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 5 11 16 26 36

y 39 47 73 100 150 200

Complete parts (a) through (e), given x = 95, y = 609, x² = 2375, y² = 81,559, x y = 13,777, and r 0.997.

(b) Verify the given sums x, y, x², y², xy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

x = y = x² = y² = xy = 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