The Partial Regression Coefficients

where the expression for the RSS is obtained by simple algebraic manipulations of (7.4.1).


The most straightforward procedure to obtain the estimators that will minimize (7.4.2) is to differentiate it with respect to the unknowns, set the resulting expressions to zero, and solve them simultaneously. As shown in Appendix 7A, Section 7A.1, this procedure gives the following normal equations [cf. Eqs. (3.1.4) and (3.1.5)]:

E YiX2i = $1 E X2i + 02 E X2i + 03 E X2iX3i (7.4.4) E ^X3i = 01 E X3i + 02 E X2iX3i + 03 E X2i (7.4.5)

which is the OLS estimator of the population intercept p1.

Following the convention of letting the lowercase letters denote deviations from sample mean values, one can derive the following formulas from the normal equations (7.4.3) to (7.4.5):

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