Chap8_Logistic%2bRegression-1

Chap8_Logistic%2bRegression-1 - Chapter 8 Logistic...

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Unformatted text preview: Chapter 8 Logistic Regression Galit Shmueli and Peter Bruce 2008 Data Mining for Business Intelligence Shmueli, Patel & Bruce Logistic Regression Extends idea of linear regression to situation where outcome variable is categorical Widely used, particularly where a structured model is useful to explain (= profiling ) or to predict We focus on binary classification i.e. Y =0 or Y =1 Why Not Linear Regression? Technically, you can run linear regression with a 0/1 response variable and obtain an output But the resulting model will not make sense For instance: Predictions will mostly not be 0 or 1 Coefficient interpretation will not make sense The Logit Goal: Find a function of the predictor variables that relates them to a 0/1 outcome Instead of Y as outcome variable (like in linear regression), we use a function of Y called the logit Logit can be modeled as a linear function of the predictors The logit can be mapped back to a probability, which, in turn, can be mapped to a class Step 1: Logistic Response Function p = probability of belonging to class 1 Need to relate p to predictors with a function that guarantees 0 p 1 Standard linear function (as shown below) does not: + q = number of predictors The Fix: use logistic response function Equation 8.2 in textbook Step 2: The Odds eq. 8.3 eq. 8.4 p p Odds- = 1 The odds of an event are defined as: p = probability of event Odds Odds p + = 1 Or, given the odds of an event, the probability of the event can be computed by: We can also relate the Odds to the...
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Chap8_Logistic%2bRegression-1 - Chapter 8 Logistic...

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