Introductory Biostatistics

to the prediction of the response over and above that achieved by other factors
already present in the model. The null hypothesis for this test may be stated as:
‘‘FactorXidoes not have any value added to the prediction of the response
given that other factors are already included in the model.’’ In other words,

H 0 :bi¼ 0

To test such a null hypothesis, one can use

ti¼

bb^i

SEðbb^iÞ

in attest withn
k
1 degrees of freedom, wherebb^iis the corresponding
estimated regression coe‰cient and SEðbb^iÞis the estimate of the standard error
ofbb^i, both of which are printed by standard computer packaged programs.

Example 8.7 Ultrasounds were taken at the time of liver transplant and again
five to ten years later to determine the systolic pressure of the hepatic artery.
Results for 21 transplants for 21 children are shown in Table 8.7; also available
are gender (1¼male, 2¼female) and age at the second measurement.

TABLE 8.7

Child

5–10 Years

Later

At
Transplant Gender Age
146 35216
240 40219
350 58219
450 71123
541 33116
670 79123
735 20113
840 19119
956 56111
10 30 26 2 14
11 30 44 1 15
12 60 90 2 12
13 43 43 2 15
14 45 42 1 14
15 40 55 1 14
16 50 60 2 17
17 66 62 2 21
18 45 26 2 21
19 40 60 1 11
20 35 27 1 9
21 25 31 1 9

MULTIPLE REGRESSION ANALYSIS 299