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Logistic Regression

Logistic regression is a statistical method widely used for binary outcome variables, where the dependent variable can take on values of 0 or 1 (e.g., success or failure). This technique is beneficial in predicting the likelihood of an event occurring based on various predictors such as spending habits or promotional offers. The analysis involves interpreting odds ratios to assess the relationship between predictors and the likelihood of outcomes. This guide also covers the use of SPSS for logistic regression analysis, including model fitting and hypothesis testing.

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Logistic Regression

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  1. Logistic Regression

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

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

  4. 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).

  5. 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.

  6. 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

  7. 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.

  8. Interpreting Odds Ratios • Odds Ratio = 1 • Equally likely to Succeed or Fail

  9. Interpreting Odds Ratios • Odds Ratio = 1 • Equally likely to Succeed or Fail • Odds Ratio = 3 • Three time more likely to Succeed than to Fail

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

  11. 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

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

  13. Model Assumption • The Model:

  14. Estimating Using SPSS • Select: Analyze/Regression/Binary Logistic

  15. 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% ôòòòòòòòòòòòôòòòòòòòòòòòô Overall 90.00% Total: 18 Total: 12 Correct =16/17 Total: 17 =11/13 Total: 13 Predicted, using model vs actual observed

  16. 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

  17. 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

  18. 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

  19. Model Choice • Full Model:

  20. Model Choice • Full Model: • Next and Final Model:

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

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

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

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

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

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

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

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

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

  30. Data 1 = Damage

  31. SPSS Analysis --------------------- 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

  32. Predicting Probability of Success • Launch Profile: • Temperature 36:

  33. Predicting Probability of Success • Launch Profile: • Temperature 36:

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