Question

Modern medical practice tells us not to encourage babies to become too fat. Is there a...

Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight x of a 1-year old baby and the weight y of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females. x (lb) 22 27 24 25 20 15 25 y (lb )123 125 125 122 130 120 145 x (lb) 21 17 24 26 22 18 19 y (lb) 130 130 130 130 140 110 115 Σx = 305, Σy = 1775, Σx2 = 6815, Σy2 = 226,113, and Σxy = 38,841.

B. Find x, y, b, and the equation of the least-squares line. (Round your answers to three decimal places.) x = y = b = ŷ = + x

C. Find the sample correlation coefficient r and the coefficient of determination r 2. (Round your answers to three decimal places.)

r = r 2 =

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)

D. If a female baby weighs 18 pounds at 1 year, what do you predict she will weigh at 30 years of age? (Round your answer to two decimal places.)

lbs =

Homework Answers

Answer #1
X Y X * Y
22 123 2706 484 15129
27 125 3375 729 15625
24 125 3000 576 15625
25 122 3050 625 14884
20 130 2600 400 16900
15 120 1800 225 14400
25 145 3625 625 21025
21 130 2730 441 16900
17 130 2210 289 16900
24 130 3120 576 16900
26 130 3380 676 16900
22 140 3080 484 19600
18 110 1980 324 12100
19 115 2185 361 13225
Total 305 1775 38841 6815 226113

Part b)



Equation of regression line is


b = 1.006



a =( 1775 - ( 1.0059 * 305 ) ) / 14
a = 104.872
Equation of regression line becomes

Part c)



r = 0.402

Coefficient of Determination

Explained variation = 0.161* 100 = 16.1%
Unexplained variation = 1 - 0.161* 100 = 83.9%

Part d)

When X = 18
= 104.872 + 1.006 X
= 104.872 + 1.006 * 18
= 122.98

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