logistic regression. what type of regression? dependent variable – y continuous – e.g. sales,...
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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 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).
Failure0,
Success1,Y
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(Success)
1 pr(Success)Odds Ratio
pr(Y =1)
1 pr(Y =1)Odds Ratio
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.
pr(Success) pr(Success)
1 pr(Success) pr(Failure)Odds Ratio
1 pr(Success) pr(Failure)
Interpreting Odds Ratios Odds Ratio = 1
Equally likely to Succeed or Fail
Odds Ratio = 3 Three time more likely to Succeed than to Fail
pr(Success) pr(Failure)
3pr(Success) pr(Failure)
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
pr(Success) pr(Failure)
4 pr(Success) pr(Failure)
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
Customer Upgrade Credit Card
Annual Spending
Possession of Additional Credit Card
Promotion
1 0 32.1007 0 02 1 34.3706 1 13 0 4.8749 0 04 1 8.1263 0 15 0 12.9783 0 06 1 16.0471 0 17 0 20.6648 0 08 1 42.0483 1 19 0 42.2264 1 0
10 1 37.99 1 111 1 53.6063 1 012 0 38.7936 0 113 0 27.9999 0 014 1 42.1694 0 115 0 56.1997 1 016 0 23.7609 0 117 0 35.0388 1 018 1 49.7388 1 119 0 24.7372 0 020 1 26.1315 1 121 0 31.322 1 022 1 40.1967 1 123 0 35.3899 0 024 0 30.228 0 125 1 50.3778 0 026 0 52.7713 0 127 1 27.3728 0 028 1 59.2146 1 129 0 50.0686 1 030 1 35.4234 1 1
1 = Upgrade
1 = Additional Credit Card
1 = Reduced Interest Rate
0 = Gift Certificate
1317N =
Customer Upgraded to Premium Card
UpgradeNo Upgrade
Cre
dit
Ca
rd S
pe
nd
ing
60
50
40
30
20
10
0
23
21
15
Customer Upgraded to Premium Card
UpgradeNo Upgrade
Per
cent
100
80
60
40
20
0
Type of Promotion
Gif t Certif icate
Reduced Interest
Customer Upgraded to Premium Card
UpgradeNo Upgrade
Per
cent
100
80
60
40
20
0
Other Credit Card
No Other Card
Has Other Card
Model Assumption The Model:
Spend Spend OtherCC OtherCCa X X ln(Odds Ratio)
Pr Promotion omotionX
1, Have other Credit Card
0, No other Credit Card OtherCCX
Pr
1, Reduced Interest
0, Gift Certificate omotionX
Interpreting SPSS OutputClassification Table for UPGRADEThe Cut Value is .50 Predicted No Upgrade Upgrade Percent Correct N UObserved No Upgrade N 16 1 94.12% Upgrade U 2 11 84.62% Overall 90.00%
Predicted, using model vs actual observed
Total: 13
Total: 17
Total: 18 Total: 12
=16/17=11/13
Correct
Interpreting SPSS Output
---------------------- Variables in the Equation ----------------------- Variable B S.E. Wald df Sig R Exp(B) OTHERCAR 3.2971 1.6417 4.0335 1 .0446 .2226 27.0332PROMOTIO 3.1350 1.2912 5.8953 1 .0152 .3080 22.9885SPENDING -.0142 .0515 .0760 1 .7828 .0000 .9859Constant -2.7946 1.5654 3.1871 1 .0742
Parameter Estimates
Spend Spend OtherCC OtherCCa X X ln(Odds Ratio)
Pr Promotion omotionX
Interpreting SPSS Output
---------------------- Variables in the Equation ----------------------- Variable B S.E. Wald df Sig R Exp(B) OTHERCAR 3.2971 1.6417 4.0335 1 .0446 .2226 27.0332PROMOTIO 3.1350 1.2912 5.8953 1 .0152 .3080 22.9885SPENDING -.0142 .0515 .0760 1 .7828 .0000 .9859Constant -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)
Hypothesis Testing
Sig. for Spending Large Remove Spending
Interpreting SPSS Output
---------------------- Variables in the Equation ----------------------- Variable B S.E. Wald df Sig R Exp(B) OTHERCAR 3.0184 1.2642 5.7003 1 .0170 .3002 20.4582PROMOTIO 3.0508 1.2466 5.9895 1 .0144 .3117 21.1323Constant -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)
Hypothesis Testing
Sig. less than 0.05 Do not Remove any more variables
Model Choice Full Model:
Next and Final Model:
Spend Spend OtherCC OtherCCa X X ln(Odds Ratio)
Pr Promotion omotionX
OtherCC OtherCCa X ln(Odds Ratio)
Pr Promotion omotionX
Predicting Probability of Success
Customer Profile: Spent $0 last year: Has no additional credit cards: 0OtherCCX
0SpendX
Predicting Probability of Success
Customer Profile: Spent $0 last year: Has no additional credit cards: Received gift certificate promotion:
ˆ -3.0994a ln(Odds Ratio)
0OtherCCX 0SpendX
Pr 0omotionX
ln(Odds Ratio) -3.0994e eOdds Ratio
0.045
Predicting Probability of Success
Customer Profile: Spent $0 last year: Has no additional credit cards: Received gift certificate promotion:
0OtherCCX 0SpendX
Pr 0omotionX
0.045Odds Ratio
pr(Success)
1 pr(Success)Odds Ratio
Odds Ratiopr(Success)1+Odds Ratio 0.045
0.043 0.0451+
Predicting Probability of Success
Customer Profile: Spent $0 last year: Has additional credit cards: 1OtherCCX
0SpendX
Predicting Probability of Success
Customer Profile: Spent $0 last year: Has additional credit cards: Received reduce interest promotion:
Prˆ ˆˆOtherCC omotion
a ln(Odds Ratio)
1OtherCCX
0SpendX
Pr 1omotionX
2.97eOdds Ratio 19.48
-3.0994 3.0184 3.0508 2.97 ln(Odds Ratio)
Predicting Probability of Success
Customer Profile: Spent $0 last year: Has additional credit cards: Received gift certificate promotion:
1OtherCCX 0SpendX
Pr 1omotionX
19.48Odds Ratio
pr(Success)1-pr(Success)
Odds Ratio
Odds Ratiopr(Success)1+Odds Ratio
19.48 0.951 19.48
Space Shuttle Analysis How does temperature influence the
probability of damage occurring to the Space Shuttle’s engines?
1, Damage
0, No Damage Y
Data
Index Number Damage Temperature
1 0 0 662 1 1 703 0 0 694 0 0 805 0 0 686 0 0 677 0 0 728 0 0 739 0 0 70
10 1 1 5711 1 1 6312 0 0 7813 1 1 7014 0 0 6715 2 1 5316 0 0 7517 0 0 6718 0 0 7019 0 0 8120 0 0 7621 0 0 7922 2 1 7523 0 0 7624 1 1 58
1 = Damage
SPSS Analysis
--------------------- Variables in the Equation ----------------------- Variable B S.E. Wald df Sig R Exp(B) TEPMERATURE -.2360 .1074 4.8320 1 .0279 -.3126 .7898Constant 15.2954 7.3281 4.3565 1 .0369
Sig. for Temperature < 0.05
Temperature Influences Damage
Predicting Probability of Success
Launch Profile: Temperature 36:
ˆˆTemperature Temperature
a X ln(Odds Ratio)
36TemperatureX
6.79eOdds Ratio 897.3
15.29 0.236 36 6.79 ln(Odds Ratio)