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 3 4 8 16 26 36 y 45 53 75 100 150 200 Complete parts (a) through (e), given Σx = 93, Σy = 623, Σx2 = 2317, Σy2 = 82,959, Σxy = 13,647, and r ≈ 0.998. (a) Draw a scatter diagram displaying the data. Selection Tool Line Ray Segment Circle Vertical Parabola Horizontal Parabola Point No Solution Help 510152025303540102030405060708090100110120130140150160170180190200210 Clear Graph Delete Layer Fill WebAssign Graphing Tool Graph LayersToggle Open/Closed After you add an object to the graph you can use Graph Layers to view and edit its properties. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = y hat = + x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (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? (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 13 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.) kg

Answer 1

gla 8 4 16 526 150 36 200 EX total 93.0 623.0000 9.00 16.00 64.00 256.00 676.00 1296.00 2025.0000 2809.0000 5625.0000 10000.0000 22500.0000 40000.0000 135.00 212.00 600.00 1600.00 3900.00 7200.00 EXY 13647.0 2317.0 82959.00 X=18m Y=zY! sx=(x-(2x)*in)/(n-1)= sy=vizy-czy}*/n)/(n-1)= Cov=sxy=[EXY-(EX:Y]/n)/(n-1)= r=Covl(Sx"Sy) 6.0000 15.5000 103.8333 13.2325 60.4497 798.1000 0.998 slope B- intercepts 8. - 1'S,/S - (Ey-B,2x] 4.558 33.185

0 5 10 15 20 25 30 35 40

b)

ΣX =	93.000
ΣY=	623.000
ΣX2 =	2317.000
ΣY2 =	82959.000
ΣXY =	13647.000
r =	0.998

c)

X̅=ΣX/n =	15.50
Y̅=ΣY/n =	103.83
ŷ =	33.185+4.558x

e)

coefficient of determination r2 =				0.995
explained =				99.5%
unexplained=				0.5%

f)

predicted value =33.185+4.558*13=

92.44