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 \(\beta_1 \times 100\%\)