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 4 11 16 26 36

y 41 46 75 100 150 200

Complete parts (a) through (e), given x = 94, y = 612, x2 = 2366, y2 = 81,922, xy = 13,750, and r 0.997.

(a) Draw a scatter diagram displaying the data.

(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 y hat = 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 hat =

+

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 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