# In linear regression, in what situation(s) would you transform the response variable BEFORE having checked the assumptions?

I have a non-normally distributed, right-skewed response (dependent) variable which will be used in an (OLS) linear regression model. Why would I want to transform this before having checked the residual plots?

I've read multiple threads on here with regards to the 'normality' assumption only referring to the error terms (and not the response variable as often misinterpreted). However, I have also read that if the response variable is non-normally distributed, then it will result in the error terms not coming from a normal distribution. Therefore, would this result in the situation where you would routinely transform the response variable BEFORE having checked the residual plots?

• What about the situation where the response variable consists of only positive values and using linear regression (rather than GLM)?
– Jen
Commented Apr 26 at 14:36

You write:

However, I have also read that if the response variable is non-normally distributed, then it will result in the error terms not coming from a normal distribution.

I don't know where you read that, but it is demonstrably wrong in some cases. Here is some R code to show this (anything after a # is a comment):

set.seed(1234)

y <- c(rnorm(100, 0, 4), rnorm(100, 5, 2))
x <- c(rep(1, 100), rep(2, 100))

plot(density(y)) #Bimodal, not normal

m1 <- lm(y~x)
plot(density((m1$residuals))) #very close to normal  As to your question, I would transform Y before running a model when a transformation makes substantive sense. For instance, it often makes sense to take logs of variables relating to money. This is because we often think of these things in multiplicative rather than additive terms. E.g. if you make \$20,000 per year, a \$5,000 raise is huge. If you make \$200,000 per year, then a \\$5,000 raise is not so good