Sir, I'm attaching a paper of ours where our modeling approach might be of some interest to you. Given that you have not cited the paper it's hard to do much more than that. If these approaches don't help I suggest that you contact the original authors. BTW given your brief description it's not entirely clear that least squares is appropriate. Best wishes David Booth

Using the build-in dataset "InsectSprays" (https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/InsectSprays.html) as an example:

model1

Thank you so much for your suggestions @david eugene booth , @jochen wilhelm. Really appreciated.

I'm attaching the link to the paper, also the citation. Hope it helps to make my question more understandable.

https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=gordy+snail+host+species&btnG=#d=gs_qabs&t=1670319517086&u=%23p%3Dcsmy92ZSFTUJ

Gordy, M. A., Kish, L., Tarrabain, M., & Hanington, P. C. (2016). A comprehensive survey of larval digenean trematodes and their snail hosts in central Alberta, Canada. Parasitology Research, 115(10), 3867-3880.

Here's some references that might be helpful for you. I do notice that F statistics are not used to compare models but AIC is recommended instead. I added a copy of our previous paper that used AIC and may have some references for you. Good luck with your research

David Booth

David Eugene Booth, AIC allows you to compare models with different probability distributions, and non.nested models. This is a way to say which model performs better on the sample data (the model under which the data are less surprising "wins"), considering possibly different numbers of parameters. However, afaik, the AIC cannot be tested.

Jochen you are quite correct about statistical testing I should have said comparison. The important point here is F tests are inappropriate for these models and that AIC is equivalent to Mallow 's Cp statistic for ols regression, Which leads one to the comparison concept. Best wishes, David Booth