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 39% of all fatal accidents of 17-year-olds are due to speeding.
Complete parts (a) through (e), given
Σx = 329, Σy = 117, Σx2 = 18,263, Σy2 = 2807, Σxy = 4059, and r ≈ −0.933.
(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.)
(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.)
(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.)
(f) Predict the percentage of all fatal accidents due to speeding for 60-year-olds. (Round your answer to two decimal places.)
|Total||Σx = 329||Σy = 117||Σx2 = 18263||Σy2 = 2807||Σxy =4059|
correlation coefficeint r = = -0.933
b = Sxy/Sxx = -1440/2800 = -0.514
a = = 16.71 - (-0.514)*47 = 40.868
y = 40.868 - 0.514* x
e) R2 = (b*Sxy)/Syy = -0.514*(-1440)/851.43 = 0.869
explained 86.9 %
f) given x = 60
y = 40.868 - 0.514* 60 = 10.03
Get Answers For Free
Most questions answered within 1 hours.