Data for this problem are based on information taken from The Wall Street Journal. 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 36% of all fatal accidents involving 17-year-olds are due to speeding.

Complete parts (a) through (e), given ˆ‘x = 329, ˆ‘y = 115, ˆ‘x2 = 18,263, ˆ‘y2 = 2639, ˆ‘xy = 4015, and r ‰ˆ ˆ’0.959.
(a) Draw a scatter diagram displaying the data.
(b) Verify the given sums ˆ‘x, ˆ‘y, ˆ‘x2, ˆ‘y2, and ˆ‘xy and the value of the sample correlation coefficient r.
(c) Find x, y, a, and b. Then find the equation of the least-squares line ŷ = α + bx.

(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?
(f) Predict the percentage of all fatal accidents due to speeding for 25-year-olds.

Transcribed Image Text:

17 27 37 4757 67 77 36 25 20 12 10 7 5