The slope of the regression line, b, can be found by:

(5.9)

(5.10)

(5.10)

The standard error of the regression line can be found in terms of the sam-
ple moments.

(5.11)

(5.11)

The major benefits in calculating the sample moments are that the cor-
relation coefficient, r, and the coefficient of determination, r^2 , can easily be
found.

(5.12)

(5.12)

r

M

MM

Rr

XY

XX YY

=

=

()()

(^2) ()
S
MM M
NN M
SS
e
XX YY XY
XX
ee
2
2
2
2

−
−

()( )
()
aˆ
Y
N
b
X
N
ybX
i
i
N
i
i
N
=− =−==
∑∑
11
bˆ M
M
XY
XX

MyYY
NY Y
YY
i
N
i
N
i
N
i
i
N
==−






−

==
∑∑
∑∑
1
2
1
2
1
1
2
1
2
1
()
()
MxyXXYY
NXY X Y
XY i i i i
i
N
i
N
ii i
i
N
i
N
i
i
N
==−−
=−












= =

∑ ∑
∑∑∑
()()
1 1
111

The Linear Regression Model 77