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 S 11 16 26 36 y 39 47 73 100 150 200 Complete parts (a) through (e), given 2x = 95, 2y = 609, 2X2 = 2375, 2y2 = 81,559, 2X y = 13,777, and r: 0.997. (a) Make a scatter diagram of the data. (Select the correct graph.) CHoIcE A CHOICE B CHOICE c Y Y Y 200 o 200 , 200 . 150 0 150 . 150 . 100 C 100 . 100 O I o o 50 . o 50 50 o ' o ' _,_._._._.___._._._;_._._._.___._._._L x O 10 20 30 40 O 10 20 30 40 O 10 20 30 40 CHoIcE D Y 200 o 150 O 100 0 c 50 o (In wash... v\" v.,2 v..2 v., (b) Verify the given sums 2X, 2y, 2x2, Zyz, EX y, and the value of the sample correlation coefficient r. (For each answer, enter a number. Round your value for r to three decimal places.) (c) Find ;, and 7. Then nd the equation of the least-squares line 9 = a + b x. (For each answer, enter a number. Round your answers for ; and 7 to two decimal places. Round your answers for a and b to three decimal places.) iii i (d) Graph the least-squares line. Be sure to plot the point (2 Y) as a point on the line. (Select the correct graph.) CHOICE A CHOICE B CHOICE c Y Y Y 200 200 200 150 150 150 100 100 100 50 50 50 1'''''''''~'''~''''''' x x x O 10 20 30 40 O 10 20 30 40 O 10 20 30 40 CHOICE D Y 200 150 100 50 (e) Find the value of the coefficient of determination . 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? (For each answer, enter a number. Round your answer for 2 to three decimal places. Round your answers for the percentages to one decimal place.) 12 = explained = % unexplained = |% (f) The calves you want to buy are 11 weeks old. What does the least-squares line predict for a healthy weight (in kg)? (Enter a number. Round your answer to two decimal places.) kg