Ranching: Cattle 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 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). The following information is based on data taken from The Merck Veterinary Manual (a reference used by many ranchers). 3 10 16 26 36 y 42 50 75 100 150 200 Complete parts (a) through (e), given Ex = 92, Ey = 617, Ex² = 2338, Ey = 82,389, Exy = 13,642, and r = 0.998.

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8. | Ranching: Cattle 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 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).
The following information is based on data taken from The Merck Veterinary
Manual (a reference used by many ranchers).
1
3
10
16
26
36
y
42
50
75
100
150
200
Complete parts (a) through (e), given Ex = 92, Ey = 617, Ex²
Ey = 82,389, Exy = 13,642, and r = 0.998.
(f) The calves you want to buy are 12 weeks old. What does the least-squares
line predict for a healthy weight?
2338,
Transcribed Image Text:8. | Ranching: Cattle 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 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). The following information is based on data taken from The Merck Veterinary Manual (a reference used by many ranchers). 1 3 10 16 26 36 y 42 50 75 100 150 200 Complete parts (a) through (e), given Ex = 92, Ey = 617, Ex² Ey = 82,389, Exy = 13,642, and r = 0.998. (f) The calves you want to buy are 12 weeks old. What does the least-squares line predict for a healthy weight? 2338,
For Problems 7-18, please do the following.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums Ex, Ey, Ex², Ey², and E.xy and the value of the
sample correlation coefficient r.
(c) Find x, y, a, and b. Then find the equation of the least-squares line
ý = a + bx.
(d) Graph the least-squares line on your scatter diagram. Be sure to use the
point (T, y) as one of the points on the line.
(e) Interpretation Find the value of the coefficient of determination r. 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?
Answers may vary slightly due to rounding.
Transcribed Image Text:For Problems 7-18, please do the following. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums Ex, Ey, Ex², Ey², and E.xy and the value of the sample correlation coefficient r. (c) Find x, y, a, and b. Then find the equation of the least-squares line ý = a + bx. (d) Graph the least-squares line on your scatter diagram. Be sure to use the point (T, y) as one of the points on the line. (e) Interpretation Find the value of the coefficient of determination r. 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? Answers may vary slightly due to rounding.
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