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.

(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

(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 14 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

Given :

Σx = 95,

Σy = 609,

Σx2 = 2375,

Σy2 = 81,559,

Σx y = 13,777, and

r ≈ 0.997.

n = 6

(c)

= Σx /n = 95/6

= 15.83

= Σy /n = 609/6

= 101.5

value of b coefficient x

=  

=

= 24807 / 5225

= 4.748

value of a coefficient =

=101.5 - ( 4.748*15.83)

= 26.327

= 26.327 + 4.748x

(e)

=   

= 0.994

explained = 99.4%

unexplained = 0.6 %

(f)

We are given x = 14

= 26.327 + (4.748 *14)

= 92.80 kg