Regression Analysis > Beta Weight
What is a Beta Weight?
A beta weight is a standardized regression coefficient (the slope of a line in a regression equation). They are used when both the criterion and predictor variables are standardized (i.e. converted to z-scores).
A beta weight will equal the correlation coefficient when there is a single predictor variable. β can be larger than +1 or smaller than -1 if there are multiple predictor variables and multicollinearity is present.
If the independent/dependent variables are not standardized, they are called B weights. B weights aren’t as useful as β-weights because cross-comparisons of different units are only possible if they are standardized.
What Does a Beta Weight Tell You?
The beta weight shows you how much the criterion variable increases (in standard deviations) when the predictor variable is increased by one standard deviation — assuming other variables in the model are held constant.
Beta weights can be rank ordered to help you decide which predictor variable is the “best” in multiple linear regression. β is a measure of total effect of the predictor variables, so the top-ranked variable is theoretically the one with the greatest total effect. However, you shouldn’t rely on beta weights as the sole variable in your decision, especially when there are large numbers of predictors (as this increases the possibility of multicollinearity). You should only use rank ordered βs in this way if you are sure no multicollinearity exists (Pedhazhur) or if your model is specified perfectly (Courville & Thompson). Otherwise, β doesn’t necessarily predict the criterion variable and should only be used as a starting point for further investigation. Other techniques you can use to investigate the shared variance between variables in your regression equation include:
- Commonality analysis,
- Product Measure,
- Relative Weights,
- Structure Coefficients,
- Zero-Order Correlation.
Courville, T., & Thompson, B. (2001). Use of structure coefficients in published multiple regression articles: β is not enough. Educational and Psychological Measurement, 61, 229-248
Pedhazur, E. J. (1997). Multiple regression in behavioral research: Explanation and prediction (3rd ed.). Stamford, CT: Thompson Learning