13.13 Variable transformation

1. give the variable statistical properties that play more nicely with regressions (e.g. skew)

• but it’s fine for an outlier to affect the OLS slope

1. linear relationship between variables

• $Wealth = InitialWealth \times e^{10 \times InterestRate}$
• $ln(Wealth) = ln(InitialWealth) + 10 ln(InterestRate) $

13.13.1 Options

• log (can’t handle zeros)
• $log(x+1)$
• square root
• asinh: $ln(x + \sqrt{x^2 + 1})$ –> similar to log
• winsorizing: cut off values
• standardizing: $(X - mean(X))/ sd(X)$

13.13.2 Interpretation of log

• for values close to 0 (up to .1): basically $\beta_1 \times 100\%$