[R] coefficient of logistic regression

[Thomas W Blackwell]

Ahmet  -

In a logistic regression model, fitted probabilities make
sense for individual cases (rows in the data set), as well
as for future cases (predictions) for which no outcome
(success or failure) has been observed yet.  Fitted
probabilities are calculated from the matrix formula:

  Pr[success]  =  exp( X %*% beta) / (1 + exp( X %*% beta)

where  X  is an [n x (p+1)] matrix, containing all p predictor
variables as columns, preceded by a column of 1s for the
intercept, and  beta  is the [(p+1) x 1] vector of logistic
regression coefficients.

One can interpret the sign and the magnitude of an individual
regression coeffient by saying that an increase of 1 unit in
predictor variable [i] will increase or decrease the odds of
success by a multiplier of  exp(beta[i]).  When  beta[i] > 0
the odds increase, because  exp(beta[i]) > 1,  and when
beta[i] < 0  the odds decrease, because  exp(beta[i]) < 1.

I hope this explanation helps.

-  tom blackwell  -  u michigan medical school  -  ann arbor  -

On Tue, 3 Jun 2003, orkun wrote:

> Hello
>
> in logistic regression,
> I want to know that it is possible to get probability values of each
> predictors by
> using following formula for each predictor one by one (keeping constant
> the others)
>  <<< exp(coef)/(1+exp(coef)) >>>
>
> thanks in advance
> Ahmet Temiz