# checking linearity assumption in logistic regression for continuous variable, truly linear?

One assumption of running a logistic regression is that the continuous predictors are linearly related with the log odds.

However, wouldn't it technically be better if it was shaped as is the logit function below, not really linear? I understand that the logit function is roughly linear when probabilities are between .3 and .7, but what about for very high or low probabilities where you test your assumption and it might not look, strictly speaking, linear? • It would be that S-shape for the probability, not the log-odds.
– Dave
Jan 20, 2021 at 21:04
• sorry, not quite "S" I suppose, I will rephrase and edit Jan 20, 2021 at 21:08
• It isn’t a generalized linear model because a line fits that curve in the middle of the curve. It’s a generalized linear model because it posits that the log-odds literally follows a linear pattern. (But then the probability does not!)
– Dave
Jan 20, 2021 at 21:45
• gotcha! Really helpful, thanks Jan 20, 2021 at 21:46