A Pareto-like effect in regression ?

This note investigates if a Pareto-like effect exists in a multiple linear regression context. The Pareto law, which states that roughly 80 per cent of all effects can be explained by 20 per cent of the causes, has been observed in economics and other social sciences and has gained recent popularity in the field of quality management. In multiple linear regression the Pareto effect translates to see if 20 per cent of the explanatory variables can explain 80 per cent of the variation in the response variable. This conjecture is investigated through analysis of various data sets, and the conclusion appears to be in the affirmative. Possible implications of such a meta-law are discussed.