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Logistic Regression - ƽ ȸͺм [̷] 2019.06.10
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http://www.mysas.co.kr/sas_tiptech/a_all.asp?b_no=11114&cmd=content&bd_no=33


ȳϼ ڼԴϴ.


̹ð Ӻ зǴ 쿡 ִ ȸ ƽ ȸ м(Logistic Regression) ڽϴ.

 



1. Instroduction

 


,  ϰ мϰ ͽϴ. ׷ ؼ 0 1 Ȯ ǥ Ǿ ϴµ Ϲ ȸ м ׷ . ׷ 0 1 Ȯ Ÿ ȸ͸ ƽ ȸ м̶ մϴ.


 


2. Configuration


ƽ ȸͺм ߿ Ҵ ũ ֽϴ. ϳ Odds Ҹ ĶͿ, ̸ ̿ " ȯ" ׸ °  "ñ׸̵ Լ" ֽϴ. 


2.1 Odds


п Ǵ »̶ θ⵵ մϴ. p/(1  p) (p Ȯ ) Ǿ ִµ, ؼ Ͼ Ȯ Ͼ Ȯ մϴ. P Ȯ̹Ƿ, [0, ] ˴ϴ. ó Ȯ 1 ǰ, » ũ ̷ ˴ϴ.{\displaystyle [-\infty ,+\infty ]} p=0.8 ִٸ, Odds 4 ǰ, Ͼ Ȯ 4 » ִٴ ֽϴ.


 2.2  Logit


Odds ذ Ǽ̴ٸ, Logit ڽϴ. ƽ ȸ м ,


,


Ǿ ֽϴ. Ϲ ȸ͸ ϸ Y log(p/1-p) Ǿ ִ ֽϴ. LOG(Odds) ƽ ȸ Ǵ . Ȯ Odds [0, ] ȸͺм [-, +] ȯϱ ؼ, ȯ̶ θϴ.

 


2.3 ñ׸̵ Լ


P ˰ Դϴ. , ߻ Ȯ ϸ ߻, ƴϸ ߻ ֱ . ϸ,,,



ó P Ͽ Լ ñ׸̵ Լ մϴ.  [0,1] Ȯ ٲִ . ñ׸̵ ´ ϴ.



X , X 1 ش, 0 ش Ȯ ԼԴϴ.


 


3. Prove


Լ Ǿ غڽϴ.



 

ϰ Դϴ.

 

̸ ñ׸̵ Լ ڽϴ.

 



, Է° p [0,1] (, ͷκ 0 1 Ȯ) ° [-, +] ǵ ( P/1-P ) ȯ ݴϴ.



ȯ X Լ ϹǷ, ϸ



˴ϴ.



׸ ϰ ϸ ñ׸̵ Լ Ǿϴ.̸ ϸ, Pi ϰ ϴ Ư x, Ӻ Ͼ Ȯ ϴ .


 

4.


ִ밡ɵ ̿ؼ մϴ. Likelihood ϴµ, κ ִ밡ɵ MLE ڼ ٷ絵 ϰڽϴ. ɵ ī ٻμ ϴµ, ڼ ٷ絵 ϰڽϴ.


 


ð University Edition Ͽ ƽ ȸ ǽ ϰڽϴ.


 
 
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