Question

x	1	4	9	16	26	36
y	39	46	76	100	150	200

Complete parts, given Σx = 92, Σy = 611, Σx² = 2326, Σy² = 81,913, Σxy = 13,607, and r ≈ 0.998.

a) 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 =

b) Find x, and y. Then find the equation of the least-squares line  = 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	=
	=	+  x

c) 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	= %

d) The calves you want to buy are 19 weeks old. What does the least-squares line predict for a healthy weight? (Round your answer to two decimal places.)
=_____ kg

Answer 1

a)

ΣX =	92.000
ΣY=	611.000
ΣX2 =	2326.000
ΣY2 =	81913.000
ΣXY =	13607.000
r =	0.998

b)

X̅=ΣX/n =	15.33
Y̅=ΣY/n =	101.83
ŷ =	30.834+4.63x

c)

coefficient of determination r2 =				0.997
explained =				99.7%
unexplained=				0.3%

d)

predicted value =30.834+4.63*19=

118.80