You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms).
x 3 2 11 16 26 36
y 38 53 76 100 150 200
Complete parts (a) through (e), given Σx = 94, Σy = 617, Σx2 = 2362, Σy2 = 82,529, Σxy = 13,756, and r ≈ 0.993.
(b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
Σx = Σy = Σx2 = Σy2 = Σxy = r =
(c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)
x =
y =
^y =____+____x
(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)
r2 =
explained %
unexplained %
(f) The calves you want to buy are 11 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
___ kg