Introductory Biostatistics

zu¼ 0 : 642 þ 1 : 96

ffiffiffiffiffi

1

12

r

¼ 1 : 207

rl¼

expð 0 : 152 Þ
 1

expð 0 : 152 Þþ 1

¼ 0 : 076

ru¼

expð 2 : 414 Þ
 1

expð 2 : 414 Þþ 1

¼ 0 : 836

or a 95% confidence interval for the population coe‰cient of correlation of
(0: 076 ; 0 :836), indicating a positive association between a woman’s age and her
systolic blood pressure; that is, older women are likely to have higher systolic
blood pressure (it is just a coincidence thatzl¼rl).

Example 4.14 Table 4.11 gives the values for the birth weight (x) and the
increase in weight between days 70 and 100 of life, expressed as a percentage of
the birth weight (y) for 12 infants. The descriptive analysis in Example 2.8
yieldsr¼
0 :946 and we have

z¼

1

2

ln

1
0 : 946

1 þ 0 : 946

¼
 1 : 792

zl¼ 0 : 014 
 1 : 96

ffiffiffi

1

9

r

¼
2 : 446

zu¼ 0 : 014 þ 1 : 96

ffiffiffi

1

9

r

¼
1 : 139

TABLE 4.11

x(oz) y(%) x(oz) y(%)

112 63 81 120

111 66 84 114

107 72 118 42

119 52 106 72

92 75 103 90

80 118 94 91

170 ESTIMATION OF PARAMETERS