A method of quantify confounding in regression analyses applied to data on diet and CHD incidence

We present a method to display the results of linear regression when the independent variables are highly correlated. In this method the sum of squares of regression (SSR) for pairs of variables are partitioned into orthogonal and shared components. A shared component is the reduction in the SSR of one of the variables when the other variable is added to the regression equation. This method shows how the SSR for one variable depends on the other variables present in the regression equation and explains apparent inconsistencies between forward and backward stepwise regression. To demonstrate the potential usefulness of this method we reanalyzed previously reported data on the relationship between coronary heart disease (CHD) and diet. The analysis suggested that carbohydrate and alcohol intake are negatively associated with CHD because they are associated with greater caloric intake. Protein and fat intake are also associated with greater caloric intake, but in addition they are associated with factors that increase the risk of CHD.