Problem $2$: The Negative Binomial Model was built for fatal crashes, injury crashes and PDO crashes for the segment of the roadway as shown in the table below. The segment has the following characteristics: $4-$Lanes, $15,000vpd,12-$ft lane width, $6$ ft shoulder width, $24-$ ft median width, urban $($coded as $1)$ and rural coded as $0,$ rolling terrain $($coded as $1)$ and level coded as $0,$ curved section $($coded as $1,$ while straight is coded $0),$ and speed limit above $55$ mph $($coded $1)$ and all other speed coded as $0.$ The variables are considered significant at $95\%$ confidence level.

i$.$ Identify and discuss significant variables in each model, justify your variable pick

ii$.$ Formulate the Prediction equation for Fatal Crashes

iii. Formulate the Prediction equation for Injury Crashes

iv$.$ Formulate the Prediction equation for PDO Crashes

v$.$ Predict the number of fatal crashes for this segment

vi$.$ Predict the number of injury crashes for this segment

vii. Predict the number of PDO crashes for this segment

viii. Supporting with calculations, what will happen to the number of Injury Crashes if the section speed limit is changed from $55$ mph to $40$ mph

ix$.$ Will the PDO crashes increase or decrease if shoulder width is increased from $6$ to $8$ ft $,$ why?

x$.$ Supporting with calculations, what will be the percentage increase or decrease in the number of fatal crashes if the AADT is decreased from $15,000vpd$ to $14,805vpd$

$\backslash$table$[[,$Fatal Crashes,Injury Crashes,PDO Crashes$],[,$Coefficient,Z$-$Value,Coefficient,Z$-$Value,Coefficient,Z$-$Value$],[$Number of Lanes $($N$),1\mathrm{.}15,2\mathrm{.}55,0\mathrm{.}20,3\mathrm{.}23,1\mathrm{.}43,0\mathrm{.}71],[$AADT $($A$),-0\mathrm{.}003,3\mathrm{.}72,-0\mathrm{.}002,1\mathrm{.}35,0\mathrm{.}007,2\mathrm{.}99],[$Lane Width $($L$),0\mathrm{.}22,1\mathrm{.}69,0\mathrm{.}18,1\mathrm{.}36,-2\mathrm{.}00,1\mathrm{.}00],[$Shoulder Width $($SW$),-0\mathrm{.}41,1\mathrm{.}62,0\mathrm{.}66,5\mathrm{.}68,-3\mathrm{.}08,1\mathrm{.}54],[$Median Width $($M$),-0\mathrm{.}16,1\mathrm{.}66,1\mathrm{.}25,0\mathrm{.}77,-2\mathrm{.}85,1\mathrm{.}42],[$Urban Area $($U$),7\mathrm{.}80,0\mathrm{.}79,-0\mathrm{.}11,4\mathrm{.}15,,],[$Rolling Terrain $($R$),7\mathrm{.}25,1\mathrm{.}24,1\mathrm{.}22,1\mathrm{.}22,,],[$Curved Section $($C$),-1\mathrm{.}88,1\mathrm{.}11,-4\mathrm{.}10,7\mathrm{.}09,6\mathrm{.}07,2\mathrm{.}02],[$Speed Limit above $45$ mph $($SL$),12\mathrm{.}22,2\mathrm{.}41,-0\mathrm{.}40,-3\mathrm{.}21,-2\mathrm{.}41,-1\mathrm{.}20],[$Constant $(),20\mathrm{.}05,0\mathrm{.}98,,,-1\mathrm{.}01,-0\mathrm{.}51]]$