[R] Poisson regression

[Federico Gherardini]

Dear all,

First of all sorry if this is a dumb question...
I'm trying to fit a linear model between the logarithm of two numerical 
variables (log(y) ~ log(x)). A log-log plot shows that the variance of 
log(y) is decreasing with the mean of log(x), in other words the points 
are quite dispersed for low values of log(x) and approach a straight 
line as log(x) increases. I have tried the following glm model
fit <- glm(y ~ log(x), data = tab, family = poisson)
The residuals seem very good but I have a doubt: I have used y and not 
log(y) in  the model formula because, as far as I understand, the 
poisson regression assumes a logarithmic transformation of the response. 
Is this correct? I mean is it correct to watch a y ~ log(x) poisson 
regression line on a log(y) ~ log(x) xyplot or I am confusing the two 
things?

Thank you very much

Federico