Question

The average gestational age (time from conception to birth) of a newborn infant is 40 weeks. The following table presents the gestational age in weeks (?) and the corresponding birth weight in pounds (?) for 14 female infants born in the US.

x	36	37	32	36	41	39	38	40	42	32	31	37	39	41
y	7.2	7.5	5.1	5.9	8.9	7.8	7.2	8.0	8.8	4.2	3.9	6.9	7.8	9.1

(a) Compute the least-squares regression line for predicting a newborn baby girl’s weight based on gestational age.

(b) Predict the weight of a newborn baby girl with a gestational age of 35 weeks.

(c) Is it possible to interpret the ?-intercept of the least squares regression line? Explain why or why not.

(d) If the gestational age of two newborn baby girls differs by 2.5 weeks, by how much would you predict their weights to differ?

Answer 1

S.no	x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
1	36	7.2	1.47	0.03	-0.22
2	37	7.5	0.05	0.23	-0.10
3	32	5.1	27.19	3.69	10.02
4	36	5.9	1.47	1.26	1.36
5	41	8.9	14.33	3.53	7.11
6	39	7.8	3.19	0.61	1.39
7	38	7.2	0.62	0.03	0.14
8	40	8	7.76	0.96	2.73
9	42	8.8	22.90	3.16	8.51
10	32	4.2	27.19	7.96	14.71
11	31	3.9	38.62	9.74	19.40
12	37	6.9	0.05	0.01	0.03
13	39	7.8	3.19	0.61	1.39
14	41	9.1	14.33	4.32	7.87

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	521	98.3	162.3571429	36.1	74.34
mean	37.21	7.02	SSxx	SSyy	SSxy

A)

sample size ,   n =   14          
here, x̅ = Σx / n=   37.21   ,     ȳ = Σy/n =   7.02  
                  
SSxx =    Σ(x-x̅)² =    162.3571          
SSxy=   Σ(x-x̅)(y-ȳ) =   74.3          
                  
estimated slope , ß1 = SSxy/SSxx =   74.3   /   162.357   =   0.4579
                  
intercept,   ß0 = y̅-ß1* x̄ =   -10.0172          
                  
so, regression line is   Ŷ =   -10.017   +   0.458   *x
----------------------------------------------------------

B)

Predicted Y at X=   35   is                  
Ŷ =   -10.01725   +   0.457853   *   35   =   6.008

C)

it is not possible to interpretate ..............

because without gestational age, there will no birth weight

d)

predict their weights to differ by 2.5*0.4578=1.14 pounds