I'm trying to model a lognormal response variable. I want to take the log of the response variable and do a least-squares regression line over my predictive variable. However, I'm worried about this. Is this an okay thing to do? I know that for my original variable, variance grows with the mean, but would taking logs adjust for this appropriately?
I would suggest using a generalised linear model (GLM) with a log-link function instead of directly log-transforming your variables; in R you can simply use
family= gaussian(link='log') to begin with.
I say this because modelling the mean of the log-transformed variable (as you would do by simply taking the logarithms of your dependent variable) is not always the same as modelling the log of the variable's mean. The user @Corone made a very informative post about this issue here. In short, if the logarithm transformation is not perfectly appropriate it will give suboptimal results in comparison with a GLM.
A very good initial point is the paper by Lindsey & Jones on "Choosing among generalized linear models applied to medical data". (It is easily found online for free if you google/bing the title...)
I want to take the log of the response variable and do a least-squares regression line over my predictive variable.
If I expected the relationship to be linear on the log scale, that's where I'd probably start.
Is this an okay thing to do?
It can be; it depends on what else is going on.
I know that for my original variable, variance grows with the mean, but would taking logs adjust for this appropriately?
It might, or it might not. It depends on exactly how the variance is related to the mean. If the standard deviation is a constant multiple of the mean (variance proportional to mean squared), then you should end up with constant variance on the log scale. Otherwise you won't.