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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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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.
Transcribed Image Text: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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