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	2,289	3,423	3,301	2,618	2,927	3,357	2,970	2,505	3,138	3,543

A) Find the equation of the least squares regression line?

ŷ =......... + (.........)x

B) 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:

n = 10

	X	Y	XY	X2	Y2
	15	2289	34335	225	5239521
	17	3423	58191	289	11716929
	18	3301	59418	324	10896601
	15	2618	39270	225	6853924
	16	2927	46832	256	8567329
	19	3357	63783	361	11269449
	17	2970	50490	289	8820900
	16	2505	40080	256	6275025
	18	3138	56484	324	9847044
	19	3543	67317	361	12552849
Sum	170	30071	516200	2910	92039571

Now ,

Slope of the regression line is

   b = 249.65

Now , y intercept of the line is

   a = -1236.95

The equation of the regression line is

= a + bx

=   -1236.95 + (249.65)x

B)

For x = 15 , find the predicted value of y .

Put x = 15 in the regression line equation.

= -1236.95 + [(249.65) * 15 ] = 2507.8

Answer:    2507.8 g