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 34% of all fatal accidents of 17-year-olds are due to speeding.

 x 17 27 37 47 57 67 77 y 34 28 18 12 10 7 5

Complete parts (a) through (e), given

Σx = 329, Σy = 114, Σx2 = 18,263, Σy2 = 2582, Σxy = 3988, and r ≈ −0.961.

(a) Scatter diagram already complete!!! :)

(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 20-year-olds. (Round your answer to two decimal places.)
____ % b)

 ΣX = 329 ΣY= 114 ΣX2 = 18263 ΣY2 = 2582 ΣXY = 3988 r = -0.961

c)

 X̅=ΣX/n = 47.00 Y̅=ΣY/n = 16.29 ŷ = 39.282+-0.489x

d() e)

 coefficient of determination r2 = 0.924 explained = 92.4% unexplained= 7.6%

f)

 predicted value =39.282+-0.489*20= 29.5