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Logistic Regression

Logistic Regression. Outline. Simple Logistic Regression Fungsi logistik Interpretasi koefisien coefficients Multiple Logistic Regression Examples. Logistic Function. P(“Success”|X). X. Logit Transformation. The logistic regression model is given by which is equivalent to.

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Logistic Regression

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  1. Logistic Regression

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

  3. Logistic Function P(“Success”|X) X

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

  5. 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

  6. 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

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

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

  9. Interpretation of the parameter b0(determines the intercept) p x

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

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

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

  13. 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

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

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

  16. The Multiple Logistic Regression model

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

  18. The data

  19. The results

  20. Menggunakan excel memanfaatkan solver add-in • http://blog.excelmasterseries.com/2014/06/logistic-regression-performed-in-excel.html

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