343Multivariate Models
and premultiplying by the inverse of x
T
x
bxxxySS
TT
()()
(10.42)
For example if you had two dependent variables Y
1
and Y
2
and three independent variables X
1
, X
2
,
X
3
, the matrix x is n × 4, the y matrix is n × 2, and the predictor model will have a coefcient matrix
b of dimension 4 × 2. Suppose n = 6 observations
yx=
=
03
28
19
18
27
06
13
14
15
12
13
165
(10.43)
We can calculate b using the following steps
Sx xx==
T
111111
345236
224125
679835
1326
1427
1549
12188
1323
1655
=
6231
8
23 99 72 146
16 72 54 101
38 1146 101 264
(10.44)
Sx
−
=
1
4.25 1.48 1.15 0.23
1.48 1.29 1.21 0.04
1.15 1.21 1.23 0.0
−
− 33
0.23 0.04 0.03 0.04−−
Sy xy==