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X1yi + X2y2 y2

bi c2

where bi is the least squares slopes based on the first Ti observations and c2 is y2 - X2bi. The covariance matrix for the full set of estimates is s2 times the bracketed matrix. The two subvectors of residuals in this regression are ei = yi - Xibi and e2 = y2 -(X2bi + Ic2) = 0, so the sum of squared residuals in this least squares regression is just e'iei. This is the same sum of squares as appears in (7-i5). The degrees of freedom for the denominator is [ Ti + T2 - (K + T2)] = Ti - K as well, and the degrees of freedom for

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