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

2. Regressions Simple Regression Multiple Regression Logistic Regression
Y = a + bX + e
Multiple Regression
Y = a + b1X1 + b2X2 + … + bnXn + e
Logistic Regression
p = 1 / 1+e-z
Z = a + b1X1 + b2X2 + …+ bnXn + e

3. Logistic Regression and Function
p = 1 / 1+e-z
Where Logit or z = b0+b1x1+b2x2…+bpxp
P=1
P=0 Z

4. Outline
Logistic Regression
Purpose
Odds and Logit
Interpretation

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

6. Logistic Regression: Odds and Probabilities
Dichotomised Response (0/1)
Response Probability p
Non Response Probability (1-p)
Odds = p /(1-p)
P = odds/(1+odds)

7. 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)

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

9. Logistic Regression and Function
p = 1 / 1+e-z
Where Logit or z = b0+b1x1+b2x2…+bpxp
P=1
P=0 Z

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

11. Example (2) Z=-10.83 + .28 x age +2.30 x gender If Female 40 years old
where gender=0 Male
And gender =1 Female
If Female 40 years old
Z = (.28 x 40)+(2.30 x 1)
Z = 2.67
e2.67 = Odds
Logit
p = 1 / 1+e-z  p = 1 / 1+e-2.67 = .94 or
P = odds/(1+odds)  p = 14.44/( ) = .93

12. To Summarize Simple Regression Multiple Regression Logistic Regression
Y = a + bX + e
Multiple Regression
Y = a + b1X1 + b2X2 + … + bnXn + e
Logistic Regression
p = 1 / 1+e-z
Z = a + b1X1 + b2X2 + …+ bnXn + e