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	8	16	26	36
y	44	53	71	100	150	200

Complete parts (a) through (e), given Σx = 92, Σy = 618, Σx² = 2318, Σy² = 82,286, Σxy = 13,577, and r ≈ 0.997.(a) Draw a scatter diagram displaying the data.

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Submission 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 13 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
kg

5.

–/16 POINTSBBUNDERSTAT12 9.2.010.

MY NOTES

ASK YOUR TEACHER

It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game.

x	0	2	5	6
y	49	45	33	26

Complete parts (a) through (e), given Σx = 13, Σy = 153, Σx² = 65, Σy² = 6191, Σxy = 411, and

r ≈ −0.982.

(a) Draw a scatter diagram displaying the data.

Selection Tool

Line

Ray

Segment

Circle

Vertical Parabola

Horizontal Parabola

Point

No Solution

Help

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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) If a team had x = 4 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.)
%

Answer 1

From the data given we get

Where the last row gives the sums corresponding to each column, which verifies the given sums as well

The scatter plot is shown below

Using the data we have

So the equation of regression line

Using the above data above we get

Graph the least-squares line is shown below

As,

So 99.40% is explained    while 0.60% unexplained