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	2	3	11	16	26	36
y	47	49	74	100	150	200

Complete parts (a) through (e), given Σx = 94, Σy = 620, Σx² = 2362, Σy² = 82,586, Σxy = 13,755, and r ≈ 0.996.

(a) 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 =

(b) 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

(c) 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	%

(d) The calves you want to buy are 14 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
kg

Answer 1

Solution :

Here we solve this problem as below

a)

Σx = 94

Σy = 620

Σx2 = 2362

Σy2 = 82,586

Σxy = 13,755

r = 0.996.

b)

now regression equation is

Regression Equation

y = 32.13 + 4.55 x

therefroe value of a= 32.130 and b = 4.545

c)

now the value of the coefficient of determination r2

is 98.18 % (explained )

where r^2 is the percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line

and 1.8% (unexplained )

d)

using the regression eqaution we solve this as below

y = 32.13 + 4.55 x

put x = 14 we get

y = 32.13 + 4.55 * 14

therefore

y = 95.83

hence predicted healthy weight is 95.83 kg

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