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Standardised coefficient

A standardised coefficient rescales a regression predictor to units of its own standard deviation, allowing direct comparison of relative importance across predictors regardless of original measurement units. Also called a beta coefficient.

ByHoang TruongUpdated

FrameworkMultiple regression

See it move

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A coefficient of one euro of revenue cannot be compared directly with a coefficient of one year of experience — the units differ. Standardising each predictor to mean zero and standard deviation one fixes this: β* equals the raw coefficient b times the predictor's standard deviation divided by the outcome's. A β* of 0.50 beats a β* of 0.20 in relative influence, whatever units the raw data used.

Where it fits
SubjectData Analysis & StatisticsAdvancedTopicMultiple Regression & InterpretationAdvanced

The formula

LaTeX
βj=bjsxjsy\beta^*_j = b_j \cdot \frac{s_{x_j}}{s_y}

Variables

Standardised coefficient for predictor j
Raw (unstandardised) OLS regression coefficient for predictor j
Sample standard deviation of predictor j
Sample standard deviation of the outcome variable

A one-standard-deviation increase in predictor j is associated with a β*_j standard-deviation change in the outcome. The predictor with the largest absolute standardised coefficient has the greatest relative influence.

Standardised coefficient — Edlintics Glossary