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 x = 95, y = 609, x2 = 2375, y2 = 81,559, x y = 13,777, and r 0.997.

(a)

Make a scatter diagram of the data. (Select the correct graph.)

A scatter diagram with 6 points is graphed on the x y coordinate plane. The points are located at (3, 39), (7, 47), (13, 73), (18, 100), (28, 150), (38, 200). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right. A scatter diagram with 6 points is graphed on the x y coordinate plane. The points are located at (1, 29), (5, 37), (11, 63), (16, 90), (26, 140), (36, 190). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right. A scatter diagram with 6 points is graphed on the x y coordinate plane. The points are located at (3, 29), (7, 37), (13, 63), (18, 90), (28, 140), (38, 190). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right. A scatter diagram with 6 points is graphed on the x y coordinate plane. The points are located at (1, 39), (5, 47), (11, 73), (16, 100), (26, 150), (36, 200). When considering the data points as a whole, the points are loosely gathered into a mass that is lower on the left and higher on the right.

(b)

Verify the given sums x, y, x2, y2, x 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.)

x =

95

y =

x2 =

y2 =

x 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 = 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.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 = 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.

(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 25 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