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	12	16	26	36
y	44	46	77	100	150	200

Complete parts (a) through (e), given Σx = 96, Σy = 617, Σx² = 2398, Σy² = 82,481, Σxy = 13,898, and r ≈ 0.994.

(a) Draw a scatter diagram displaying the data.

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(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.)

Σx =
Σy =
Σx2 =
Σy2 =
Σxy =
r =

(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.

(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 10 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
kg

Answer 1

a)

b)

ΣX =	96.000
ΣY=	617.000
ΣX2 =	2398.000
ΣY2 =	82481.000
ΣXY =	13898.000
r =	0.994

c)

X̅=ΣX/n =	16.00
Y̅=ΣY/n =	102.83
ŷ =	28.105+4.671x

e)

coefficient of determination r2 =				0.988
explained =				98.8%
unexplained=				1.2%

f)

predicted value =28.105+4.671*10=

74.82