"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?

MATLAB: An Introduction with Applications
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"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.)"

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.
37
47
57
67
77
87
5
8.
10
19
31
46
Complete parts (a) through (e), given Ex = 372, Ey = 119, Ex2 = 24814, Ey2 = 3627, Exy = 8793, and r 0.950.
(a) Draw a scatter diagram displaying the data.
Transcribed Image Text: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. 37 47 57 67 77 87 5 8. 10 19 31 46 Complete parts (a) through (e), given Ex = 372, Ey = 119, Ex2 = 24814, Ey2 = 3627, Exy = 8793, and r 0.950. (a) Draw a scatter diagram displaying the data.
(b) Verify the given sums Ex, Ey, Ex2, Ey?, Exy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)
Ex = 372
Ey = 119
Ex?
= 24814
Ey? = 3627
%3D
Exy = 8793
r =.95
(c) Find x, and y. Then find the equation of the least-squares line ŷ
b to three decimal places.)
= a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and
X = 62
y = 19.83
ý = -30.3
+1.81
Transcribed Image Text:(b) Verify the given sums Ex, Ey, Ex2, Ey?, Exy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Ex = 372 Ey = 119 Ex? = 24814 Ey? = 3627 %3D Exy = 8793 r =.95 (c) Find x, and y. Then find the equation of the least-squares line ŷ b to three decimal places.) = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and X = 62 y = 19.83 ý = -30.3 +1.81
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