Question

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.

(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 x bar, and y bar. Then find the equation of the least-squares line y hat = a + b x. (For each answer, enter a number. Round your answers for x bar and y bar to two decimal places. Round your answers for a and b to three decimal places.)

x bar = x bar =

y bar = y bar =

y hat = value of a coefficient + value of b coefficient x

(d) Graph the least-squares line. Be sure to plot the point (x bar, y bar) as a point on the line. (Select the correct graph.) A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 132). The line enters the window at approximately y = 56 on the positive y axis, goes up and right, passes through the approximate point (15.8, 132), and exits the window in the first quadrant. A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 102). The line enters the window at approximately y = 171 on the positive y axis, goes down and right, passes through the approximate point (15.8, 102), and exits the window at approximately x = 39.1 on the positive x axis. A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 102). The line enters the window at approximately y = 26 on the positive y axis, goes up and right, passes through the approximate point (15.8, 102), and exits the window in the first quadrant. A line and a point are graphed on the x y coordinate plane. The point is located the approximate point (15.8, 132). The line enters the window at approximately y = 201 on the positive y axis, goes down and right, passes through the approximate point (15.8, 132), and exits the window in the first quadrant.

(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 16 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

Answer 1

b)

ΣX =	95.000
ΣY=	609.000
ΣX2 =	2375.000
ΣY2 =	81559.000
ΣXY =	13777.000
r =	0.997

c)

X̅=ΣX/n =	15.83
Y̅=ΣY/n =	101.50
ŷ =	26.327+4.748x

d)

e)

coefficient of determination r2 =				0.994
explained =				99.4%
unexplained=				0.6%

f)

predicted value =

26.327+4.748*16=

102.30