logistik biner
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What Does Logistic Regression
Do?The logistic regression model uses the
predictor variables, which can be categorical
or continuous, to predict th
e probability of specific outcomes.
In other words, logistic regression is
designed to describe probabilities
associated with the values of the response
variable.
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Logit Transformation
Logistic regression models transformed
probabilities called logits.
where
i indexes all cases (obser vations).
pi is the probability the event (a sale, for
example) occurs in the i th case.
log is the natural log (to the base e).
logit( ) logp pp
i i
i
!
¨ª© ¸
º¹
1
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Assumption
P i
Predictor Predictor
LogitTransform
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Logistic Regression Model
logit (pi ) = F0 + F1X1
where
logit(pi ) logit transformation of the
probability of the event
F0 intercept of the regression line
F1 slope of the regression line.
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Example of Logistic Regression Model
You want to predict the probability of
purchasing 100 dollars or more of products
for each customer based on their customer
attributes. You can postulate this model:
logit (pi ) = F0 + F1 *(GENDER) + F2 *(AGE)
+
F3 *(INCOME)
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Measures of Association
� Measures of association are statistics that
indicate the strength of the association
between two variables.
� One advantage of statistical modeling is
that measures of association are often
functions of the estimated parameters.
� One measure of association that can be
computed in logistic regression is the
odds ratio.
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What Is an Odds Ratio?
An odds rat i o indicates how much more
likely, with respect to odds, a certain event
occurs in one group relative to its
occurrence in another group.Example: How much more likely are females
to purchase 100 dollars or more in
products compared to males?
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Probability of Outcome
Outcome
Group A
Group B
20 60
10 90
30 150
80
100
180
Total
Total
Y ES NO
Probability of a
=in group AYes outcome 20/80(25%)
Probability of a
=in group ANO outcome 60/80(75%)
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Odds
Odds of Outcome in Group A
Probability of
a Nooutcome in
group A
Probability of
a Yesoutcome in
group A
0.25 0.75 = 0.33
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Odds Ratio
Odds Ratioof Group A to Group B
Odds of outcomein
group A
Odds of outcomein
group B
0.33 0.11 = 3
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Properties of the Odds Ratio
0
ODDS RATIOOF GROUP A TO GROUP B
-0.5
No
Association
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Computing Odds Ratios
Group A
Group B
Total
Outcome
YES NO
20
10
30
60
90
150
80
100
180
Odds Ratio =20 x 90
60 x 10
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Binary LogisticRegression
This demonstration illustrates fitting abinary logistic regression model.
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Multiple Logistic Regression
Purchase Gender Income Age
logit (pi) = F0 + F1X1 + F2X2 + F3X3
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Multiple LogisticRegression
This demonstration illustrates fitting amultiple logistic regression model.
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