Is the gestational age (time between conception and birth) of a low birth-weight baby useful in predicting head circumference at birth? Twenty-ve low birth-weight babies were studied at a Harvard teaching hospital; the investigators calculated the regression of head circum- ference (measured in centimeters) against gestational age (measured in weeks). The estimated regression line is

head circumference = 3.91 + 0.78 x gestational age

(a) What is the predicted head circumference for a baby whose gestational age is 28 weeks?

(b) The standard error for the coecient of gestational age is 0.35, which is associated with df = 23. Does the model provide strong evidence that gestational age is signicantly associated with head circumference?

the investigators calculated the regression of head circum- ference (measured in centimeters) against gestational age (measured in weeks). The estimated regression line is

head circumference = 3.91 + 0.78 x gestational age

a) when gestational age = 28 weeks we substitute 28 to get

head circumference [tex]= 3.91 + 0.78 *25= 23.41[/tex]

b) Set up hypotheses as

[tex]H_0: \beta=0\\B_a: \beta\neq 0[/tex]

(Two tailed test for slope coefficient)

Beta difference = 0.78

Std error = 0.35

df = 23

t statistic = beta diff/std error = [tex]\frac{0.78}{0.35} \\=2.229[/tex]

p value = 0.0359

Since p value <0.05, at 5% significant level we reject H0

There is a significant association between the two variables.