Logistic Regression

Outline Simple Logistic Regression Multiple 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 This is called the Logit Transformation

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

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

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

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

Interpretation of the parameter b0 (determines the intercept) x

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

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

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

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

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

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

The Multiple Logistic Regression model

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

The data

The results

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