When should you log-transform the response?

medium

Answer

$(1) Right-skewed positive outcomes (income, prices, spend, time-on-page).$
$(2) Multiplicative errors \to additive on log scale.$
$(3) Coefficients become interpretable as approximate percent changes for small β.$
$Cost: E[log Y] \neq log E[Y] \to back-transformed predictions are biased low (Duan smearing correction fixes it).$
$Alternatives: GLM with log link (models log of mean directly, avoids the bias), Box-Cox / Yeo-Johnson for automatic transformation search.$

Check yourself — multiple choice

Never
Right-skewed positive outcomes / multiplicative noise; β becomes % change; back-transform biases predictions low → Duan correction or GLM(log link)
Only for logistic
Random

Log transform: right-skew / multiplicative noise; β ≈ % change; back-transform biased.

#regression#eda

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