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# Regression Analysis on Speed of Vehicle

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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).

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#### 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).

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