You are the foreman of the BarS cattle ranch in Colorado A n

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? Letx be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms).

Complete parts (a) through (e), given x = 95, y = 614, x² = 2385, y² = 82,114, xy = 13,812, and r 0.993.

(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.)

(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 isunexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

(f) The calves you want to buy are 23 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
kg

Solution