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.)
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(f) Predict the percentage of all fatal accidents due to
speeding for 20-year-olds. (Round your answer to two decimal
places.) |
(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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