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 x 2 equalsx2=average annual daily traffic (number of vehicles)equals=AADT.

Interstate Highways

Variable	Parameter Estimate	Standard Error	t-value
Intercept	1.81956	0.55151	3.21
Length (X1)	0.19447	0.03716	3.06
AADT (X2)	0.00013	0.00002	5.63

Non-Interstate Highways

Variable	Parameter Estimate	Standard Error	t-value
Intercept	1.12068	0.32859	3.79421
Length (X1)	0.56536	0.01724	2.63473
AADT (X2)	0.00051	0.00011	5.49811

REFER TO TABLE OF CRITICAL VALUES OF THE T DISTRIBUTION

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

Y=1.81956+0.19447 X1+ 0.00013 X2 CORRECT ANSWER

b. Give practical interpretations of the β estimates you made in part a. Interpret the value β0. 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  X1=0 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 vehicle per day, holding roadway mileage constant.

Answer 1

b)

slope x1 interprets that We estimate the mean number of crashes per 3 years will increase by β for each additional mile of roadway, holding AADT constant

slope x2 interprets that We estimate the mean number of crashes per 3 years will increase by β for each unit increase in AADT , holding roadway length (miles) constant.

so,

option a) is correct

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

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