Researchers at Montana State University have written a tutorial on an empirical method for analyzing before and

Question:

Researchers at Montana State University have written a tutorial on an empirical method for analyzing before and after highway crash data (Montana Department of Transportation, Research Report, May 2004). The initial step in the methodology is to develop a Safety Performance Function (SPF)-a mathematical model that estimates crash occurrence for a given roadway segment. Using data collected for over 100 roadway segments, the researchers fit the model, E(y) = Î²0 + Î²1x1 + Î²2x2, where y = number of crashes per 3 years, x1 = roadway length (miles), and x2 = AADT = average annual daily traffic (number of vehicles). The results are shown in the following tables.

Interstate Highways Parameter Estimate Standard Error Variable t-Value Intercept Length (x1) AADT (x2) 1.81231 .10875 .5

a. Give the least squares prediction equation for the interstate highway model.
b. Give practical interpretations of the b estimates, part a.
c. Refer to part a. Find a 99% confidence interval for b1 and interpret the result.
d. Refer to part a. Find a 99% confidence interval for b2 and interpret the result.
e. Repeat parts a-d for the noninterstate highway model.
f. Write a first-order model for E(y) as a function of x1 and x2 that allows the slopes to differ depending on whether the roadway segment is Interstate or non-interstate.