Question

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)=β0+β1x1+β2x2​, where y=number of crashes per three​ years, x1=roadway length​ (miles), and x2=average annual daily traffic​ (number of​ vehicles) equals=AADT.   

Table of the Model Result

Interstate Highways

Variable	Parameter Estimate	Standard Error	​t-value
Intercept	1.89972	0.56355	3.17
Length (x1)	0.18575	0.02387	3.93
AADT (x2)	0.00017	0.00004	5.36

Variable

Parameter Estimate, Standard Error , t-value Intercept

1.25458, 0.28469, 3.58374

Length (x1) 0.53565, 0.02886, 3.94574

AADT (x2) 0.00048, 0.00016, 5.56854

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

y= (.....) + (.....) x1 + ..... x2

b. Give practical interpretations of the β estimates you made in part

a. Interpret the value of β0. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per​ day, holding roadway mileage constant.

B. This value has no meaningful interpretation because x1=0 and 0x2=0 are not in the observed range.

C. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of​ roadway, holding AADT constant.

Interpret the value of β1. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of​ roadway, holding AADT constant.

B. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per​ day, holding roadway mileage constant.

C. This value has no meaningful interpretation because 0 x1=0 and x2=0 are not in the observed range.

Interpret the value of β2. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of​ roadway, holding AADT constant.

B. This value has no meaningful interpretation because 0 x1=0 and 0x2=0 are not in the observed range.

C. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per​ day, holding roadway mileage constant.

c. Refer to part a. Find a 98% confidence interval for β1.   

(....), (....) (Round to five decimal places as​ needed.)   

Interpret the result. Choose the correct answer below.

A. There is not enough information to answer this question.

B. We are 98% 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. 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.

d. Refer to part a. Find a 98% confidence interval for β2.

(....), (....) (Round to five decimal places as​ needed.)   

Interpret the result. Choose the correct answer below.

A. We are 98% 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.

B. There is not enough information to answer this question.

C. 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.   

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

y=..... + ..... x 1 + .... x2

Give practical interpretations of the β estimates you made in previous part. Interpret the value of β0. Choose the correct answer below.

A. This value has no meaningful interpretation because x1=0 and x2=0 are not in the observed range.

B. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of​ roadway, holding AADT constant.

C. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per​ day, holding roadway mileage constant.

Interpret the value of β1. Choose the correct answer below.

A. This value has no meaningful interpretation because x1=0 and x2=0 are not in the observed range.

B. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per​ day, holding roadway mileage constant.

C. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of​ roadway, holding AADT constant.

Interpret the value of β2. Choose the correct answer below.

A. We estimate the mean number of crashes per 3 years will increase by β for each additional vehicle per​ day, holding roadway mileage constant.

B. We estimate the mean number of crashes per 3 years will increase by β for each additional mile of​ roadway, holding AADT constant.

C. This value has no meaningful interpretation because x1=0 and x2=0 are not in the observed range.

Find a 98% confidence interval for β1.

(.... , .....) (Round to five decimal places as​ needed.)

Find a 98% confidence interval for β2.

(.... , .... ) (Round to five decimal places as​ needed.)

Answer 1