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.



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



Assumption

P i

Predictor Predictor

LogitTransform



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.



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)



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.



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?



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%)



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



Odds Ratio

Odds Ratioof Group A to Group B

Odds of outcomein

group A

Odds of outcomein

group B

0.33 0.11 = 3



Properties of the Odds Ratio

0

ODDS RATIOOF GROUP A TO GROUP B

-0.5

No

Association



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



Binary LogisticRegression

This demonstration illustrates fitting abinary logistic regression model.



Multiple Logistic Regression

Purchase Gender Income Age

logit (pi) = F0 + F1X1 + F2X2 + F3X3





Multiple LogisticRegression

This demonstration illustrates fitting amultiple logistic regression model.

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