Change In The Sum Of Squares

Change in the sum of squares. Suppose that b is the least squares coefficient vector in the regression of y on X and that c is any other K × 1 vector. Prove that the difference in the two sums of squared residuals is (y − Xc)’ (y − Xc) − (y − Xb)’ (y − Xb) = (c − b) ‘X’X(c − b). Prove that this difference is positive.

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