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 37% of all fatal accidents of 17-year-olds are due to speeding. x 17 27 37 47 57 67 77 y 37 28 22 12 10 7 5 Complete parts (a) through (e) after verifying that Σx = 329, Σy = 121, Ex² = 18,263, Σy² = 2955, Exy = 4,187, and r = -0.9647. (a) Draw a scatter diagram displaying the data. y (percentage of all fatal accidents due to speeding) 35 30 10 80 70 60 30 10 35 80 r 70 30 20 20 5 20 30 40 50 60 70 5 10 15 20 25 30 35 20 30 40 50 60 70 5 10 15 20 25 30 35 x (age (in years)) x (age (in years)) x (age (in years)) x (age (in years)) (b) Find x (in years). (Round your answer to four decimal places.) x = years Find y (in %). (Round your answer to four decimal places.) y = % Find the equation of the least-squares line ŷ = a + bx. (Round your numerical values to four decimal places.) Ŷ = (c) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y (percentage of all fatal accidents due to speeding) 35 30 10 20 30 40 50 60 70 x (age (in years)) y (percentage of all fatal accidents due to speeding) 35 30 25 10 (d) Find the value of the coefficient of determination r². (Round your answer to four decimal places.) 2 = % 20 30 40 50 60 70 x (age (in years)) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? (Round your answer to two decimal places.) What percentage is unexplained? (Round your answer to two decimal places.) % (e) Predict the percentage of all fatal accidents due to speeding for 40-year-olds. (Round your answer to two decimal places.) % 80 80 70 60 50 40 30 20 5 10 15 20 25 30 35 x (age (in years)) 70 60 20 5 10 15 20 25 30 35 x (age (in years))
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 37% of all fatal accidents of 17-year-olds are due to speeding. x 17 27 37 47 57 67 77 y 37 28 22 12 10 7 5 Complete parts (a) through (e) after verifying that Σx = 329, Σy = 121, Ex² = 18,263, Σy² = 2955, Exy = 4,187, and r = -0.9647. (a) Draw a scatter diagram displaying the data. y (percentage of all fatal accidents due to speeding) 35 30 10 80 70 60 30 10 35 80 r 70 30 20 20 5 20 30 40 50 60 70 5 10 15 20 25 30 35 20 30 40 50 60 70 5 10 15 20 25 30 35 x (age (in years)) x (age (in years)) x (age (in years)) x (age (in years)) (b) Find x (in years). (Round your answer to four decimal places.) x = years Find y (in %). (Round your answer to four decimal places.) y = % Find the equation of the least-squares line ŷ = a + bx. (Round your numerical values to four decimal places.) Ŷ = (c) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. y (percentage of all fatal accidents due to speeding) 35 30 10 20 30 40 50 60 70 x (age (in years)) y (percentage of all fatal accidents due to speeding) 35 30 25 10 (d) Find the value of the coefficient of determination r². (Round your answer to four decimal places.) 2 = % 20 30 40 50 60 70 x (age (in years)) What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? (Round your answer to two decimal places.) What percentage is unexplained? (Round your answer to two decimal places.) % (e) Predict the percentage of all fatal accidents due to speeding for 40-year-olds. (Round your answer to two decimal places.) % 80 80 70 60 50 40 30 20 5 10 15 20 25 30 35 x (age (in years)) 70 60 20 5 10 15 20 25 30 35 x (age (in years))
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.1: Measures Of Center
Problem 9PPS
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Question
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 37% of all fatal accidents of 17-year-olds are due to speeding. Complete parts (a) through (e) after verifying that Σx = 329, Σy = 121, Σx2 = 18,263, Σy2 = 2955, Σxy = 4,187, and r ≈ −0.9647. (a) Draw a scatter diagram displaying the data. please answer parts a-e.
Transcribed Image Text: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 37% of all fatal accidents of 17-year-olds are due to speeding.
x
17
27 37 47 57
67
77
y
37
28 22 12
10
7
5
Complete parts (a) through (e) after verifying that Σx = 329, Σy = 121, Ex² = 18,263, Σy² = 2955, Exy = 4,187, and r = -0.9647.
(a) Draw a scatter diagram displaying the data.
y (percentage of all fatal accidents
due to speeding)
35
30
10
80
70
60
30
10
35
80 r
70
30
20
20
5
20
30
40
50
60
70
5
10
15
20
25
30
35
20
30
40
50
60
70
5
10
15
20
25
30
35
x (age (in years))
x (age (in years))
x (age (in years))
x (age (in years))
(b) Find x (in years). (Round your answer to four decimal places.)
x =
years
Find y (in %). (Round your answer to four decimal places.)
y =
%
Find the equation of the least-squares line ŷ = a + bx. (Round your numerical values to four decimal places.)
Ŷ =
(c) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.
y (percentage of all fatal accidents
due to speeding)
35
30
10
20
30
40
50
60
70
x (age (in years))
y (percentage of all fatal accidents
due to speeding)
35
30
25
10
(d) Find the value of the coefficient of determination r². (Round your answer to four decimal places.)
2 =
%
20
30
40
50
60
70
x (age (in years))
What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? (Round your answer to two decimal places.)
What percentage is unexplained? (Round your answer to two decimal places.)
%
(e) Predict the percentage of all fatal accidents due to speeding for 40-year-olds. (Round your answer to two decimal places.)
%
80
80
70
60
50
40
30
20
5
10
15
20
25
30
35
x (age (in years))
70
60
20
5
10
15
20
25
30
35
x (age (in years))
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