# Model regression of means different size and variance

I want to explain the relation between getting a reply and posting in a e-commerce. I want to know how much a reply increases postings.

I know I could do a regression of postings=f(replies) but the issue is that I have most of the postings getting only one reply. The distribution is skewed.

So, I could measure the means of postings by group (and the groups depends on how many replies you got), but I will have a lot of people in the first "xi" and almost nobody in the last. I think this might bring me issues because the variance in each point will be different.

How does this impact on my coefficient regression? Am I going to have issues related to heterocedasticity? How would be the most accurate way to measure this relation?

Thanks!

• Do you also count zeros, i.e., e-commerce for which no reply is posted? If so you could do some kind of poisson regression where the depended variable count the number of replys on e-commerce. Here the, though this can be relaxed, the variance changes if the mean will change. – Druss2k Aug 7 '14 at 14:33

You may want to apply negative binomial regression which relaxes the constant-variance assumption. This page has a great tutorial on this technique using R.

I am not sure what you mean by group and how your data are structured. Yet I suspect that the responses within groups may be correlated. Then, if you want to account for within-group variability, you may want to consider applying a generalized linear mixed model (GLMM) specifying group as a random factor. Again this webpage has a great tutorial.

The distribution of the predictor variable (replies) is not important in standard regression approaches (including generalized linear or many non-linear models). What you should be concerned about is the distribution of the residuals, or possibly the outcome variable for some models. Also, the functional form of the relationship between predictor and outcome is critically important. You have not provided this information, so I cannot comment further about which model to use.

Think about using dummy coding for categorical variables: those predictors may also be nearly only ones! But it's not a concern at all for standard regression models.

Here is a simple simulation in R demonstrating that a predictor with mainly ones can still yield unbiased estimates:

set.seed(0)
beta <- 1.5
n <- 100

beta.estimates <- replicate(
10^3,
expr={