# Predicted Probabilities for Logit Models

Last month I asked this question here.

After thinking about it recently, I was wondering if it makes sense to think about logit probabilities in that regards. Since the predictor of a coefficient shows the log odds change in the response variable independent of all other predictors, we would expect that plotting bid vs pr(outcome), with the curve representing a different predictor is simply not useful. So if the coefficient for variable x is 0.5, that would be the log odds change regardless of the values for y, z, or f. Therefore, I'm wondering if it makes sense to make such a graph.

1. Am I thinking about logistic regression correctly? Since logit coefficients are independent of the other predictors, wouldn't a plot like that be largely "useless."

2. If that is the case, what should be the main use for predicted probabilities when using logit models?

Just some sample code if you wish:

df=data.frame(income=c(5,5,3,3,6,5),
won=c(0,0,1,1,1,0),
age=c(18,18,23,50,19,39),
home=c(0,0,1,0,0,1))
str(df)

md1 = glm(factor(won) ~ income + age + home,


Thanks!

• It might help to change how you think about chances a little. Rather than thinking in terms of probabilities, which are numbers between $0$ and $1$, logistic regression invites (nay, forces) you to think in terms of log odds (which can be any real number). When you do that, logistic regression looks remarkably like OLS multivariate regression. Perhaps then your present question almost answers itself from this viewpoint? – whuber Aug 13 '12 at 22:06
• Ah, sorry, I was not clear in my post. Right, the coefficient are in log-odds. But those values aren't too information, so I thought people use odds ratios or predicted prob's. I'm specifically talking about the probabilities. – ATMathew Aug 13 '12 at 23:20