Question

Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way.

x	37	47	57	67	77	87
y	5	8	10	14	27	45

Complete parts (a) through (e), given Σx = 372, Σy = 109, Σx² = 24814, Σy² = 3139, Σxy = 8063, and r ≈ 0.916.

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  = 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

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(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) 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

b)

ΣX =	372.000
ΣY=	109.000
ΣX2 =	24814.000
ΣY2 =	3139.000
ΣXY =	8063.000
r =	0.916

c)

X̅=ΣX/n =	62.00
Y̅=ΣY/n =	18.17
ŷ =	-28.068+0.746x

e)

coefficient of determination r2 =				0.840
explained =				84.0%
unexplained=				16.0%

f)

predicted value =-28.068+0.746*70=

24.15