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? Letxbe the age of the calf (in weeks), and letybe 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), givenx=95,y=609,x²=2375,y²=81,559,x y=13,777,andr0.997.

(a)

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

(b)

Verify the given sumsx,y,x²,y²,x y, and the value of the sample correlation coefficientr. (For each answer, enter a number. Round your value forrto three decimal places.)

x=

y=

x²=

y²=

x 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 forandto two decimal places. Round your answers foraandbto 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 determinationr². What percentage of the variation inycan beexplainedby the corresponding variation inxand the least-squares line? What percentage isunexplained? (For each answer, enter a number. Round your answer forr²to three decimal places. Round your answers for the percentages to one decimal place.)

r²=

explained =

%

unexplained =

%

(f)

The calves you want to buy are13weeks 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