Information Technology Reference
In-Depth Information
Ta b l e 7 . 1 7
Approximation based upon two-dimensional biplot given in
Figure 7.14 of
√
n
times the chi-squared distances between the rows of the 2007/08
crime data set.
ECpe
FrSt
Gaut
KZN
Limp
Mpml
NWst
NCpe
WCpe
ECpe
0.0000
0.0374
0.4611
0.3962
0.0499
0.1421
0.1470
0.1507
0.6589
FrSt
0.0374
0.0000
0.4311
0.3591
0.0862
0.1395
0.1209
0.1829
0.6331
Gaut
0.4611
0.4311
0.0000
0.3191
0.5090
0.3702
0.4478
0.6118
0.7406
KZN
0.3962
0.3591
0.3191
0.0000
0.4416
0.4113
0.2839
0.5185
0.4227
Limp
0.0499
0.0862
0.5090
0.4416
0.0000
0.1726
0.1781
0.1036
0.6824
Mpml
0.1421
0.1395
0.3702
0.4113
0.1726
0.0000
0.2487
0.2713
0.7473
NWst
0.1470
0.1208
0.4478
0.2839
0.1781
0.2487
0.0000
0.2371
0.5127
NCpe
0.1507
0.1829
0.6118
0.5185
0.1036
0.2713
0.2371
0.0000
0.7021
WCpe
0.6589
0.6331
0.7406
0.4227
0.6824
0.7473
0.5127
0.7021
0.0000
Ta b l e 7 . 1 8
√
n
times the chi-squared distance matrix between the columns of the
2007/08 crime data set. The chi-squared distance is defined as the square root of
d
ii
as given in (7.12).
Arsn
AGBH
AtMr
BNRs
BRs
CrJk
CmAs
CmRb
DrgR
InAs
Mrd
PubV
Rape
RAC
Arsn
0.000
0.219
0.372
0.310
0.306
0.832
0.380
0.319
0.961
0.567
0.380
0.646
0.112
0.569
AGBH
0.219
0.000
0.400
0.285
0.278
0.922
0.315
0.338
0.905
0.490
0.409
0.550
0.166
0.627
AtMr
0.372
0.400
0.000
0.410
0.365
0.627
0.395
0.369
0.892
0.505
0.335
0.735
0.363
0.414
BNRs
0.310
0.285
0.410
0.000
0.216
0.843
0.232
0.277
0.758
0.392
0.463
0.468
0.231
0.546
BRs
0.306
0.278
0.365
0.216
0.000
0.773
0.186
0.199
0.743
0.321
0.378
0.462
0.262
0.454
CrJk
0.832
0.922
0.627
0.843
0.773
0.000
0.766
0.650
1.212
0.890
0.835
1.110
0.865
0.341
CmAs
0.380
0.315
0.395
0.232
0.186
0.766
0.000
0.202
0.795
0.363
0.469
0.520
0.316
0.453
CmRb
0.319
0.338
0.369
0.277
0.199
0.650
0.202
0.000
0.893
0.463
0.485
0.583
0.314
0.341
DrgR
0.961
0.905
0.892
0.758
0.743
1.212
0.795
0.893
0.000
0.466
0.765
0.613
0.885
0.958
InAs
0.567
0.490
0.505
0.392
0.321
0.890
0.363
0.463
0.466
0.000
0.425
0.417
0.496
0.585
Mrd
0.380
0.409
0.335
0.463
0.378
0.835
0.469
0.485
0.765
0.425
0.000
0.687
0.361
0.590
PubV
0.646
0.550
0.735
0.468
0.462
1.110
0.520
0.583
0.613
0.417
0.687
0.000
0.579
0.782
Rape
0.112
0.166
0.363
0.231
0.262
0.865
0.316
0.314
0.885
0.496
0.361
0.579
0.000
0.583
RAC
0.569
0.627
0.414
0.546
0.454
0.341
0.453
0.341
0.958
0.585
0.590
0.782
0.583
0.000
as well as the predicted values of (7.54) as obtained from the output list of the (two-
dimensional) biplots that include the interpolated points are given in Tables 7.22 - 7.25.
The element
out
of the output list of
cabipl
returns the predicted values and as
element
weighted.dev.mat.new
the matrix (7.54). The positions of the interpolated
points in Figure 7.22 draw our attention to the remarkable increase in the reporting of
drug related crimes (highlighted in Table 7.22) in the Western Cape since the 2003/04
period.
The contents of Tables 7.22 - 7.25 can be used to calculate the sample predictivities
for the interpolated points in Figures 7.22 and 7.23. The row predictivities for the Western
Cape province, for example, are calculated according to (7.38) as follows. First, regarding
Table 7.24 as a matrix of predicted values, calculate the diagonal of the product of this
matrix and its transpose. Do exactly the same with Table 7.22 considered as the matrix
