Biostatistics

522 CHAPTER 10 MULTIPLE REGRESSION AND CORRELATION
10.6.3 The following data were collected on 15 obese girls:
Weight in
Kilograms
(Y)
Lean Body
Weight
(X 1 )
Mean Daily
Caloric Intake
(X 2 )
79.2 54.3 2670
64.0 44.3 820
67.0 47.8 1210
78.4 53.9 2678
66.0 47.5 1205
63.0 43.0 815
65.9 47.1 1200
63.1 44.0 1180
73.2 44.1 1850
66.5 48.3 1260
61.9 43.5 1170
72.5 43.3 1852
101.1 66.4 1790
66.2 47.5 1250
99.9 66.1 1789
Total 1087.9 741.1 22739
(a) Find the multiple correlation coefficient and test it for significance.
(b) Find each of the partial correlation coefficients and test each for significance. Let a ¼ :05 for all
tests.
(c) Determine the p value for each test.
(d) State your conclusions.
10.6.4 A research project was conducted to study the relationships among intelligence, aphasia, and apraxia.
The subjects were patients with focal left hemisphere damage. Scores on the following variables were
obtained through the application of standard tests.
Y ¼ intelligence
X 1 ¼ ideomotor apraxia
X 2 ¼ constructive apraxia
X 3 ¼ lesion volumeðpixelsÞ
X 4 ¼ severity of aphasia
The results are shown in the following table. Find the multiple correlation coefficient and test
for significance. Let a ¼ :05 and find the p value.
Subject Y X 1 X 2 X 3 X 4
1 66 7.6 7.4 2296.87 2
2 78 13.2 11.9 2975.82 8
3 79 13.0 12.4 2839.38 11
4 84 14.2 13.3 3136.58 15
(Continued )