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 39% of all fatal accidents of 17-year-olds are due to speeding.
x | 17 | 27 | 37 | 47 | 57 | 67 | 77 |
y | 39 | 22 | 22 | 12 | 10 | 7 | 5 |
Complete parts (a) through (e), given
Σx = 329, Σy = 117, Σx^{2} = 18,263, Σy^{2} = 2807, Σxy = 4059, and r ≈ −0.933.
(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 |
(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 60-year-olds. (Round your answer to two decimal places.)
__________________ %
b)
Sl.No. | x | y | x^2 | y^2 | xy |
1 | 17 | 39 | 289 | 1521 | 663 |
2 | 27 | 22 | 729 | 484 | 594 |
3 | 37 | 22 | 1369 | 484 | 814 |
4 | 47 | 12 | 2209 | 144 | 564 |
5 | 57 | 10 | 3249 | 100 | 570 |
6 | 67 | 7 | 4489 | 49 | 469 |
7 | 77 | 5 | 5929 | 25 | 385 |
Total | Σx = 329 | Σy = 117 | Σx2 = 18263 | Σy2 = 2807 | Σxy =4059 |
Sxx | 2800 |
Syy | 851.43 |
Sxy | -1440 |
correlation coefficeint r = = -0.933
c)
= 47
= 16.71
b = Sxy/Sxx = -1440/2800 = -0.514
a = = 16.71 - (-0.514)*47 = 40.868
y = 40.868 - 0.514* x
e) R2 = (b*Sxy)/Syy = -0.514*(-1440)/851.43 = 0.869
r2 =
0.869
explained 86.9 %
unexplained 13.1%
f) given x = 60
y = 40.868 - 0.514* 60 = 10.03
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