Highway crash data analysis. 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 per formance function (SPF)—a mathematical model that estimates the probability of occurrence of a crash for a given segment of roadway. Using data on over 100 segments of roadway, the researchers fit the model E1y2 = b0 + b1 x1 + b2 x2, where y = number of crashes per three years, x1 = roadway length (miles), and x2 = average annual daily traffic 1number of vehicles2 =

AADT. The results are shown in the following tables.

Interstate Highways Variable Parameter Estimate Standard Error t-Value Intercept 1.81231 .50568 3.58 Length 1x12 .10875 .03166 3.44 AADT 1x22 .00017 .00003 5.19 Non-Interstate Highways Variable Parameter Estimate Standard Error t-Value Intercept 1.20785 .28075 4.30 Length 1x12 .06343 .01809 3.51 AADT 1x22 .00056 .00012 4.86

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

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

c. Refer to part

a. Find a 95% confidence interval for b1 and interpret the result.

d. Refer to part

a. Find a 95% confidence interval for b2 and interpret the result.

e. Repeat parts a–d for the non-interstate-highway model.