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
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