I want to model the association of a score (range 0-125) and age with an exponential approach because my scatterplot show an exponential progression.

My approach is:

I do log(score)

-> do a linear regression with age as covariate

-> do exp(regression coefficients)

The problem is: log(0) does not exist.

Just that it works I did log(score+0.01), but that is mathematically not correct.

Another Idea is to shift the score values systematically to the range 1-126. But this is also not a clean way.

Are there other possibilities or ideas to model an exponential fit to the data despite 0 values?

I would be very happy for every comment on this topic

Thanx in advance.

Best wishes

Icke