -z Where Logit or z = b 0 +b 1 x 1 +b 2 x 2 …+b p x p P=1 P=0 Z -6 -4 -2 0 2 4 6

9. Example (1) Z=-10.83 + (.28 x age) +(2.30 x gender) Where gender=0  Male et gender =1  Female If Male 40 years old Z = -10.83+(.28 x 40)+(2.30 x 0) Z =.37  Logit e.37 = 1.448  Odds Thus p = 1 / 1+e -z  p = 1 / 1+e -.37 =.59 or P = odds/(1+odds)  p = 1.448/(1+1.448) =.59

10. Example (2) Z=-10.83 +.28 x age +2.30 x gender where gender=0  Male And gender =1  Female If Female 40 years old Z = -10.83+(.28 x 40)+(2.30 x 1) Z = 2.67 e 2.67 = 14.44  Odds  Logit p = 1 / 1+e -z  p = 1 / 1+e -2.67 =.94 or P = odds/(1+odds)  p = 14.44/(1+14.44) =.93

11. Logistic Regression (1) Dependant Variable (0/1) Direct Marketing Customer Propensity to Buy Determine classification threshold Save scoring file Run Binary Logistic Regression Define category and metric variables Determine classification threshold Examine coefficients Save scoring xml file Compare classifications

12. Logistic Regression (2) Score Validation or Customer file Create Deciles (Visual Binning) Compare Means: Expected response rate per deciles Import Compare means into Excel Excel: Mkt metrics