Consider the data of Table 12.8, where measurements were taken for nine infants. The purpose of the experiment was to arrive at a suitable estimating equation relating the length of an infant to all or a subset of the independent variables. The sample correlation coefficients, indicating the linear dependency among the independent variables, are displayed in the symmetric matrix
x1
x2
x3
x4
1.0000
0.9523
0.5340
0.3900
0.2626
0.1549
0.7847
Table 12.8: Data Relating to Infant Length∗
Infant Length,
Age,
Length at
Weight at
Chest Size at
(cm)
(days)
Birth, x2 (cm)
Birth, x3 (kg)
Birth, x4 (cm)
57.5
78
48.2
2.75
29.5
52.8
69
45.5
2.15
26.3
61.3
77
46.3
4.41
32.2
67.0
88
49.0
5.52
36.5
53.5
67
43.0
3.21
27.2
62.7
80
48.0
4.32
27.7
56.2
74
2.31
28.3
68.5
94
53.0
4.30
30.3
69.2
102
58.0
3.71
28.7
∗Data analyzed by the Statistical Consulting Center, Virginia Tech, Blacksburg, Virginia.
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