Non-linear regression analysis in R
I'm a R novice but I'm looking for a way to determine the three parameters A, B and C related by the following function in R:
y = A * (x1^B) * (x2^C)
Can someone give me some hints about R method(s) that would help me to achieve such a fitting?
Answer
One option is the nls function as @SvenHohenstein suggested. Another option is to convert your nonlinear regression into a linear regression. In the case of this equation just take the log of both sides of the equation and do a little algebra and you will have a linear equation. You can run the regression using something like:
fit <- lm( log(y) ~ log(x1) + log(x2), data=mydata)
The intercept will be log(A) so use exp to get the value, the B and C parameters will be the 2 slopes.
The big difference here is that nls will fit the model with normal errors added to the original equation and the lm fit with logs assumes that the errors in the original model are from a lognormal distribution and are multiplied instead of added to the model. Many datasets will give similar results for the 2 methods.