# Approximating GLM with a linear model

Let's say I have a model of $y$ with a single continuous independent variable $x$ that satisfies the GLM assumptions, but for computational reasons I prefer to run OLS instead.

I replace $y$ with moving average of $y$ (as I change $x$), in the hope that in the new model the error becomes distributed closer to normal due to law of large numbers.

Assuming that $x$ is sufficiently dense, would my OLS be a decent approximation for the GLM (in terms of both estimates and p-values), or am I missing something?

• Note that the variance of a GLM depends on the mean, whereas a LM has fixed variance. – Alex R. Mar 21 '16 at 23:24
• @AlexR. And now I think it also doesn't even have to be normal after I average them. It's quite possible that the large-window moving average is, for example, relatively fixed with an occasional drop - which would be a highly asymmetric distribution. – max Mar 25 '16 at 23:35