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(1) 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 33% of all fatal accidents of 17-year-olds are due to speeding.

 x 17 27 37 47 57 67 77 y 33 28 22 12 10 7 5

Complete parts (a) through (e), given

Σx = 329, Σy = 117, Σx2 = 18,263, Σy2 = 2675, Σxy = 4119, and r ≈ −0.972.

(a) Draw a scatter diagram displaying the data.

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(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 speeding for 35-year-olds. (Round your answer to two decimal places.)
%
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Step 1

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Given data of x be the age in years of licensed automobile driver and y be percentage of fatal accidents and its scatter plot is shown below. help_outlineImage Transcriptionclose33 35 28 30 22 15 12 10 10 10 20 30 40 50 60 70 80 90 age of licensed automobile driver (x) 17 33 27 28 37 22 47 12 57 10 67 77 5 7 V un . 20 O Fatal accidants percentage fullscreen
Step 2

From given data we calculate the required sums to and use the correlation coeffi... help_outlineImage TranscriptioncloseΧ^2 y^2 Χ Σ 33 xy 561 17 289 1089 1 2 27 28 729 784 756 3 37 22 1369 484 814 47 12 2209 144 564 4 5 57 10 3249 100 570 67 7 4489 49 469 25 7 77 5 5929 385 Total Σx=329 Σy 117 Σ^2132 63| Σy2 2675| Σν 4119| n (Σ3v)-(Σ x(Σy) ν ηΣ-Σ) (ΗΣΥ - (Σy) 7(4119)-(329 117) ν(7*18263- (329)*)(7 * 2675 - (117') 9660 =-0.972 ν19600) (503 6) fullscreen

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