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, Σx^{2} = 24814, Σy^{2} = 3139, Σxy = 8063, and r ≈ 0.916.
b) Verify the given sums Σx, Σy, Σx^{2}, Σy^{2}, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
Σx = | |
Σy = | |
Σx^{2} = | |
Σy^{2} = | |
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
r^{2}. 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 r^{2}
to three decimal places. Round your answers for the percentages to
one decimal place.)
r^{2} = | |
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.)
%
b)
ΣX = | 372.000 |
ΣY= | 109.000 |
ΣX^{2} = | 24814.000 |
ΣY^{2} = | 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 r^{2} = | 0.840 | |||
explained = | 84.0% | |||
unexplained= | 16.0% |
f)
predicted value =-28.068+0.746*70= | 24.15 |
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