Introductory Biostatistics

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