Comparing the fits of 2 continuous variables I have a data set with continuous x and y values that appear to be related in a exponential way. I then have different treatment groups , which appear to shift the x and y relationships. I would like to quantify if there are indeed shifts in the exponential relationships after treatment. Therefore i was wondering what are the best and most reliable statistical tests to carry out? Thanks
 A: Sounds like a job for a simple regression analysis. If the $y-x$ relationship follows an exponential form, then a log transform of the outcome will yield data which are related linearly. You may regress the log of $y$ onto $x$ adjusting for treatment assignment as a categorical variable. If treatment assignment is found to be statistically significant, we say that "$y$ differed $\exp(\beta_{treat})$-fold comparing groups in the treatment arm and control having the same value of $x$".
Depending on the nature of the data, a GLM is likely to model these data in a more "scientific" way, esp if the "y" variable is a rate, count, or proportion. For instance, a Poisson GLM would compare the relative rate of $Y$ (a count variable) between treatment and control having the same value of $x$. This line of reasoning (conditioning on the other adjustment variables) is the main rationale for multivariate regression models. (When I say multivariate I mean more than 1 regressor or covariate in the model).
