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Logistic Regression

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 Dependent Variable – Y

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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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