# Logarithmic Transformation for Beginners | by Jae Kim

Consider, for simplicity, Y = 1 + 2X, where Y is the response variable and X is the input variable. We are often interested in how much Y changes in response to a change in X. Let Δ denote the change operator. That is,

ΔY = Y1 — Y0: change of Y from Y0 to Y1; and

ΔX = X1 — X0: change of X from X0 to X1.

Suppose, with our example (Y = 1 + 2 X), X changes from 1 to 3. Then, in response to this, Y changes from 3 to 7. That is, ΔY = 4 and ΔX = 2.

The slope (or derivative) measures how much Y changes in response to one-unit change of X. It is defined as

β ≡ ΔY/ΔX,

and β = 2 in our example. A slope coefficient that we encounter in a linear regression or a machine learning model has the same interpretation. The slope is a standardized measure, but it is unit-dependent. That is, interpretation of a slope coefficient requires a careful consideration of their units.

Consider the function Y = log(X), where log() denotes the natural logarithm.