Logistic Regression

What Type of Regression? Dependent Variable – Y Continuous – e.g. sales, height Dummy Variable or Multiple Regression

What Type of Regression? Dependent Variable – Y Continuous – e.g. sales, height Dummy Variable or Multiple Regression Binary (0 or 1) – Purchased product or didn’t purchase Logistic Regression

Logistic Regression A logistic regression can be viewed as regression where the dependent variable Y is a Dummy variable or a binary variable (0 or 1).

Examples A success may be defined in terms of having a credit card client upgrade from a standard card to a premium card. A success may be defined in terms of launching the Space Shuttle successfully and not having any damage to the secondary motors during the launch and flight.

Odds Ratio Odds Ratio: a logistic regression is based on the idea of an odds ratio, the probability of a success over the probability of a failure. pr = probability

Odds Ratio Odds Ratio: a logistic regression is based on the idea of an odds ratio, the probability of a success over the probability of a failure.

Interpreting Odds Ratios Equally likely to Succeed or Fail

Interpreting Odds Ratios Equally likely to Succeed or Fail Odds Ratio = 3 Three time more likely to Succeed than to Fail

Interpreting Odds Ratios Equally likely to Succeed or Fail Odds Ratio = 1/4 Four time more likely to Fail than to Succeed

Upgrading a Credit Card A manager would like to know what influences the chance that a credit card customer would upgrade their credit card from a standard to a premium card Possible Predictors of Chance Customer Upgrades Annual Credit Card Spending If they posses additional credit cards Introductory offers Gift certificate to a local restaurant Reduced Interest rate for six months

Data 1 = Upgrade 1 = Additional Credit Card 1 = Reduced Interest Rate 0 = Gift Certificate

Model Assumption The Model:

Estimating Using SPSS Select: Analyze/Regression/Binary Logistic

Interpreting SPSS Output Classification Table for UPGRADE The Cut Value is .50 Predicted No Upgrade Upgrade Percent Correct N ó U Observed ôòòòòòòòòòòòôòòòòòòòòòòòô No Upgrade N ó 16 ó 1 ó 94.12% ôòòòòòòòòòòòôòòòòòòòòòòòô Upgrade U ó 2 ó 11 ó 84.62% Overall 90.00% Total: 18 Total: 12 Correct =16/17 Total: 17 =11/13 Total: 13 Predicted, using model vs actual observed

Interpreting SPSS Output Parameter Estimates ---------------------- Variables in the Equation -----------------------   Variable B S.E. Wald df Sig R Exp(B) OTHERCAR 3.2971 1.6417 4.0335 1 .0446 .2226 27.0332 PROMOTIO 3.1350 1.2912 5.8953 1 .0152 .3080 22.9885 SPENDING -.0142 .0515 .0760 1 .7828 .0000 .9859 Constant -2.7946 1.5654 3.1871 1 .0742

Interpreting SPSS Output Hypothesis Testing ---------------------- Variables in the Equation -----------------------   Variable B S.E. Wald df Sig R Exp(B) OTHERCAR 3.2971 1.6417 4.0335 1 .0446 .2226 27.0332 PROMOTIO 3.1350 1.2912 5.8953 1 .0152 .3080 22.9885 SPENDING -.0142 .0515 .0760 1 .7828 .0000 .9859 Constant -2.7946 1.5654 3.1871 1 .0742 Wald = like t-statistic or z-statistic (Large Reject Null) Sig. = like p-value (Small Reject Null) Sig. for Spending Large Remove Spending

Interpreting SPSS Output Hypothesis Testing ---------------------- Variables in the Equation -----------------------   Variable B S.E. Wald df Sig R Exp(B) OTHERCAR 3.0184 1.2642 5.7003 1 .0170 .3002 20.4582 PROMOTIO 3.0508 1.2466 5.9895 1 .0144 .3117 21.1323 Constant -3.0994 1.1491 7.2750 1 .0070 Wald = like t-statistic or z-statistic (Large Reject Null) Sig. = like p-value (Small Reject Null) Sig. less than 0.05 Do not Remove any more variables

Model Choice Full Model:

Model Choice Full Model: Next and Final Model:

Predicting Probability of Success Customer Profile: Spent $0 last year:

Predicting Probability of Success Customer Profile: Spent $0 last year: Has no additional credit cards:

Predicting Probability of Success Customer Profile: Spent $0 last year: Has no additional credit cards: Received gift certificate promotion:

Predicting Probability of Success Customer Profile: Spent $0 last year: Has no additional credit cards: Received gift certificate promotion:

Predicting Probability of Success Customer Profile: Spent $0 last year:

Predicting Probability of Success Customer Profile: Spent $0 last year: Has additional credit cards:

Predicting Probability of Success Customer Profile: Spent $0 last year: Has additional credit cards: Received reduce interest promotion:

Predicting Probability of Success Customer Profile: Spent $0 last year: Has additional credit cards: Received gift certificate promotion:

Space Shuttle Analysis How does temperature influence the probability of damage occurring to the Space Shuttle’s engines?

Data 1 = Damage

SPSS Analysis Sig. for Temperature < 0.05 --------------------- Variables in the Equation -----------------------   Variable B S.E. Wald df Sig R Exp(B) TEPMERATURE -.2360 .1074 4.8320 1 .0279 -.3126 .7898 Constant 15.2954 7.3281 4.3565 1 .0369 Sig. for Temperature < 0.05 Temperature Influences Damage

Predicting Probability of Success Launch Profile: Temperature 36:

Predicting Probability of Success Launch Profile: Temperature 36: