Tss

and in the three-variable case

6Note: y2 = £(Y — Y)2 = £ Y2 — nY'2 = y'y — nY2. Therefore, without the correction term, y'y will give simply the raw sum of squares, not the sum of squared deviations.

APPENDIX C: THE MATRIX APPROACH TO LINEAR REGRESSION MODEL 937

Generalizing we obtain for the k-variable case

By using (C.3.16) and (C.3.17), Eq. (C.4.1) can be written as which gives the matrix representation of R2. For our illustrative example,

ßXy = [24.3571 0.5079] = 131,409.831 y'y = 132,100

1,110 205,500

and nY2 = 123,210

Plugging these values into (C.4.2), we see that R2 = 0.9224, which is about the same as obtained before, save for the rounding errors.

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