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 | 17 | 32 | 46 |
Complete parts (a) through (e), given Σx = 372, Σy = 118, Σx2 = 24814, Σy2 = 3618, Σxy = 8736, and r ≈ 0.942.
(a) Draw a scatter diagram displaying the 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 |
(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 70-year-olds. (Round your answer to two
decimal places.)
%