# For linear regression, why do people usually standardize the X variables and log transform Y variables to make them normally distributed?

In many Kaggle competitions where linear regression has been applied, I see people plot the y distribution and then take the log of (or other transformation of) the dependent variable to make y normal distributed. What would happen if we don't do this step: transform the dependent variable into a normal distribution?

I have a few thoughts but wasn't sure which one is more correct and which one is wrong.

1. if y is skewed, after running the linear regression model, we could have the heteroscedasticity problem (variance is not constant along the predicted y)
2. we know the linear regression coefficients are still unbiased even if y is skewed; however, the t-test of the coefficient wouldn't make sense anymore because y is not a normal distribution.
3. Because X is usually standardized, y's distribution should match X's normal distribution.
• Is that for the regression or just the graph?
– Dave
Commented Sep 28, 2022 at 4:12
• taking log doesn't make a distribution normal Commented Sep 28, 2022 at 5:14
– mkt
Commented Sep 28, 2022 at 10:36
• @Galen, standardizing non-normal variables can never make them normal, as the family of Normal distributions is closed under changes of location and scale. Commented Sep 28, 2022 at 17:04
• @RichardHardy Agreed. I could have stated the problem more strongly. My comment alludes to existence of counterexamples, but we can use the universal quantifier here. Commented Sep 28, 2022 at 17:06