Log and Box-Cox Transformations Quiz

Answers and explanations appear as you take the quiz.

1. What effect can a logarithm have on a strongly right-skewed positive variable?
   • Adds the same constant to every large value
   • Guarantees a normal distribution for every sample
   • Compresses large values relative to small ones
   • Converts every signed value to a positive value without changing its meaning
2. What input restriction applies to the standard Box-Cox transformation?
   • All inputs must be nonnegative, including zero
   • Inputs must be strictly positive
   • Inputs must already follow a normal distribution
   • Inputs must lie between zero and one
3. Which transformation family can accommodate zero and negative values without an arbitrary shift?
   • Standard Box-Cox
   • Plain natural logarithm
   • Square root of every signed value
   • Yeo-Johnson
4. Why must a learned transformation be fitted only on each training fold?
   • To prevent validation or test data from influencing fitted parameters
   • To guarantee identical distributions in every evaluation fold
   • To force every model family to use the same input representation
   • To permit new fitted mappings at inference without a model update
5. What should happen to predictions from a model trained on log-transformed targets?
   • Treat log predictions directly as original-unit amounts
   • Round log predictions before applying every inverse
   • Apply a justified inverse mapping to recover original units
   • Assume exponentiation always returns the original-scale conditional mean
6. Why may exponentiating a mean log prediction fail to equal the original-scale conditional mean?
   • The exponential function is linear on prediction ranges
   • Nonlinear inverse transformations do not preserve averages
   • Every log-scale mean equals the original-scale mean
   • Transforming the target removes all variation around its conditional mean
7. Which statement about a more Gaussian-looking feature is sound?
   • It guarantees unbiased estimates for every estimator
   • It proves extreme observations were removed
   • It guarantees the same gain for trees and linear models
   • It does not guarantee improved held-out prediction
8. Which issue is introduced by adding an arbitrary constant before taking logs?
   • The transformed scale and interpretation depend on that choice
   • The transform becomes the standard Box-Cox family
   • All negative values become meaningfully comparable
   • It guarantees an unbiased original-scale mean