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 y be the weight of the calf (in kilograms). x 3 5 8 16 26 36 y 42 47 77 100 150 200 Complete parts (a) through (e), given ?x = 94, ?y = 616, ?x2 = 2326, ?y2 = 82,402, ?xy = 13,677, and r ? 0.996. (a) Draw a scatter diagram displaying the data. Get Flash Player Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website. Submission Data Correct: Your answer is correct. (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 = 94 Correct: Your answer is correct. ?y = 616 Correct: Your answer is correct. ?x2 = 2326 Correct: Your answer is correct. ?y2 = 82402 Correct: Your answer is correct. ?xy = 13677 Correct: Your answer is correct. r = .996 Correct: Your answer is correct. (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 = 15.67 Correct: Your answer is correct. y = 102.67 Correct: Your answer is correct. y hat = 28.739 Correct: Your answer is correct. + 4.718 Correct: Your answer is correct. x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Changed: Your submitted answer was incorrect. Your current answer has not been submitted. (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 22 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.) kg

Answer 1

(a)

Following is the scatter plot:

(b)

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	3	42	9	1764	126
	5	47	25	2209	235
	8	77	64	5929	616
	16	100	256	10000	1600
	26	150	676	22500	3900
	36	200	1296	40000	7200
Total	94	616	2326	82402	13677

(c)

The mean is:

(d)

(e)

explained : 99.2%

unexplained : 100% - 99.2% = 0.8%

(f)

y' = 28.751+ 4.718*22 =132.547

Answer: 132.55 kg