Question

Medical researchers have noted that adolescent females are much more likely to deliver low-birth-weight babies than are adult females. Because low-birth-weight babies have a higher mortality rate, a number of studies have examined the relationship between birth weight and mother's age. One such study is described in the article "Body Size and Intelligence in 6-Year-Olds: Are Offspring of Teenage Mothers at Risk?"† The following data on maternal age (in years) and birth weight of baby (in grams) are consistent with summary values given in the article and also with data published by the National Center for Health Statistics.

Mother's age	15	17	18	15	16	19	17	16	18	19
Birth weight	2,319	3,393	3,301	2,648	2,867	3,297	2,970	2,535	3,138	3,573

(c)

Find the equation of the least-squares regression line.

ŷ = ________ + (________) x

(g)

Use the regression line to predict for birth weight, in grams, of a baby born to a 15-year-old mother?

_________ g

Answer 1

Solution:

X	Y	XY	X^2	Y^2
15	2319	34785	225	5377761
17	3393	57681	289	11512449
18	3301	59418	324	10896601
15	2648	39720	225	7011904
16	2867	45872	256	8219689
19	3297	62643	361	10870209
17	2970	50490	289	8820900
16	2535	40560	256	6426225
18	3138	56484	324	9847044
19	3573	67887	361	12766329

,   

n	10
sum(XY)	515540.00
sum(X)	170.00
sum(Y)	30041.00
sum(X^2)	2910.00
sum(Y^2)	91749111.00
Numerator	48430.00
Denominator	54825.96
r	0.8833
r square	0.7803
Xbar(mean)	17.0000
Ybar(mean)	3004.1000
SD(X)	1.4907
SD(Y)	394.4424
b	242.1500
a	-1112.4500

Q . Find the equation of the least-squares regression line.

ŷ = a + (b) x

ŷ = -1112.45+ (242.15) x

Q. Use the regression line to predict for birth weight, in grams, of a baby born to a 15-year-old mother?

Put x = 15 in the equation.

ŷ = -1112.45+ [(242.15) * 15]

ŷ = 2516.8 g