Question

In: Statistics and Probability

Medical researchers have noted that adolescent females are much more likely to deliver low-birth-weight babies than...

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

Solutions

Expert Solution

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

orchestra answered 2 years ago
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