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, Σx^{2} = 18,263, Σy^{2} = 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
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 speeding
for 20-year-olds. (Round your answer to two decimal places.)
____ %
b)
ΣX = | 329.000 |
ΣY= | 114.000 |
ΣX^{2} = | 18263.000 |
ΣY^{2} = | 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 r^{2} = | 0.924 | |||
explained = | 92.4% | |||
unexplained= | 7.6% |
f)
predicted value =39.282+-0.489*20= | 29.50 |
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