(c) Find x, and y. Then find the equation of the least-squares line y = a + bx. (For each answer, enter a number. Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)5:14:19х3y =ý =%3Dх(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. (Select the correct graph.)yУУy200200200200150150150150100100100100505050хххх203020304010203040301040101020(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? (For each answer, enter a number. Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.)explained =unexplained =(f) The calves you want to buy are 10 weeks old. What does the least-squares line predict for a healthy weight (in kg)? (Enter a number. Round your answer to two decimal places.)kg

Question
Asked Feb 26, 2020
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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 11 16 26 36
y 39 47 73 100 150 200

 

(c) Find x, and y. Then find the equation of the least-squares line y = a + bx. (For each answer, enter a number. Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)
5:14:19
х3
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(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. (Select the correct graph.)
y
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200
200
150
150
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150
100
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100
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20
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(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? (For each answer, enter a number. Round your answer for r
2 to three decimal places. Round your answers for the percentages to one decimal place.)
explained =
unexplained =
(f) The calves you want to buy are 10 weeks old. What does the least-squares line predict for a healthy weight (in kg)? (Enter a number. Round your answer to two decimal places.)
kg
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(c) Find x, and y. Then find the equation of the least-squares line y = a + bx. (For each answer, enter a number. Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) 5:14:19 х3 y = ý = %3D х (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. (Select the correct graph.) y У У y 200 200 200 200 150 150 150 150 100 100 100 100 50 50 50 х х х х 20 30 20 30 40 10 20 30 40 30 10 40 10 10 20 (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? (For each answer, enter a number. Round your answer for r 2 to three decimal places. Round your answers for the percentages to one decimal place.) explained = unexplained = (f) The calves you want to buy are 10 weeks old. What does the least-squares line predict for a healthy weight (in kg)? (Enter a number. Round your answer to two decimal places.) kg

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Expert Answer

Step 1

Consider x and y be the age of the calf (in weeks) and the weight of the calf (in kilograms), respectively.

(c) Excel is used to obtain the required mean and least square line.

Steps for obtaining mean;

  1. Enter the data into spreadsheet.
  2. Use the Excel formula =Average(range of x) which gives the mean of x as 15.83.
  3. Use the Excel formula =Average(range of y) which gives the mean of y as 101.50.
Step 2

Steps for obtaining least square line is,

  1. Enter the data into spreadsheet.
  2. Go to Data>Data analysis>Regression>ok.
  3. Insert the range of Y and X and tick the labels.
  4. Click ok.
  5. The result is obtained as;

Statistics homework question answer, step 2, image 1

Step 3

(d) The point of (x-mean, y-mean) is obtained as (15.83, 101.50).

The predicted value of y at x=0 is obtained as;

Statistics homework question answer, step 3, image 1

...

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