# Can pseudo $R^2$ be used to describe Fraction of Variance Explained?

I have recently done some Logistic regression analysis whose results I will be presenting to my non-mathematician colleagues. One of the key aspects to this is how well the regression fits the data in each specific case.

I'm using the McFadden Pseudo $R^2$ for this work, which is $1-\frac{null~deviance}{residual ~ deviance}$ , and I'm aware of others.

In linear regression, $R^2$ can be described as a measure of 'the fraction of variance explained'.

How well can this be generalised to a pseudo $R^2$ derived from a logistic regression?

For the purposes of talking to (albeit technical) non mathematicians, is it permissible to say that 'given an $R^2$ of X, my model explains X% of the behaviour that we have observed in the data'?

• Short answer is No. See threads stats.stackexchange.com/questions/68066/… and stats.stackexchange.com/questions/129585/… for discussion. Key points (1) it's possible to calculate variance explained directly (2) this may be of interest or use, but it's not what it is being maximised in logit regression (3) it's not the same necessarily as any other substitute (whether labelled pseudo or not) for $R^2$ May 17, 2018 at 12:02