k x 1

where y = n x 1 column vector of observations on the dependent variable Y X = n x k matrix giving n observations on k — 1 variables X2 to Xk, the first column of 1's representing the intercept term (this matrix is also known as the data matrix) P = k x 1 column vector of the unknown parameters fa, fa,..., fa u = n x 1 column vector of n disturbances ui

Using the rules of matrix multiplication and addition, the reader should verify that systems (C.1.2) and (C.1.3) are equivalent.

System (C.1.3) is known as the matrix representation of the general (k-variable) linear regression model. It can be written more compactly as



P + u

n x 1

n x k

Where there is no confusion about the dimensions or orders of the matrix X and the vectors y, P, and u, Eq. (C.1.4) may be written simply as y = X p + u (C.1.5)

As an illustration of the matrix representation, consider the two-variable consumption-income model considered in Chapter 3, namely, Y = fa + faXi + Ui, where Y is consumption expenditure and X is income. Using the

2Fo]lowing the notation introduced in App. B, we shall represent vectors by lowercase boldfaced letters and matrices by uppercase boldfaced letters.


data given in Table 3.2, we may write the matrix formulation as

70" 65 90 95 110 115 120 140 155 _ 150 _


"1 80" 1 100 1 120 1 140 1 160 1 180 1 200 1 220 1 240 1 260

r 01" Lß2.


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