Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair states that 5% of all fatal accidents of 37-year-olds are due to failure to yield the right of way.
Complete parts (a) through (e), given Σx = 372, Σy = 113, Σx2 = 24814, Σy2 = 3311, Σxy = 8351, and r ≈ 0.935.
(a) Draw a scatter diagram displaying the data.
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(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.)
(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.)
(f) Predict the percentage of all fatal accidents due to failing to yield the right of way for 70-year-olds. (Round your answer to two decimal places.)
ΣX = 372
ΣY = 113
ΣX * Y = 8351
ΣX2 = 24814
ΣY2 = 3311
r = 0.935
Equation of regression line is Ŷ = a + bX
b = 0.769
a =( Σ Y - ( b * Σ X) ) / n
a =( 113 - ( 0.7686 * 372 ) ) / 6
a = -28.818
Equation of regression line becomes Ŷ = -28.818 + 0.769 X
Coefficient of Determination
Explained variation = 0.874* 100 = 87.4%
Unexplained variation = 1 - 0.874* 100 = 12.6%
When X = 70
Ŷ = -28.818 + 0.769 X
Ŷ = -28.818 + ( 0.769 * 70 )
Ŷ = 25.01
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