A database has been prepared $06$ Data.xls$),$ which provides details of more than $4000$ miles of two$-$lane highways throughout the state of Michigan. All segments have a posted speed limit of $55$ mph$.$ Centerline rumble strips were installed on all of these segments. Additional details of available data for these segments is included here:

$$ Segment$\_$ID $$ unique identifier for each segment

$$ AADT $$ annual average daily traffic $($veh$/$day$)$

$$ Length $$ segment length $($mi$)$

$$ Lane$\_$Width $$ lane width $($ft$)$

$$ Shoulder$\_$Width $$ right shoulder width $($ft$)$

$$ Passing$\_$Lane $1$ if passing lane is present; $0$ otherwise

$$ Rolling$\_$Terrain $1$ if terrain is rolling; $0$ if terrain is level

$$ Total$\_$Crashes $$ number of total crashes

$$ Lane$\_$Departure$\_$Crashes $$ number of lane departure crashes

$1.$ Using the safety performance function $($SPF$)$ for rural two$-$lane highway segments from Chapter $10$ of the Highway Safety Manual, calculate a calibration factor for the Michigan roadway network. $($Be sure to incorporate crash modification factors where applicable.$)$

$2.$ Using this calibrated SPF$,$ calculate the expected number of crashes for each road segment using the full HSM predictive method. State any necessary assumptions.

$3.$ Discuss the practical impacts of the results. Does the default HSM model under or over predict crashes $($and why$)?$ Are there any limitations to the results? Are there any recommendations as to how the utility of the predictive method could be improved by future work?