LM Model Assumptions: Transforming Data in R using log() I have a dataset in which I am trying to fit a model for:
model <- lm(expression_fold~distance, data = pairwise_sub)

However the data set is heteroscedastic, to overcome this assumption I want to transform the data, I used the below which works:
best_model <- lm(log(expression_fold+5)~distance, data = pairwise_sub)

However, I would like to know if I can '+5' instead of '+1' and wether this will change my data.
 A: It depends, are you in it for prediction, or does interpretation matter to you as well? At least when interpreting the slope, it won't make a difference, see this paper, which deals with your specific issue
A: Heterosckedasticity can take different forms so without seeing a scatter plot of expression_fold versus distance, it is difficult to comment pertinently on how you could best incorporate it in your modelling. 
One possibility is to model the nature of heterosckedasticity directly (without transforming your outcome variable) using the gls() function in R, which comes from the nlme package.  This function has a weights = argument which can be used to model the specific nature of heterosckedasticity. See the Appendix to the article "Marginal Models Via GLS: A Convenient Yet Neglected Tool for the Analysis of Correlated Data in the Behavioural Sciences" by Stano Pekar et al. for some specific examples: https://onlinelibrary.wiley.com/doi/abs/10.1111/eth.12514. 
Another possibility is to use the lm() function (again, without transformation of the outcome variable) to obtain the estimated coefficients but obtain heterosckedasticity-corrected standard errors, as explained for instance here: 
https://bookdown.org/ccolonescu/RPoE4/heteroskedasticity.html.  This comes handy when the form of the heterosckedasticity may be too complicated to adequately model. 
