Question

You are the foreman of the Bar-S cattle rench in Coloredo. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Ber-S herd. How much should a healthy call weigh? Let x be the age of the calf (in weeks), and let y be the weight of the call (in kilograms). x 1 5 11 16 26 36 Ty391773 100 150 200 Complete parts (a) through (e), given Ex - 95, y - 509, zx - 2375, 2) 2 - 81,559, 2x y - 13,777, and r»0.997. (a) Make a scatter diagram of the date. (Select the correct graph.) (b) Verify the given sums Ex, Ey, 2x2, E2, Exy, and the value of the sample correlation coefficient. (For each answer, enter a number. Round your value for r to three decimal places.) Ey = r? - 2/2 - Ex y = (c) Find, and ;. Then find the equation of the least squares line, = 2 + bx. (For each answe', enter a number. Round your answers for and to two decimal places. Round your answers for a and b to three decimal places.) (d) Graph the least-squares line. Be sure to plot the point ) as a point on the line. (Select the correct graph.) (0) Find the value of the coefficient or determination 2. 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 to three decimal places. Round your answers for the percentages to one decimal place.) 2 -

Answer 1

S.No 1.0000 25.0000 121.0000 256.0000 676.0000 1296.0000 1521.0000 2209.0000 5329.0000 10000.0000 22500.0000 40000.0000 XY 39.00 235.00 803.00 1600.00 3900.00 7200.00 ΣΧΥ 13777.0000 200 ΣΥ 609.0000 total 95.0000 2375.0000 81559.0000 n= 6.0000 15.8333 101.5000 13.1972 10 20 30 40 X=ΣΧ/η Y=ΣΥ/η s=(V(Σx-(Σx)/n)/(n-1))= 5=(V(Σy-(ΣΚΑΙ)/n)/(n-1))= Cov=Sxy=(ΣΧΥ-(ΣΧΣΥ)/n)/(n-1)= r=Cov/(Sx*Sy)= 62.8419 826.9000 0.997

a)

scatter plot is attached above

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

d)

3rd graph from left is correct

e)

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

f)

predicted value =

26.327+4.748*24=

140.28