The Relationship between the magnitudes of SSR(X(2)) and SSR(X(2)|X(1)): a geometric description
Abstract
We use geometric methods to investigate the relative magnitudes of SSR(x(2)), the sum of squares for regression on x(2) alone, and SSR(x(2)|x(1)), the increase in the regression sum of squares resulting from the addition of x(2) to a model that already contains x(1). We examine a variety of cases, emphasizing those in which SSR(x(2)|x(1)) > SSR(x(2)). We also point out that SSR(x(2)) and SSR(x(2)|x(1)) can be equal even when x(1) and x(2) are correlated. We present contrived data sets illustrating these points, and examine the relative magnitudes of SSR(x(2)) and SSR(x(2)|x(1)) for two real data sets (Refer to PDF file for exact formulas).
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