Question

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

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, Σx2 = 18,263, Σy2 = 2807, Σxy = 4059, and r ≈ −0.933.

(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 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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