# Why do we log variables if normality is not required? [duplicate]

I recently learned log-transforming a variable and it helps when our data is skewed. But, I also learned that the normality assumption of the data/variables is not required. The only requirement is the error being normally distributed. In that case, why would one log a variable? I used to think it was because the data needs to be normally distributed, but since it's not, I started wondering why?

• Taking the log of Y can help make the error distribution more normal, and more homoscedastic (constant variance). It can also reduce high leverage data (outliers). Etc. Apr 20 at 19:58
• The duplicate answers the question in one specific circumstance, thereby demonstrating that you need to make your question more specific -- and different -- to differentiate it from the other one. There are many threads here on CV about taking logarithms of variables, so please review some of them.
– whuber
Apr 20 at 20:50

One good reason to take the $$\log$$ of a variable is to change the interpretation. While this interpretation can break down, using a $$\log$$ transformation phrases the regression in terms of percent change. That is, instead of saying that a one-unit increase in a feature leads to the outcome increasing by $$3$$, you can say that a one-unit increase in a feature leads to a $$3\%$$ increase in the outcome. This can be quite convenient. For instance, if the outcome is money, the impact a $$\3$$ increase has depends on how much money you have, and a natural way to think is in terms of percent increase. Whether you are a billionaire or a child with a piggybank, increasing wealth by $$3\%$$ has a considerable meaning, but a $$\3$$ increase is much more impactful on the child than the billionaire.
If you're modeling a response which is fundamentally multiplicative rather than additive in terms of the contributions of respective effects, consider taking the log so that you have a more meaningful summary of the difference. For instance, in a study of farms of heterogeneous acreages, the effect of a novel fertilizer should be modeled as a % increase in yields. The mean difference on the log scale, and its CI, can be exponentiated to produce proportional changes. For instance, $$\exp(0.05) \approx 1.05$$ which can be interpreted as a 5% increase.