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

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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
Complete parts, given
  • Σx = 95,
  •  
  • Σy = 609,
  •  
  • Σx2 = 2375,
  •  
  • Σy2 = 81,559,
  •  
  • Σx y = 13,777, and
  •  
  • r ≈ 0.997.
a. Verify the given sums Σx, Σy, Σx2, Σy2, Σx y, and the value of the sample correlation coefficient r. (For each answer, enter a number. Round your value for r to three decimal places.)
Σx = 
Σy = 
Σx2 = 
Σy2 = 
Σx y = 
r = 
 
b. Find x, and y . Then find the equation of the least-squares line  = a + b x. (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.)
 = x bar =
 = y bar =
 = value of a coefficient + value of b coefficient x
 
c. 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.)
r2 = 
explained =  %
unexplained =  %
 
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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