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AMDA-2008-Session 16

# AMDA-2008-Session 16 - Logistic Regression Simple Logistic...

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Logistic Regression

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Simple Logistic Regression ( 29 ( 29 ( 29 ( 29 x x x β α π π π π π π π π π + = + = = - = = = = = = = = (x) logit is model regression logistic The (x) logit by determined uniquely is (x) Thus . e 1 e (x) then (x) logit t If ) ( 1 ) ( ln (x) logit Define, x X when success of y probabilit x) X | 1 P(Y (x) Let (success) 1 and (failure) 0 values only two takes Y y variable explanator X variable response Y Let t t
The logistic function

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Interpreting Logistic Regression Equation Parameters chance. 50% has outcome each at which level the represents This . EL by denoted is and level effective median called is x of value This . - x 0.5 (x) 0.5 to equal is (x) e point wher at the maximum is (x) (x) value the and on depends (x) of change of rate The (x)). - (x)(1 (x) Note (x) on impact no has X in increase An 0 50 β α π π π π β π π βπ π π β = = = =
Odds Ratio Interpretation β β α β α π π e e e x x x = + = + = - at x success of Odds 1 at x success of Odds have we ) ( ) exp( ) ( 1 (x) Since

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Estimation of α and β ). , L( maximizing y numericall by obtained are ˆ and ˆ e 1 1 e 1 e )) ( 1 ( )) (x ( ) , L( is likelihood The 1 1 x x x 1 1 i i i i β α β α π π β α β α β α β α = - + + + = - + + = - = n i y y n i y i y i i i i x
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AMDA-2008-Session 16 - Logistic Regression Simple Logistic...

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