ASSIGNMENT 12
MULTIPLE CORRELATION
=====================================================================================
Example: Let X1(Y) = Board Examination Rating (BER)
X2 = Academic Performance in College (APC)
X3= IQ Score
Required : Solve the Adjusted Coefficient of
Multiple Determination and interpret.
r12=n
(
Σ xy
)
−(Σ x )(Σ y)
√
¿¿¿
=
0.77
r13=n
(
Σ xy
)
−(Σ x )(Σ y)
√
¿¿¿
=
0.78
r23 =n
(
Σ xy
)
−(Σ x)(Σ y)
√
¿¿¿
=
0.83
A.
R123
=
√
0.772+0.7 82−2
(
0.77
) (
0.7 8
) (
0.83
)
1−0.832
=
√
0.5929+0.6084 −0.9842
1−0. 6889
=
√
1. 2013−0.9842
0.3111
=
√
0.2171
0.3111
R123
= 0.8353 = 0.84
There is a very high correlation between the board exam rating and the
combination of academic performance in college and IQ score.
B.
R2
= (0.84)2 = 0.6977
C.
RAdj
2
= 1 –
(
1−R2
)
(
n−1
)
n−k−1
= 1-
(
1−0.6977
) (
15−1
)
15−2−1
RAdj
2
= 1 –
(
1−0.6977
) (
14
)
15−2−1
X1 X2 X3
78 84 94
70 78 90
73 80 102
82 87 108
85 88 115
75 80 110
75 82 95
83 90 121
76 88 112
86 92 118
72 75 90
84 85 107
80 77 96
88 90 124
77 86 100
