R help - Mar 2026 - Regression on transformed variable

Hi,

In many case, we need to transform the dependent variable before
fitting a regression equation, to make it "well-behaved" like close to
normal curve etc.

like,

f(y) = alpha + beta1 X1 + beta2 X2 + ... + epsilon

Now for prediction, R will typically calculate E[f(y)] based on the
fitted coefficients. However, in real scenario, we actually need to
find E[y].

Typically, we perform reverse transformation like on fitted E[f(y)] directly.

However, I believe that in this process, we also need to make some
additional correction for non-linearity in the f() to correctly
calculate  E[y]. Onr possible way to do it, may be using Taylors
approximation.

My question is there any R function that would directly do that based
on the shape of f()?

Thanks for your time.

There are functions in the emdbook, metafor, and car packages that
do some version of the delta method (although people use "delta
method" to refer both to adjusting E[f(y)] using a second-order
correction [since the first-order term disappears] and to adjusting
V[f(y)] using a first-order correction ...)

  emmeans also has such capabilities, search the vignettes for "bias
correction"

   cheers
   Ben Bolker

On Thu, Mar 19, 2026 at 8:57?AM Christofer Bogaso
<bogaso.christofer at gmail.com> wrote:
>
> Hi,
>
> In many case, we need to transform the dependent variable before
> fitting a regression equation, to make it "well-behaved" like
close to
> normal curve etc.
>
> like,
>
> f(y) = alpha + beta1 X1 + beta2 X2 + ... + epsilon
>
> Now for prediction, R will typically calculate E[f(y)] based on the
> fitted coefficients. However, in real scenario, we actually need to
> find E[y].
>
> Typically, we perform reverse transformation like on fitted E[f(y)]
directly.
>
> However, I believe that in this process, we also need to make some
> additional correction for non-linearity in the f() to correctly
> calculate  E[y]. Onr possible way to do it, may be using Taylors
> approximation.
>
> My question is there any R function that would directly do that based
> on the shape of f()?
>
> Thanks for your time.
>
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