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 35% of all fatal accidents of 17-year-olds are due to speeding.
x 17 27 37 47 57 67 77
y 35 24 19 12 10 7 5
given:
Σx = 329, Σy = 112, Σx2 = 18,263, Σy2 = 2480, Σxy = 3934, and r ≈ -0.958.
(a) 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 =
(b) Find x, and y. Then find the equation of the least-squares line y hat = 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 hat = ______+ ______x
(c) 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 20-year-olds. (Round your answer to two decimal places.)
_______%