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 E(y) = β0 + β1x1 + β2x2, 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

Non-Interstate Highways

a. Give the least squares prediction equation for the interstate highway model.
b. Give practical interpretations of the β estimates you made in part a.
c. Refer to part a. Find a 99% confidence interval for β1 and interpret the result.
d. Refer to part a. Find a 99% confidence interval for β2 and interpret the result.
e. Repeat parts a-d for the non-interstate-highway model.

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Parameter Estimate Standard Error t-Value Variable .50568 .03166 .00003 Intercept Length (x1) AADT (x2) 3.58 1.81231 .10875 .00017 3.44 5.19 Parameter Estimate Standard Error t-Value Variable 1.20785 .06343 .00056 .28075 Intercept Length (x1) AADT (x2) 4.30 3.51 4.86 .01809 .00012