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 26 19 12 10 7 5 Complete parts (a) through (e), given Σx = 329, Σy = 116, Σx2 = 18,263, Σy2 = 2724, Σxy = 4022, and r ≈ −0.954. (a) Draw a scatter diagram displaying the data. Selection Tool (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 30-year-olds. (Round your answer to two decimal places.) %

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	26	19	12	10	7	5

Complete parts (a) through (e), given

Σx = 329, Σy = 116, Σx² = 18,263, Σy² = 2724, Σxy = 4022, and r ≈ −0.954.

(a) Draw a scatter diagram displaying the data.

Selection Tool

(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 30-year-olds. (Round your answer to two decimal places.)
%

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