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? Letxbe the age of the calf (in weeks), and letybe the weight of the calf (in kilograms).x1 2 10 16 26 36 y 38 45 79 100 150 200

Complete parts (a) through (e), givenx=91,y=612,x²=2333,y²=82,210,xy=13,618,andr0.9986.(a) Draw a scatter diagram displaying the data.

(b) Verify the given sumsx,y,x²,y²,xy, and the value of the sample correlation coefficientr. (Round your value forrto four decimal places.)x=y=x²=y²=xy=r=

(c) Findx, andy. Then find the equation of the least-squares line=a+bx. (Round your answers to four decimal places.)x=y==+x

(d) Graph the least-squares line. Be sure to plot the point (x,y) as a point on the line.

(e) Find the value of the coefficient of determinationr². What percentage of the variation inycan beexplainedby the corresponding variation inxand the least-squares line? What percentage isunexplained? (Round your answer forr²to four decimal places. Round your answers for the percentages to two decimal place.)r²=explained%unexplained%

(f) The calves you want to buy are11weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)

kg