R^2 and r^2 in multivariate regression to exponential function

#1
R^2 (model fit, correlation of Y-hat with Y) is r^2 (correlation of X with Y) in "simple linear regression."

I have two explanatory variables and an OLS model fitted to an exponential curve, y = ae^(b1x1 + b2x2), so I gather the two are different. Is it still possible to derive one from the other? Or -- if that is a relationship I really want to explore -- is it better to log-transform everything to have a linear situation?
 
#3
Although R^2 is not trivially equal to r^2, is there a way to derive R^2 from, or relate R^2 to, the combination of the separate correlations of the two independent variables with the dependent?
 
#6
“Researchers and reviewers should be aware that R2 is inappropriate when used for demonstrating the performance or validity of a certain nonlinear model. It should ideally be removed from scientific literature dealing with nonlinear model fitting or at least be supplemented with other methods such as AIC or BIC or used in context to other models in question.”
 
#7
I am not sure what you are asking. But r^2 lower case or capitalize is the same measure in a linear model. It is the proportion of the variance in the response that is explained by the linear relationship with the predictor(s). Thus, r^2 would not be an appropriate measure if the relationship is not linear.
 
#8
r^2 and R^2 are not equal if there are more than one dependent variable. For example, in the linear case, r1^2 + r2^2 = R^2. I was hoping there was an analogous formula for an exponential function, something like R^2 = e^(r1^2 + r2^2), but it looks like (1) the answer is no and (2) you shouldn't be using R^2 to evaluate non-linear models anyway.
 

Dason

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#11
Their previous post which is now deleted did mention the caveat that it only holds when the predictors are uncorrelated. In which case I believe it's a true statement. But that certainly wouldn't hold for the specific nonlinear case mentioned.