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	2	10	16	26	36
y	44	54	72	100	150	200

Complete parts (a) through (e), given Σx = 92, Σy = 620, Σx² = 2336, Σy² = 82,536, Σxy = 13,616, and r ≈ 0.994.

(a) Draw a scatter diagram displaying the data.

Selection Tool

Line

Ray

Segment

Circle

Vertical Parabola

Horizontal Parabola

Point

No Solution

Help

5

10

15

20

25

30

35

40

10

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

210

Clear Graph

Delete Layer

Fill

WebAssign Graphing Tool

Graph LayersToggle Open/Closed

• After you add an object to the graph you can use Graph Layers to view and edit its properties.

(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 17 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 = 92
ΣY = 620
ΣX * Y = 13616
ΣX2 = 2336
ΣY2 = 82536

r = 0.994

Part c)

X̅ = Σ( Xi / n ) = 92/6 = 15.33
Y̅ = Σ( Yi / n ) = 620/6 = 103.33

Equation of regression line is Ŷ = a + bX


b = 4.441
a =( Σ Y - ( b * Σ X) ) / n
a =( 620 - ( 4.4409 * 92 ) ) / 6
a = 35.239
Equation of regression line becomes Ŷ = 35.239 + 4.441 X

Part e)

Coefficient of Determination
= 0.988
Explained variation = 0.988* 100 = 98.8%
Unexplained variation = 1 - 0.988* 100 = 1.2%

part f)

When X = 17
Ŷ = 35.239 + 4.441 X
Ŷ = 35.239 + ( 4.441 * 17 )
Ŷ = 110.74