1. Logistic Regression

3. Outline Simple Logistic Regression Multiple Logistic Regression
Fungsi logistik
Interpretasi koefisien coefficients
Multiple Logistic Regression
Examples

4. Logistic Function
P(“Success”|X) X

5. Logit Transformation The logistic regression model is given by
which is equivalent to
This is called the Logit Transformation

6. The logisitic Regression Model
Let p denote P[y = 1] = P[Success].
This quantity will increase with the value of x.
is called the odds ratio
The ratio:
This quantity will also increase with the value of x, ranging from zero to infinity.
The quantity:
is called the log odds ratio

7. Example: odds ratio, log odds ratio
Suppose a die is rolled:
Success = “roll a six”, p = 1/6
The odds ratio
The log odds ratio

8. The logisitic Regression Model
Assumes the log odds ratio is linearly related to x.
i. e. :
In terms of the odds ratio

9. The logisitic Regression Model
Solving for p in terms x. or

10. Interpretation of the parameter b0 (determines the intercept)x

11. Interpretation of the parameter b1 (determines when p is 0
Interpretation of the parameter b1 (determines when p is 0.50 (along with b0)) p
when x

12. Also
when
is the rate of increase in p with respect to x when p = 0.50

13. Interpretation of the parameter b1 (determines slope when p is 0.50 )x

14. The data The data will for each case consist of
a value for x, the continuous independent variable
a value for y (1 or 0) (Success or Failure)
Total of n = 250 cases

16. Estimation of the parameters
The parameters are estimated by Maximum Likelihood estimation and require a statistical package such as SPSS

17. Here is the output
The Estimates and their S.E.

19. The Multiple Logistic Regression model

20. Here we attempt to predict the outcome of a binary response variable Y from several independent variables X1, X2 , … etc

21. The data

22. The results

23. Menggunakan excel memanfaatkan solver add-in