Question

# Let x be the age of a licensed driver in years. Let y be the percentage...

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 14 27 45

Complete parts (a) through (e), given Σx = 372, Σy = 109, Σx2 = 24814, Σy2 = 3139, Σxy = 8063, and r ≈ 0.916.

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 70-year-olds. (Round your answer to two decimal places.)
%

b)

 ΣX = 372 ΣY= 109 ΣX2 = 24814 ΣY2 = 3139 ΣXY = 8063 r = 0.916

c)

 X̅=ΣX/n = 62.00 Y̅=ΣY/n = 18.17 ŷ = -28.068+0.746x

e)

 coefficient of determination r2 = 0.840 explained = 84.0% unexplained= 16.0%

f)

 predicted value =-28.068+0.746*70= 24.15

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