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?
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2$\begingroup$ 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. $\endgroup$– gung - Reinstate MonicaApr 20 at 19:58
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2$\begingroup$ 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. $\endgroup$– whuber ♦Apr 20 at 20:50
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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.
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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.
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$\begingroup$ Is that when both independent and dependent variables are log transformed? $\endgroup$ Apr 21 at 4:16