Explore BrainMass

Explore BrainMass

    Regression Analysis on Speed of Vehicle

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    The State Department of Transportation has conducted a study of 100 randomly selected vehicles in which the speed of the vehicle and age of the driver were measured. The Data were collected from a stretch of highway that produces an unusually high accident rate. A regression model was developed, with vehicle speed being predicted using age as the independent variable. The results obtained were:

    ŷ = 56.78 + 0.124x

    s
    b = 2.88
    1

    a) Develop a 95% interval estimate for the true regression slope and interpret.
    b) Based on your response to part a, can you conclude that age and speed are linearly related? Explain your answer.
    c) Construct a 98% interval estimate for the difference in speed that drivers travel whose ages are 20 years apart. (Hint: Consider carefully the parameter that would measure this difference).

    © BrainMass Inc. brainmass.com June 3, 2020, 5:08 pm ad1c9bdddf
    https://brainmass.com/statistics/regression-analysis/regression-analysis-speed-vehicle-15235

    Attachments

    Solution Preview

    a.)
    <br>Because,
    <br>b = <X> = 0.124
    <br>s = 2.88
    <br>n =100
    <br>for 95% confidence interval
    <br>z(alpha/2) = 1.96
    <br>hence,
    <br><X> - z*s/sqrt(n) < mu <<X> + z*s/sqrt(n)
    <br>=> 0.124 - (1.96*2.88/sqrt(100)) < mu < 0.124 + (1.96*2.88/sqrt(100))
    <br>=> -0.44048 < mu < ...

    Solution Summary

    The State Department of Transportation has conducted a study of 100 randomly selected vehicles in which the speed of the vehicle and age of the driver were measured. The Data were collected from a stretch of highway that produces an unusually high accident rate. A regression model was developed, with vehicle speed being predicted using age as the independent variable. The results obtained were:

    &#375; = 56.78 + 0.124x

    s
    b = 2.88
    1

    a) Develop a 95% interval estimate for the true regression slope and interpret.
    b) Based on your response to part a, can you conclude that age and speed are linearly related? Explain your answer.
    c) Construct a 98% interval estimate for the difference in speed that drivers travel whose ages are 20 years apart. (Hint: Consider carefully the parameter that would measure this difference).

    $2.19

    ADVERTISEMENT