In: Statistics and Probability
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 | 13 | 31 | 41 |
Complete parts (a) through (e), given Σx = 372, Σy = 108, Σx2 = 24814, Σy2 = 3000, Σxy = 7956, and r ≈ 0.927.
(a) Draw a scatter diagram displaying the data.
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Submission Data |
(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 75-year-olds. (Round your answer to two
decimal places.)
%
a)
b)
ΣX = | 372.000 |
ΣY= | 108.000 |
ΣX2 = | 24814.000 |
ΣY2 = | 3000.000 |
ΣXY = | 7956.000 |
r = | 0.927 |
c)\
X̅=ΣX/n = | 62.00 | |
Y̅=ΣY/n = | 18.00 | |
ŷ = | -26.64+0.72x |
e)
coefficient of determination r2 = | 0.859 | |||
explained = | 85.9% | |||
unexplained= | 14.1% |
f)
predicted value =-26.64+0.72*75= | 27.36 |