A1. A development engineer examined the relationship between the speed a vehicle is trav- elling (in miles per hour, mph), and the stopping distance (in metres, m) for a new braking system fitted to the vehicle. The following data were obtained in a series of independent tests conducted on a particular type of vehicle under identical road con- ditions. Speed of vehicle (x): Stopping distance (y): 5 Σr= 280, Σν- 241, Σ14000, Σ 11951 , Σ εy= 12790. 10 20 30 40 50 60 70 10 23 34 40 54 75 (a) Construct a scatter plot of the data, and comment on whether a linear regression is appropriate to model the relationship between the stopping distance and speed. (b) Calculate the equation of the least-squares fitted regression line. (c) Calculate a 95% confidence interval for the slope of the underlying regression line, and use this confidence interval to test the hypothesis that the slope of the underlying regression line is equal to 1. (d) Use the fitted line obtained in part (b) to calculate estimates of the stopping distance for a vehicle travelling at 50 mph and for a vehicle travelling at 100 mph. Comment briefly on the reliability of these estimates.

A1. A development engineer examined the relationship between the speed a vehicle is trav- elling (in miles per hour, mph), and the stopping distance (in metres, m) for a new braking system fitted to the vehicle. The following data were obtained in a series of independent tests conducted on a particular type of vehicle under identical road con- ditions. Speed of vehicle (x): Stopping distance (y): 5 Σr= 280, Σν- 241, Σ14000, Σ 11951 , Σ εy= 12790. 10 20 30 40 50 60 70 10 23 34 40 54 75 (a) Construct a scatter plot of the data, and comment on whether a linear regression is appropriate to model the relationship between the stopping distance and speed. (b) Calculate the equation of the least-squares fitted regression line. (c) Calculate a 95% confidence interval for the slope of the underlying regression line, and use this confidence interval to test the hypothesis that the slope of the underlying regression line is equal to 1. (d) Use the fitted line obtained in part (b) to calculate estimates of the stopping distance for a vehicle travelling at 50 mph and for a vehicle travelling at 100 mph. Comment briefly on the reliability of these estimates.

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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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

A1. A development engineer examined the relationship between the speed a vehicle is trav-
elling (in miles per hour, mph), and the stopping distance (in metres, m) for a new
braking system fitted to the vehicle. The following data were obtained in a series of
independent tests conducted on a particular type of vehicle under identical road con-
ditions.
Speed of vehicle (x):
Stopping distance (y): 5
Σ-280, Συ-241, Σ-14000 , Σ 11951, Σ sy- 12790.
10
20
30
40 50
60 70
10
23
34
40
54
75
(a) Construct a scatter plot of the data, and comment on whether a linear regression
is appropriate to model the relationship between the stopping distance and speed.
(b) Calculate the equation of the least-squares fitted regression line.
(c) Calculate a 95% confidece interval for the slope of the underlying regression
line, and use this confidence interval to test the hypothesis that the slope of the
underlying regression line is equal to 1.
(d) Use the fitted line obtained in part (b) to calculate estimates of the stopping
distance for a vehicle travelling at 50 mph and for a vehicle travelling at 100 mph.
Comment briefly on the reliability of these estimates.

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