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You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves...

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 1 2 10 16 26 36
y 38 55 73 100 150 200

Complete parts (a) through (e), given Σx = 91, Σy = 616, Σx2 = 2333, Σy2 = 82,298, Σxy = 13,578, and r ≈ 0.994.

(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 =  
=   +   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 19 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
  kg

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