You are the foreman of the BarS cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the BarS 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 
2 
12 
16 
26 
36 
y 
47 
55 
71 
100 
150 
200 
Complete parts (a) through (e), given Σx = 93, Σy = 623, Σx^{2} = 2377, Σy^{2} = 82,775, Σxy = 13,709, and r ≈ 0.985.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums Σx, Σy,
Σx^{2}, Σy^{2}, Σxy, and
the value of the sample correlation coefficient r. (Round
your value for r to three decimal places.)
(c) Find x, and y. Then find the equation of the leastsquares 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 leastsquares line. Be sure to plot the point
(x, y) as a point on the line.
r^{2} = 

explained 
% 
unexplained 
% 
(e) Find the value of the coefficient of determination r^{2}. What percentage of the variation in y can be explained by the corresponding variation in x and the leastsquares line? What percentage is unexplained? (Round your answer for r^{2} to three decimal places. Round your answers for the percentages to one decimal place.)
(f) The calves you want to buy are 25 weeks old. What does the
leastsquares line predict for a healthy weight? (Round your answer
to two decimal places.)
kg
b)
Σx = 93,
Σy = 623,
Σx^{2} = 2377,
Σy^{2} = 82,775,
Σxy = 13,709, and
r ≈ 0.985
c)
xbar =15.50
ybar=103.83
yhat=36.689+4.332x
e)
coefficient of determination r^{2} =0.971
explained =97.1%
unexplained =2.3%
f)
predicted value =36.689+4.332*25 =144.99
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