U U

Although in principle U'U can be computed from the estimated residuals, in practice it can be obtained directly as follows. Recalling that ^u^ (= RSS) = TSS — ESS, in the two-variable case we may write e u = E y2—$2 e x2 (3.3.6)

and in the three-variable case e u = e y2 — $2 E yxi — $3 E y^ (7.4.19)

By extending this principle, it can be seen that for the k-variable model

ESS: P2J2yiX2i + ■■■ + P^yiXki = (3'X'y — nY2 (C.3.17)

936 APPENDIX C: THE MATRIX APPROACH TO LINEAR REGRESSION MODEL

where the term nY2 is known as the correction for mean.6 Therefore, u u = y'y - p'X'y (C.3.18)

Once u'u is obtained, a2 can be easily computed from (C.3.14), which, in turn, will enable us to estimate the variance-covariance matrix (C.3.13). For our illustrative example,

Was this article helpful?

0 0
Rules Of The Rich And Wealthy

Rules Of The Rich And Wealthy

Learning About The Rules Of The Rich And Wealthy Can Have Amazing Benefits For Your Life And Success. Discover the hidden rules and beat the rich at their own game. The general population has a love / hate kinship with riches. They resent those who have it, but spend their total lives attempting to get it for themselves. The reason an immense majority of individuals never accumulate a substantial savings is because they don't comprehend the nature of money or how it works.

Get My Free Ebook


Post a comment