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.

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

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

	n=	6.0000
	X̅=ΣX/n	15.8333
	Y̅=ΣY/n	101.5000
	sx=(√(Σx2-(Σx)2/n)/(n-1))=	13.1972
	sy=(√(Σy2-(Σy)2/n)/(n-1))=	62.8419
	Cov=sxy=(ΣXY-(ΣXΣY)/n)/(n-1)=	826.9000
	r=Cov/(Sx*Sy)=	0.997
	slope= β̂1 =r*Sy/Sx=	4.7478
	intercept= β̂0 ='y̅-β1x̅=	26.3273

b)

ΣX =	95.000
ΣY=	609.000
ΣX2 =	2375.000
ΣY2 =	81559.000
ΣXY =	13777.000
r =	0.997

c)

X̅=ΣX/n =	15.83
Y̅=ΣY/n =	101.50
ŷ =	26.327+4.748x

e)

coeff of determination r2 =		0.994
explained =		99.4%
unexplained=		0.6%

f)

predicted val=26.33+16*4.75=

102.29