Question

x	37	47	57	67	77	87
y	5	8	10	14	31	45

Complete parts, given Σx = 372, Σy = 113, Σx² = 24814, Σy² = 3371, Σxy = 8371, and r ≈ 0.926.

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) Predict the percentage of all fatal accidents due to failing to yield the right of way for 70-year-olds. (Round your answer to two decimal places.)
_____ %

Answer 1

Part a)

	X	Y	X * Y	X2	Y2
	37	5	185	1369	25
	47	8	376	2209	64
	57	10	570	3249	100
	67	14	938	4489	196
	77	31	2387	5929	961
	87	45	3915	7569	2025
Total	372	113	8371	24814	3371

r = 0.926

Part b)

X̅ = Σ( Xi / n ) = 372/6 = 62
Y̅ = Σ( Yi / n ) = 113/6 = 18.83

Equation of regression line is Ŷ = a + bX

b = ( 6 * 8371 - 372 * 113 ) / ( 6 * 24814 - ( 372 )2)
b = 0.78
a =( Σ Y - ( b * Σ X) ) / n
a =( 113 - ( 0.78 * 372 ) ) / 6
a = -29.527
Equation of regression line becomes Ŷ = -29.5267 + 0.78 X

Part c)

Coefficient of Determination
R2 = r2 = 0.857
Explained variation = 0.857* 100 = 85.7%
Unexplained variation = 1 - 0.857* 100 = 14.3%

Part d)

When X = 70
Ŷ = -29.527 + 0.78 X
Ŷ = -29.527 + ( 0.78 * 70 )
Ŷ = 25.07