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.

(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 =

x^{2 =}

y^{2 =}

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.)

Y bar =

X bar =

^y =

(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.)

r^{2 =}

^{explained =_______________%}

^{unexplained = _______________%}

(f) The calves you want to buy are23weeks 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