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In the matrix and vector notation Eq.(G.2):

The X matrix; Each column X contains the value for a particular indevendent
variable. The elements of a particular row of X, say row r, are the coefficients on

the corresponding parameters in  which give. Notice that 0 has the constant
coefficien 1 for all observations; hence, the column vector 1 is the first column of

X. The vectors Y and  are random vectors; the elements of these vectors are

random variables. The matrix X is considered to be a matrix of known
constants.

5.2.2 ASSUMPTIONS IN MULTIPLE REGRESSION

For estimation purposes, the above model it is assumed that the random

vector  have a multivariate normal distribution with mean vector 0 and
variance-covariance matrix I . written brief   N ( 0, I ).
2
2
Mean vector 0 is a vector of size (n x 1), with all its elements 0. Variance-

2
covariance matrix I is a matrix of size (n x n), the diagonal element is the
2
variance  jj (variance) of each random variable j. While the nondiagonal
elements (k, l) is covariance between k and l.

Review the model Y = X + , therefore X and  constant, then the rate
of X in the model is a constant. By adding a vector of random error , causing

Y is a random vector, with mean vector X, and variance-covariance matrix I ,
2
is written “ Y  N( X , I ) ”.
2

2. Estimate of  or Model

Estimation for the model Y = X , conducted through the estimate of the

ˆ
parameter . Estimator for  is β . By using the method of least squares sum,

2
ˆ
the  ( Y − β ) minimum, then we obtain the following normal equation
X

ˆ
X’X β = X’Y (G.3)

~~* CHAPTER 5 THE MULTIPLE LINEAR REGRESSION MODEL *~~