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 =
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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