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normally distributed, which causes Y j also normally distributed. Overall this

assumption is stated in brief as follows.

2
2
 j ~ NID ( 0,  ) , and imply that Y j ~ NID ( 0+  1Xj ,  )

Estimate of the regression coefficients using least squares estimation
procedure, and for the purposes of testing significance or interval estimation, it is

assumed to be normally, identically and independent distrubuted and with

2
2
mean 0 and variance  , or  j ~ NID (0,  ). Estimation procedure with the least
squares method is the amount of effort to minimize the (smallest) sum of

squared deviations between Y j and its the estimated value, ie the sum of

ˆ
squares for e = Y − Y are minimum. This deviation is called residual, and will
j
j
j
ˆ
ˆ
be obtained after gain estimation results coefficient β and β .
0
1

ˆ
2
SSR =  (Y − Y )
j
j
ˆ
SSR =  (Y − β ( ˆ 0 + β 1 X ) )
2
j
j

By using calculus, derivatives of the sum of squared residuals (SSR)
ˆ
ˆ
according to each β and β equated to 0. Furthermore, the system of equations
1
0
obtained is called the normal equation, ie

ˆ
ˆ
(n) β + ( Xj ) β = Y j
1
0
( R3 )
ˆ
2 ˆ
( Xj )β + ( Xj ) β = XjY j
0
1
The solution of the equation system will obtain the estimated value of each  0
and  1, ie

~~* CHAPTER 5 LINEAR REGRESSION MODEL *~~