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.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	X2	Y2
	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 Ŷ = a + bX


b = 4.748
a =( Σ Y - ( b * Σ X) ) / n
a =( 609 - ( 4.7478 * 95 ) ) / 6
a = 26.327
Equation of regression line becomes Ŷ = 26.327 + 4.748 X

When X = 16
Ŷ = 26.327 + 4.748 X
Ŷ = 26.327 + ( 4.748 * 16 )
Ŷ = 102.30