The Matrix Approach To Linear Regression Model

This appendix presents the classical linear regression model involving k variables (Y and X2, X3, ... , Xk) in matrix algebra notation. Conceptually, the k-variable model is a logical extension of the two- and three-variable models considered thus far in this text. Therefore, this appendix presents very few new concepts save for the matrix notation.1

A great advantage of matrix algebra over scalar algebra (elementary algebra dealing with scalars or real numbers) is that it provides a compact method of handling regression models involving any number of variables; once the k-variable model is formulated and solved in matrix notation, the solution applies to one, two, three, or any number of variables.

C.1 THE ^-VARIABLE LINEAR REGRESSION MODEL

If we generalize the two- and three-variable linear regression models, the k-variable population regression model (PRF) involving the dependent variable Y and k — 1 explanatory variables X2, X3, . . . , Xk may be written as

PRF: Y = Pi + 02X2i + faX3i + ••• + faXki + Ui i = 1, 2, 3,..., n

where 01 = the intercept, 02 to 0k = partial slope coefficients, u = stochastic disturbance term, and i = ith observation, n being the size of the population. The PRF (C.1.1) is to be interpreted in the usual manner: It gives the mean or expected value of Y conditional upon the fixed (in repeated sampling) values of X2, X3,..., Xk, that is, E(Y | X2i, X3i,..., Xki).

1Readers not familiar with matrix algebra should review App. B before proceeding any further. Appendix B provides the essentials of matrix algebra needed to follow this appendix.

APPENDIX C: THE MATRIX APPROACH TO LINEAR REGRESSION MODEL 927

Equation (C.1.1) is a shorthand expression for the following set of n simultaneous equations:

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