10 Logistic Regression

10 Logistic Regression - Statistics 191: Introduction to...

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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Statistics 191: Introduction to Applied Statistics Logistic regression Jonathan Taylor Department of Statistics Stanford University March 3, 2010 1 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Topics Today’s class Binary outcomes. Logistic regression. Generalized linear models. Deviance. 2 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Logistic regression Binary outcomes Most models so far have had response Y as continuous. Many responses in practice fall into the YES / NO framework. Examples: 1 medical: presence or absence of cancer 2 financial: bankrupt or solvent 3 industrial: passes a quality control test or not 3 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Logistic regression Modelling probabilities For 0 - 1 responses we need to model π ( x 1 , . . . , x p ) = P ( Y = 1 | X 1 = x 1 , . . . , X p = x p ) That is, Y is Bernoulli with a probability that depends on covariates { X 1 , . . . , X p } . Note: Var( Y ) = π (1 - π ) = E ( Y ) · (1 - E ( Y )) Or, the binary nature forces a relation between mean and variance of Y . 4 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University Logistic regression Flu shot example A local health clinic sent fliers to its clients to encourage everyone, but especially older persons at high risk of complications, to get a flu shot in time for protection against an expected flu epidemic. In a pilot follow-up study, 50 clients were randomly selected and asked whether they actually received a flu shot. Y = Shot In addition, data were collected on their age X 1 = Age and their health awareness X 2 = Health . Aware 5 / 1
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Statistics 191: Introduction to Applied Statistics Jonathan Taylor Department of Statistics Stanford University
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10 Logistic Regression - Statistics 191: Introduction to...

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