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rnon-linear-regression

how do i write this exponential model as a function in R?

For y = B0 + B1x, I can write it as lm(y ~ x). However I am not sure how to write y = B0eB1x into a model function in R.

I have tried lm(log(y) ~ x), lm(y ~ exp(x)), lm(y ~ log(x)), and lm(log(y) ~ log(x)), but I am not sure which is correct. I get different results for each model.

Solution

  • The two ways that you can do this that are actually faithful to the original statistical model (Gaussian errors with constant variance) are:

    glm(y ~ x, family = gaussian(link = "log"), data = ...)

    (but you'll have to exponentiate the intercept parameter) or

    nls(y ~ b0*exp(b1*x), start = ..., data = ...)

    (but you'll have to provide starting values in the form list(b0 = 1, b1 = 1) (for some sensible values).

    y = b0*exp(b1*x) implies log(y) = log(b0) + b1*x, but transforming the response variable in this way will change the statistical model ... so lm(log(y) ~ x, data = ...) will give you similar but not identical answers to the preceding two recipes.