Why does logistic regression not have variance, but have deviance?

Question

In this blog of Section 5.2, the author said:

For the linear regression, we evaluate the overall model fit by looking at the variance explained by all the predictors. For the logistic regression, we cannot calculate a variance. However, we can define and evaluate the deviance instead.

Why the logistic model cannot calculate the "variance"? The dependent variable has already been logit transformed, and becomes a continuous variable from $-\infty$ to $\infty$. Why does it different from the "regular linear regression", as is written is Section 2:

Different from the regular linear regression, no residual is used in the model.

Answer 1

You seem to be confused, and really need to read a good elementary introduction to logistic regression (or generalized linear models). On this site, you could start with Interpretation of coefficients in logistic regression output and Understanding R output in Logistic Regression.

In short, sums of squares in normal-distribution based linear regression is (a transformation of) log likelihoods, but in generalized linear regression models (glm's) such as logistic regression, log likelihood can take very different forms. I take it that with variance you refer to these various sums-of-squares. Deviance is a generalization (replacement) for these used in glm's. For the details you need to read a good intro or tutorial.