What does it mean to "hold a variable constant" using multiple regression?

The answer to this question reveals both major strengths and weaknesses of the regression technique for analyzing data. When we include an explanatory variable in a model, what we would really like to know is how this variable influences the response variable. The obvious difficulty is that it is almost impossible to separate the influence of this variable from that of other variables. For example, the amount of exercise a person gets will influence the person's weight, but so will the amount of food the person eats. To complicate matters, the amount that a person eats will be influenced by the amount of exercise the person gets.

Multiple regression handles this problem by taking into account the correlation among explanatory variables as well as the correlation of these variables with the response variable. The model provides a means to predict the response variable from the explanatory variables. The predicted value depends on the value of each of the explanatory variables. This fact allows researchers to study individual variables by manipulating the values of other variables in the model. For example, we can set the amount that a person eats as a constant in the model and watch what happens to the prediction for weight when we only vary exercise. This is what is meant by holding other variables in the model constant. The implication is that if we only study people who eat a certain amount, say the average caloric intake, then we can know how exercise impacts weight without worrying about the amount a person eats.

This point reveals the weakness of the regression technique. Obviously we haven't held eating constant in our study, so we can't be certain what would happen if we did that. Statistical control is not the same as experimental control. Whereas the model may tell us that increasing exercise by one hour per day will cause a five-pound per month weight loss if all other variables held constant, it may in fact be the case that holding eating constant at 20,000 calories per day will cause a weight increase (or adverse medical conditions) no matter what we do to exercise. About the best we can do is state our average expectation for the relationship of one explanatory variable to the response variable if we were to control for other explanatory variables in the model.

URL http://edpsych.ed.sc.edu/seaman/edrm711/questions/regression.htm

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This page last updated on 07 April 2000 .

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