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.

(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 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

Answer 1

a)

b)

c)

d)


f) x = 25

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