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.

(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 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 =

y bar =

y hat = ____ + _______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 16 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

	X	Y	X * Y
	1	39	39	1	1521
	5	47	235	25	2209
	11	73	803	121	5329
	16	100	1600	256	10000
	26	150	3900	676	22500
	36	200	7200	1296	40000
Total	95	609	13777	2375	81559

r = 0.997

Equation of regression line is


b = 4.748

a =( 609 - ( 4.7478 * 95 ) ) / 6
a = 26.327
Equation of regression line becomes

Coefficient of Determination

Explained variation = 0.994* 100 = 99.4%
Unexplained variation = 1 - 0.994* 100 = 0.6%

When X = 16
= 26.327 + 4.748 X
= 26.327 + 4.748 * 16
= 102.3