Reference no: EM132363812
Question
1. 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 (a) through (e), given Σx = 95, Σy = 609, Σx2 = 2375, Σy2 = 81,559, Σx y = 13,777, and r ≈ 0.997.
(a) Make a scatter diagram of the data. (Select the correct graph.)
(b) 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 =
(c)
Find , and . Then find the equation of the least-squares line = a + b x. (For each answer, enter a number. Round your answers for and 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
(d) Graph the least-squares line. Be sure to plot the point (, ) as a point on the line. (Select the correct graph.)
(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.)
r2 =
explained =
%
unexplained =
%
(f) The calves you want to buy are 23 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
2. Compute P5,4. (Enter an exact number.)