Question

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	18	31	46

Complete parts (a) through (e), given Σx = 372, Σy = 118, Σx² = 24814, Σy² = 3590, Σxy = 8726, and r ≈ 0.946.

(a) 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 =

(b) Find x, and y. Then find the equation of the least-squares line ŷ = 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=

ŷ = +   x

(c) 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 =    %

(d) Predict the percentage of all fatal accidents due to failing to yield the right of way for 65-year-olds. (Round your answer to two decimal places.)
= %

Answer 1

(a) 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.)

(b) Find x, and y. Then find the equation of the least-squares line ŷ = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(c) 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 =0.895

explained = 89.5 %

unexplained = 1- 0.895 =0.105 (10.5 %)

(d) Predict the percentage of all fatal accidents due to failing to yield the right of way for 65-year-olds. (Round your answer to two decimal places.)
= 22.0829%