Question

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 37% of all fatal accidents of 17-year-olds are due to speeding.

x 17 27 37 47 57 67 77

y 37 23 18 12 10 7 5

Complete parts (a) through (e), given Σx = 329, Σy = 112, Σx² = 18,263, Σy² = 2540, Σxy = 3904, and r ≈ −0.940.

(a) Draw a scatter diagram displaying the data.

Submission 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 =

^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 25-year-olds. (Round your answer to two decimal places.)

%

Answer 1