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	8	16	26	36
y	38	47	70	100	150	200

Complete parts (a) through (e), given Σx = 89, Σy = 605, Σx² = 2297, Σy² = 81,053, Σxy = 13,392, and r ≈ 0.998.

(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.)

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

Answer 1

Part a)

Part b)

ΣX = 89
ΣY = 605
ΣX * Y = 13392
ΣX2 = 2297
ΣY2 = 81053

r = 0.998

Part c)
X̅ = Σ( Xi / n ) = 89/6 = 14.83
Y̅ = Σ( Yi / n ) = 605/6 = 100.83

Equation of regression line is Ŷ = a + bX


b = 4.523
a =( Σ Y - ( b * Σ X) ) / n
a =( 605 - ( 4.5226 * 89 ) ) / 6
a = 33.748
Equation of regression line becomes Ŷ = 33.748 + 4.523 X

Part e)
Coefficient of Determination
= 0.997
Explained variation = 0.997* 100 = 99.7%
Unexplained variation = 1 - 0.997* 100 = 0.3%

Part f)
When X = 11
Ŷ = 33.748 + 4.523 X
Ŷ = 33.748 + ( 4.523 * 11 )
Ŷ = 83.50