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.
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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Researchers developed a safety performance function (SPF), which estimates the probability of occurrence of a crash...
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