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)=AADT.

Interstate Highways

Variable	Parameter Estimate	Standard Error	​t-value
Intercept	1.83708	0.57788	3.19
Length (x1)	0.15372	0.03744	3.02
AADT (x2)	0.00015	0.00003	5.25

​Non-Interstate Highways

Variable	Parameter Estimate	Standard Error	​t-value
Intercept	1.16268	0.27568	3.103633
Length (x1)	0.67195	0.02722	2.54644
AADT (x2)	0.000580.00058	0.00014	6.84273

refered to a table of critical values of the t distribution

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.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 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  x1=0 and x2=0 are not in the observed range.

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.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 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  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 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.

c. Refer to parta. 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 2​% 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.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 vehicle per day is between left limit and right​ limit, holding roadway mileage constant.

C.We are 2​% 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.

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

y=______+________x1+______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 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 β1. 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 x2=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 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.This value has no meaningful interpretation because  x1=0 and x2=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

.

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