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 1 5 11 16 26 36 y 39 47 73 100 150 200 Complete parts (a) through (e), given Σx = 95, Σy = 609, Σx2 = 2375, Σy2 = 81,559, Σx y = 13,777, and r ≈ 0.997. (a) Make a scatter diagram of the data. (Select the correct graph.) (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σx y, and the value of the sample correlation coefficient r. (For each answer, enter a number. Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σx y = r = (c) Find , and . Then find the equation of the least-squares line = a + b x. (For each answer, enter a number. Round your answers for and to two decimal places. Round your answers for a and b to three decimal places.) = x bar = = y bar = = value of a coefficient + value of b coefficient x (d) Graph the least-squares line. Be sure to plot the point (, ) as a point on the line. (Select the correct graph.) (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? (For each answer, enter a number. 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 13 weeks old. What does the least-squares line predict for a healthy weight (in kg)? (Enter a number. Round your answer to two decimal places.) kg

Answer 1

Ans:

	x	y	xy	x^2	y^2
1	1	39	39	1	1521
2	5	47	235	25	2209
3	11	73	803	121	5329
4	16	100	1600	256	10000
5	26	150	3900	676	22500
6	36	200	7200	1296	40000
Total	95	609	13777	2375	81559

Correlation coefficient,r=(6*13777-95*609)/SQRT((6*2375-95^2)*(6*81559-609^2))=0.997

slope,b1=(6*13777-95*609)/(6*2375-95^2)=4.748

slope,b0=(609-4.74775*95)/6=26.327

x-bar=95/6=15.833

y-bar=609/6=101.500

Regression equation:

y'=26.327+4.748*x

Coeffciient of determination,R^2=0.997^2=0.994

99.4% of the variation in y can be explained by the corresponding variation in x and the least-squares line.

Explained=99.4%

Unexplained=0.6%

when x=13

y'=26.327+4.748*13=88.05