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Data Analysis and Statistics for Geography, Environmental Science, and Engineering
book

Data Analysis and Statistics for Geography, Environmental Science, and Engineering

by Miguel F. Acevedo
December 2012
Beginner content levelBeginner
557 pages
19h 5m
English
CRC Press
Content preview from Data Analysis and Statistics for Geography, Environmental Science, and Engineering
343Multivariate Models
and premultiplying by the inverse of x
T
x
bxxxySS
TT
xy
==
−−
()()
11
(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 coefcient matrix
b of dimension 4 × 2. Suppose n = 6 observations
yx=
=
03
28
19
18
27
06
13
26
14
27
15
49
12
18
13
23
165
55
(10.43)
We can calculate b using the following steps
Sx xx==
T
111111
345236
224125
679835
1326
1427
1549
12188
1323
1655
=
6231
63
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==
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Publisher Resources

ISBN: 9781439885017