Question

Let x be the age in years of a licensed automobile driver. Let y be the percentage of all fatal accidents (for a given age) due to speeding. For example, the first data pair indicates that 34% of all fatal accidents of 17-year-olds are due to speeding.

x	17	27	37	47	57	67	77
y	34	28	18	12	10	7	5

Complete parts (a) through (e), given

Σx = 329, Σy = 114, Σx² = 18,263, Σy² = 2582, Σxy = 3988, and r ≈ −0.961.

(a) Scatter diagram already complete!!! :)

(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 speeding for 20-year-olds. (Round your answer to two decimal places.)
____ %

Answer 1

b)

ΣX =	329.000
ΣY=	114.000
ΣX2 =	18263.000
ΣY2 =	2582.000
ΣXY =	3988.000
r =	-0.961

c)

X̅=ΣX/n =	47.00
Y̅=ΣY/n =	16.29
ŷ =	39.282+-0.489x

d()

e)

coefficient of determination r2 =				0.924
explained =				92.4%
unexplained=				7.6%

f)

predicted value =39.282+-0.489*20=

29.50