Suppose the distribution of X for subjects having Y=1 is normal , and suppose the distribution of X for subjects having Y=0 is normal . Then why is a logistic regression curve?

And why ?

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- Mar 23rd 2011, 04:36 AMnoob mathematicianNormally distributed X implies logistic regression for Y
Suppose the distribution of X for subjects having Y=1 is normal , and suppose the distribution of X for subjects having Y=0 is normal . Then why is a logistic regression curve?

And why ? - Mar 23rd 2011, 10:52 AMtheodds
Note that Y is Bernoulli with probability (say) and we are given that . Just calculate

and see what you get. I haven't done it all the way through, but it looks to me like you will get a function whose inverse is the logit.