Note on the Independent Contribution of a Predictor

Research q ~ ~ e s t i o n s usually involve specific variables that have been observed. Few investigators are interested in the contribution of a hypothetical predictor variable, no matter how "close" i t is to the predictor variable under study. When an investigator is interested in the contribution of the predictor variable "Age in Years," for example, he is not likely to transfer this interest co some hypothetical "Variable S" just for the sake of having orchogonal predictors. Therefore, Gibson's recent suggestion ( 1762 ) seems irrelevant to research questions of practical importance. As Hoffman ( 1962 ) remarks, the term "independent" has more than one meaning. My comments ( 1962 ) concerning the independenc concrib~~cion of a predictor are based upon the following considerations. Suppose, for example, we have a sample consisting of observations on each of n people. Each person has a criterion value, Y, and three predictor values, XI, X2, and X:,. Consider the regression model