Six Sigma Binary Logistic Reg.ppt

Learning Objectives
Understand how to test hypotheses with discrete Y’s
Understand what Logit is
Estimate the transfer function
Estimtate predicted probabilities
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Logarithm Vs. Logistics
Logistic Regression means a regression equation using natural logarithm
Although it has nothing to do with the logistics in business operations or military sciences, sometimes logistic regression can be used to analyse data from logistics
Remember:
X = ey, or X = EXP(Y)
Ln(X) = Y
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Types of Logistic Regression
Binary: Y value takes on only two possible levels
Yes/No, Defective/Not Defective
Really examining the rate of defect occurrence
Ordinal: Y value takes on 3 or more values, that are ordered
No Defect, Slight Defect, Moderate Defect, Serious Defect
Agree, Neutral, Disagree
Nominal: Y value it categorical, but not related or ordered
Phoenix, Atlanta, Detroit
Red, Blue, Yellow, Green
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Some Definitions
The values of probability (P) are limited to the range from 0 to 1
Odds=P/(1-P) can take any nonnegative values
Log Odds= Ln[P/(1-P)] can take any real numbers
Another name for Log Odds is logit
Odds Ratio=Odds1/Odds2
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Some Formulas and Examples
Odds=P/(1-P)
If P of ess=, then Odds of ess=/(1-)= , odds of ess is times as likely as failure
P=Odds/(1+Odds)
If Odds of ess is , then probability of ess =/(1+) =
If Log (Odds)=3, then Odds=Exp(3)=20
If Odds of Yes for female=3 and for male=2, their Odds Ratio=
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Logisitic Regression Model
Log[P/(1-P)]=a+b1x1+b2x2+...bnxnwhere P is the probability of ess
This is a general formula for logistic regression model, where P is the probability for Y=ess or Y=no.
We call Y the response variable. Also, we call X covariate when it is