Comparing apples to oranges with standardized betas

Question

Your regression has one predictor measured in basis points and another measured in millions of dollars. Their raw coefficients differ by orders of magnitude, and someone concludes the big-coefficient variable "matters more."

Explain why raw coefficients cannot be compared for importance, and how standardized coefficients fix this.

Accepted Answer

Raw coefficients carry units. A regression coefficient is "change in y per one-unit change in x," and a "unit" of basis points is tiny while a "unit" of millions of dollars is huge. So a small coefficient on a small-unit variable can represent a larger real effect than a big coefficient on a big-unit variable. Comparing the bare numbers is meaningless, rescale either predictor and its coefficient changes proportionally, with no change in the model's fit. Standardize to a common scale. Convert each variable to standard-deviation units (subtract its mean, divide by its standard deviation) befor…

Comparing apples to oranges with standardized betas

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