Question

Let x be the age in years of a licensed automobile driver. Let y be the...

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.

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

(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
(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.)
____ %

Homework Answers

Answer #1

(c)

b = SSxy / SSxx = -1370 / 2800 =  -0.489

a = y - b x = 16.29 - (-0.489) * 47 =  39.273

y = 39.273 - 0.489 x

(e)

r2 = SSxy^2 / (SSxx * SSyy) = (-1370)^2 / (2800 * 725.4286) =  0.924

explained % = 92.4 %

unexplained = 100 - 92.4 = 7.6 %

(f)

For x = 20,

y = 39.273 - 0.489 * 20 =  29.493

The percentage of all fatal accidents due to speeding for 20-year-olds is  29.49

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