Example 8.3 For the birth-weight problem of Examples 2.8 and 8.1, we have
n¼ 12
r¼ 0 : 946
leading to
t¼ð 0 : 946 Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
10
1 ð 0 : 946 Þ^2
s
¼ 9 : 23
Ata¼ 0 :05 and df¼10, the tabulatedtcoe‰cient is 2.228, indicating that the
null hypothesis of independence should be rejected (t¼ 9 : 23 < 2 :228). In
this case, the weight on day 70 (X) would account for
r^2 ¼ 0 : 895
or 89.5% of the variation in growth rates.
Example 8.4 For the blood pressure problem of Examples 2.9 and 8.2, we
have
n¼ 15
r¼ 0 : 566
leading to
t¼ð 0 : 566 Þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
13
1 ð 0 : 566 Þ^2
s
¼ 2 : 475
Ata¼ 0 :05 and df¼13, the tabulatedtvalue is 2.16. Since
t> 2 : 16
we have to conclude that the null hypothesis of independence should be
rejected; that is, the relationship between age and systolic blood pressure is real.
However, a woman’s age (X) would account for only
r^2 ¼ 0 : 32
or 32% of the variation among systolic blood pressures.
SIMPLE REGRESSION ANALYSIS 291