Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 53

Draw a scatter diagram displaying the data.
(b) Verify the given sums x , y , x 2 , y 2 , and xy , and the value of the sample correlation coefficient r.
(c) Find
, a , and b. Then find the equation of the least-squares line = a + bx.
(d) Graph the least-squares line on your scatter diagram. Be sure to use the point(
) as one of the points on the line.
(e) Interpretation Find the value of the coefficient of determination r 2. 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 Answers may vary slightly due to rounding.
Ranching: Cattle 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). The following information is based on data taken from The Merck Veterinary Manual (a reference used by many renchers).

Complete parts (a) through (e), given x = 92, y = 617, x 2 = 2338, y 2 = 82,389, xy = 13,642, and r 0.998.
(f) The calves you want to buy are 12 weeks old. What does the least-squares line predict for a healthy weight