文档介绍：Logistic Regression
Module Objectives
Understand the three different types of logistic regression available for the modeling of Attribute Responses:
Binary Response Variables
Ordinal Response Variables
Nominal Response Variables
Be able to apply Logistic Regression using Minitab for both categorical and continuous input variables
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Logistic Regression
Logistic or “Logit” Regression investigates the relationship between response variables (Y’s) and one or more predictor variables (X’s) where:
Y’s are categorical, not continuous
X’s can be either continuous or categorical
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Logistic Regression in Minitab
Binary Logistic: Regresses the independent variables on a binary response (two categories)
Ordinal Logistic: Regresses the independent variables on an ordinal response with 3 or more categories
Nominal Logistic: Regresses the independent variables on a nominal response with 3 or more categories.
The logistic procedures in Minitab can fit up to
9 categorical inputs (factors), and
50 continuous inputs (covariates)
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Examples of Different Types of Models
Number of
Categories
Examples
BINARY
2
Pass, Failure
Yes, No
ORDINAL
3 or more
None, mild, severe
Strongly Disagree,
Disagree, Agree,
Strongly agree
NOMINAL
3 or more
Two levels
Natural ordering
of the levels
No natural ordering
of the level
Blue, black, red
Sunny, rainy, cloudy
Characteristics
Variable
Type
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Binomial data violates normality, equal variance assumption
k = nxp = nxpx(1-p) = k x(1-p)
Variance changes as the mean changes
The relationship between p, the likelihood of “ess” and the predictor variables might not be linear
Why Logistic Regression ?
Prob(ess) = a+bx ???
Prob(ess):
Increases slowly,
Has a “linear” phase, then
Decreases slowly as p ->
OR……..
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Introducing Odds and Odds Ratios
Odds = p/(1-p) = pr(event occurs)/pr(event does not occur) = O
p = O/(O+1)
For example, define an event as : an account is paid in 30 days:
If the odds are 6 to 1, this im