Changing the unit of measurement of any independent variable, where log of the independent variable appears in the regression:

Question

BlackTom AI · Accepted Answer

Consider the regression setup where the independent variable is transformed by taking its natural logarithm, so the model includes log(X) as a predictor. This means that changing the unit of X scales X by a constant factor k: X_new = kX. Consequently, log(X_new) = log(kX) = log(X) + log(k).

Option A: 'affects only the slope coefficient.' If log(X) is used as a regressor, adding a constant log(k) to log(X) is equivalent to shifting the overall regression line up or down, which changes the intercept but not the slope. Therefore this option is incorrect.

Option B: 'affects both the slope and intercept coefficients.' Since the regressor is log(X), a constant addition to log(X) translates into a change in the intercept term only; the slope with respect to log(X) remains unchanged. Hence this option is incorrect.

Option C: 'affects neither the slope nor the intercept coefficient.' Changing the unit of X induces a shift in log(X) by a constant, which does affect the intercept. Thus this option is incorrect.

Option D: 'affects only the intercept coefficient.' As shown, replacing X by kX leads to log(X) → log(X) + log(k), which increases the intercept by log(k) while leaving the coefficient on log(X) (the slope) unchanged. This description aligns with the mathematical consequence of a unit change on X when the model uses log(X) as a regressor, making this option the correct interpretation.

AS.440.606.80.SP25 M06: Assignment

Changing the unit of measurement of any independent variable, where log of the independent variable appears in the regression:

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