The Biggest Loser (Regression Style)

Our goal with many research questions is to determine which variable is the biggest predictor of something. For example, we may want to predict endorsement for a public policy from variables such as income, gender, and party loyalty. Which predictor is strongest? Alternatively, which is the biggest loser? Is it the respondent's income? Is it gender? Or, is it some unobservable such as the degree to which they are loyal to a particular party?

The statistical technique we use here, multiple regression, is fairly elementary. However, the interpretation of results is often erroneous. This is because we often want to compare the regression coefficients in the output to decide which predictor is strongest.

Why might this be erroneous? Consider a simple example of comparing height and temperature. Is a height of 40 inches greater than a temperature of 24 degrees? We can't even answer that question. It's a comparison of apples and oranges. Technically, they are on different scales.

In statistics, we typically standardize variables to put them on a level playing field so as to more validly make comparisons. In the original example, we shouldn't compare something like income in dollars to party loyalty, which might be on a 10-point agreement scale. So, we would want to look at the standardized regression coefficients, not the unstandardized regression coefficients. (In common language, these standardized regression coefficients are sometimes loosely called "the betas"; however, we should seek clarification because, technically, the unstandardized regression coefficients use the Greek beta symbol.)

The downfall to standardized regression coefficients is that they are more difficult to interpret. Since the standardization puts the variables on standard deviation scales, we wind up interpreting in terms of changes in standard deviations. So, we would still want to look at unstandardized regression coefficients when wanting to explain how much the response variable changes on average given a one-unit change in the predictor variable. The standardized regression coefficients are the better choice when wanting to determine which variable is the strongest predictor of the response variable...the biggest winner...or the biggest loser.
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Dr. Miller