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	2	12	16	26	36
y	47	55	71	100	150	200

Complete parts (a) through (e), given Σx = 93, Σy = 623, Σx² = 2377, Σy² = 82,775, Σxy = 13,709, and r ≈ 0.985.

(a) Draw a scatter diagram displaying the data.

(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.)

(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.

r2 =
explained	%
unexplained	%

(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.)

(f) The calves you want to buy are 25 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
kg

Answer 1

b)

Σx = 93,

Σy = 623,

Σx² = 2377,

Σy² = 82,775,

Σxy = 13,709, and

r ≈ 0.985

c)

xbar =15.50

ybar=103.83

yhat=36.689+4.332x

e)

coefficient of determination r² =0.971

explained =97.1%

unexplained =2.3%

f)

predicted value =36.689+4.332*25 =144.99