Question

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 ybe the weight of the calf (in kilograms).

x 3 2 10 16 26 36
y 37 51 71 100 150 200

Complete parts (a) through (e), given Σx = 93, Σy = 609, Σx2 = 2341, Σy2 = 81,511, Σxy = 13,623, and r ≈ 0.994.

(a) Draw a scatter diagram displaying the data. Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website.

(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 = 93
Σy = 609
Σx2= 2341
Σy2 = 81,511
Σxy = 13,623
r = 0.994

(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

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

Answer 1