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Researchers developed a safety performance function (SPF), which estimates the probability of occurrence of a crash for a given segment of roadway. Using data on over 100 segments of roadway, they fit the model E(y) =  b0 + b1*x1 + b2*x2 ,
where y = number of crashes per three years, x1 = roadway length (miles), and x2 =
average annual daily traffic (number of vehicles) =  AADT.

 

 

1. Give the least squares prediction equation for the interstate highway model.

A. We are 99% confident that the increase in mean number of crashes for each additional  mile of roadway is between left limit and right limit, holding AADT constant.
Your answer is correct.
B. We are 1 %  confident that the increase in mean number of crashes for each additional mile of roadway is between left limit and right limit, holding AADT constant.
C.There is not enough information to answer this question.

7.  Refer to part a. Find a 99% confidence interval for beta 2

8. Interpret the result. Choose the correct answer below.

A. There is not enough information to answer this question.
B. We are 1 % confident that the increase in mean number of crashes for each additional vehicle per day is between left limit and right limit, holding roadway mileage constant.
C. We are 99% confident that the increase in mean number of crashes for each additional vehicle per day is between left limit and right limit, holding roadway mileage constant.

9. Give the least squares prediction equation for the interstate non-highway model.

10. Give practical interpretations of the beta estimates you made in previous part. Interpret the value of beta 0. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by beta for each additional mile of roadway, holding AADT constant.
B. We estimate the mean number of crashes per 3 years will increase by beta  
for each additional vehicle per day, holding roadway mileage constant.
C.This value has no meaningful interpretation because nbsp x1 = 0 and x2 = 0 are not in the observed range.

11. Give practical interpretations of the beta estimates you made in previous part. Interpret the value of beta 0. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by beta for each additional mile of roadway, holding AADT constant.
B. We estimate the mean number of crashes per 3 years will increase by beta  
for each additional vehicle per day, holding roadway mileage constant.
C.This value has no meaningful interpretation because nbsp x1 = 0 and x2 = 0 are not in the observed range.

12. Interpret the value of beta 1. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by beta for each additional mile of roadway, holding AADT constant.
Your answer is correct.
B. We estimate the mean number of crashes per 3 years will increase by beta for each additional vehicle per day, holding roadway mileage constant.
C. This value has no meaningful interpretation because nbsp x1 = 0 and x2 = 0 are not in the observed range.

13. Interpret the value of beta 2. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by beta for each additional mile of roadway, holding AADT constant.
B. We estimate the mean number of crashes per 3 years will increase by beta for each additional vehicle per day, holding roadway mileage constant.
C. This value has no meaningful interpretation because nbsp x1 = 0 and x2 = 0 are not in the observed range.

Find a 99 % confidence interval for beta 1.

Find a 99% confidence interval for beta 1.