What does beta mean in regression?

Written by mark koltko-rivera
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What does beta mean in regression?
Multiple regression can bring order to a set of data. (Numbers image by Paul Hampton from Fotolia.com)

Multiple regression is a technique that involves the use of a number of predictor variables (like patients' ages, ethnicities, diets or lifestyles) to predict a criterion variable (like the probability that a patient will develop a certain type of cancer). One statistic that comes out of regression analysis is the beta weight of a predictor.

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Meaning

The beta weight tells you the relative importance of a predictor in predicting the criterion. The larger the absolute value of the beta weight, the more influence this factor has on predicting the criterion. You can directly compare the absolute values of the respective beta weights of the different predictors in a regression equation to see which are relatively more and which are relatively less important in predicting the criterion variable.

Interpretation

Square the value of a given beta weight. This gives you the proportion of the variance in the criterion variable that is associated with the predictor variable.

Misconception

Probably the greatest misconception about beta weights is that they are the same as the B weights of the predictors. These are associated but distinct statistics. The B weight allows you to write an equation to make the predictors predict the criterion variable; this equation will be in everyday units for the predictors involved, such as number of hours studied. However, the relative magnitudes of the B weights mean absolutely nothing. Only the Beta weights permit you to say which are the relatively more important predictors.

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