It might work.

The assumption of normality is with the residuals not the distribution of the independent variables.

Do you use a GLM of the Poisson family?

As I am yet new to GLM, my hope is to keep it in linear regression. Thank you, Dr. Ebert, for that important clarification! Re: Dr. Wilhelm, I was under the impression that Poisson regression had to be with discrete variables/counts, whereas my variable is continuous. Is there an appropriate GLM operation for continuous variables with a poisson distribution?

You said your dependent variable has a Poisson distibution - that implies that this is a "count-like" discrete variable. If you meant to say that your dependent variable is continuous, strictly positive and has a right-skewed distribution, then a log-normal or a gamma model might be a good choice. The log-nomal would be simple - just do a standard regression using log(Y) instead of Y. The gamma model is a member of the exponential family of distributions, so like Poisson you can fit this in the GLM framework.

PS: Note that the standard regression is a GLM of the normal family with identity link, so if you did that, you are actually not completely new to GLMs ;)

You may be new to GLM but a) you were once new to regression, and from your photo you look young enough to learn another trick, and b) the simplest GLM is linear regression (actually, it's the t-test, but the t-test is a linear regression with a single binary predictor).

So go and find out about GLM. You wouldn't try eating soup with a fork, just because you already had one, would you?

You may have a look here, as a start:

http://www.sagepub.com/upm-data/21121_Chapter_15.pdf

@Joachen

Might you, please, tell me which book is the chapter you suggested taken from ?

John Fox: Applied Regression Analysis and Generalized Linear Models

SAGE Publications, 2015

ISBN 1483321312

Thank you !

A very interesting Stata blog entry by Bill Gould which should be recommended reading for anyone thinking of taking the log of their dependent variable:

https://blog.stata.com/2011/08/22/use-poisson-rather-than-regress-tell-a-friend/

Thanks for these great answers over time. For anyone interested in this question in the future, turns out I was looking for a gamma model, which can easily handle continuous, right-skewed data (although an OLS model with a log-transformed dependent variable should work just fine too).