#Set up •rm(list=ls(all=TRUE)) •library(xlsReadWrite) •library(ggplot2) •theme_set(theme_bw()) •library(quantreg) •library(gplots) •setwd("I:/Project/2017 LD GHG Rule/Footprint_analysis/Outputs") •fleetorig <- xlsReadWrite::read.xls("I:/Project/2017 LD GHG Rule/Footprint_analysis/fleet/2010_20120509_fleet.xls")

#Drop Electrics and Diesels, keep hybrids like DOT did in NPRM. fleet<-fleetorig[fleetorig$Engine.Cycle %in% c("H","G","R"),]

##Calculate Weights - Don't remove vehicles after this, as these are based on total
volumes •a<-subset(fleet,NHTSA.Defined.New.NHTSA.Car.Truck == "C") •car.vol<-sum(a$Volume.2021) •b<-subset(fleet,NHTSA.Defined.New.NHTSA.Car.Truck == "T") •truck.vol<-sum(b$Volume.2021) •fleet$Weight<-ifelse(fleet$NHTSA.Defined.New.NHTSA.Car.Truck=="C",fleet$Volume.2021/car.v ol,fleet$Volume.2021/truck.vol)

• annot<-function(a) •{paste(signif(coef(a)[[1]],digits=3),"+",signif(coef(a)[[2]],digits=3),"x : R2=",signif(summary(a)[[8]],digits=3),sep = "")}

• annotrq<-function(a) •{paste(signif(coef(a)[[1]],digits=3),"+",signif(coef(a)[[2]],digits=3),"x",sep = "")}

•

analysis<-function(x) {
•#Create Fleet

• •fleet1<-subset(fleet,NHTSA.Defined.New.NHTSA.Car.Truck == x)

•• •#Diagnostics •#HP/WT ~ Footprint •lm.1<-lm(fleet1$Horsepower/fleet1$Curb.Weight ~ fleet1$Footprint, weights=fleet1$Weight) •#HP/WT ~ Footprint Squared •lm.2<-lm(fleet1$Horsepower/fleet1$Curb.Weight ~ poly(fleet1$Footprint,2,raw=TRUE), weights=fleet1$Weight) •#WT/FP ~ FP •lm.12<-lm(I(fleet1$Curb.Weight/fleet1$Footprint) ~ fleet1$Footprint, weights = fleet1$Weight) •#HP ~ WT •lm.3<-lm(fleet1$Horsepower~poly(fleet1$Curb.Weight,1, raw=TRUE), weights=fleet1$Weight) •#HP ~WT Squared •lm.4<-lm(fleet1$Horsepower~poly(fleet1$Curb.Weight,2, raw=TRUE), weights=fleet1$Weight) •#CO2 ~ Footprint •lm.5<-lm(fleet1$CO2.Package.1 ~ fleet1$Footprint, weights=fleet1$Weight) •#CO2 ~ HP/WT + WT •lm.8<-lm(fleet1$CO2.Package.1 ~ I(fleet1$Horsepower/fleet1$Curb.Weight)+I(fleet1$Curb.Weight),weights = fleet1$Weight)

•#Create CO2 w/ Adjustments •#HP/WT Adjusted CO2 •fleet1$hp.wt.avg<-sum(fleet1$Horsepower/fleet1$Curb.Weight*fleet1$Weight) •fleet1$hp.wt.CO2<-(fleet1$CO2.Package.1-(fleet1$Horsepower/fleet1$Curb.Weight-fleet1$hp.w t.avg)*coef(lm.8)[2]) •#WT/FP adjusted CO2 •fleet1$crb.wt.fp.avg<-sum(fleet1$Curb.Weight/fleet1$Footprint*fleet1$Weight) •fleet1$crbwt.norm.CO2<-(fleet1$CO2.Package.1-coef(lm.8)[3]*(fleet1$Curb.Weight-fleet1$crb .wt.fp.avg*fleet1$Footprint)) •#HP/WT and WT/FP Adjusted CO2•fleet1$hpwt.crbwt.norm.CO2<-(fleet1$hp.wt.CO2-coef(lm.8)[3]*(fleet1$Curb.Weight-fleet1$cr b.wt.fp.avg*fleet1$Footprint))

•#Return Answers •ans<-list(fleet1,lm.1,lm.2,lm.12,lm.3,lm.4,lm.5,lm.8) •invisible(return(ans)) }

#Function for the regressions needed on each of the CO2 datasets. regressions<-function(dataset){ •datasetb<-data.frame(dataset[1]) •#List the datasets here •CO2set<-data.frame(datasetb$CO2, datasetb$No.Tech.CO2, datasetb$CO2.Package.1, datasetb$hp.wt.CO2, datasetb$crbwt.norm.CO2, datasetb$hpwt.crbwt.norm.CO2) ••runr<-function(dsb){ •••weighted.ols•<-lm(dsb~datasetb$Footprint,weights = datasetb$Weight) •••unweighted.ols•<-lm(dsb~datasetb$Footprint,weights = NULL) •••weighted.mad•<-rq(dsb~datasetb$Footprint, tau=.5, weights = datasetb$Weight) •••unweighted.mad•<-rq(dsb~datasetb$Footprint, tau=.5,weights = NULL) ••invisible(return(regr<-list(weighted.ols,unweighted.ols,weighted.mad,unweighted.mad))) ••} •invisible(return(j<-lapply(CO2set,runr))) •}

#Create the Datasets, and excute the regressions, then merge the car and truck fleets cars.egr<-analysis("C") car.regressions<-regressions(cars.egr) trucks.egr<-analysis("T") truck.regressions<-regressions(trucks.egr) fleet4<-data.frame(rbind(cars.egr[[1]], trucks.egr[[1]]))

• car_base_equation<-annot(cars.egr[[8]]) truck_base_equation<-annot(trucks.egr[[8]])

••

summarize_regressions<-function(name,number){•• •name<-data.frame(rbind( ••cbind(name,"weighted OLS",annot(car.regressions[[number]][[1]]),annot(truck.regressions[[number]][[1]])), ••cbind(name,"unweighted OLS",annot(car.regressions[[number]][[2]]),annot(truck.regressions[[number]][[2]])), ••cbind(name,"weighted MAD",annotrq(car.regressions[[number]][[3]]),annotrq(truck.regressions[[number]][[3]])), ••cbind(name,"unweighted MAD",annotrq(car.regressions[[number]][[4]]),annotrq(truck.regressions[[number]][[4]])) ••))

• •return(name) •}

• all_regressions<-rbind(• summarize_regressions("2010",1), summarize_regressions("No.Tech",2), summarize_regressions("Tech.Normalized",3), summarize_regressions("HP/WT-Tech-Normalized",4), summarize_regressions("WT/FP-Tech-Normalized",5), summarize_regressions("HP/WT&WT/FP-Tech-Normalized",6) ) colnames(all_regressions)<-c("Dataset","Regression","Car Equation", "Truck Equation") all_regressions

dchart<-function(tit,jj,mult){ •fleet4$RCO2<-fleet4[,jj] •base.chart<-ggplot(data=fleet4, aes(y=RCO2, x=Footprint, size=Volume.2021,weight=Weight, group=NHTSA.Defined.New.NHTSA.Car.Truck))+ ••geom_point(aes(shape=1))+ ••labs(x="Footprint", y="CO2", size="2021 Projected Sales")+ ••opts(title=paste(tit,"CO2 v. Footprint"))+ ••facet_wrap(~NHTSA.Defined.New.NHTSA.Car.Truck)+ ••scale_x_continuous(limits=c(35,80))+ ••#weighted lines ••geom_smooth(method=lm, formula= y~ poly(x,1, raw=TRUE), se=FALSE) + ••geom_quantile(quantiles=.5, colour="red")+ ••#unweighted lines ••geom_smooth(method=lm, formula= y~ poly(x,1, raw=TRUE), se=FALSE, weight=I(1),linetype=5) + ••geom_quantile(quantiles=.5, colour="red",weight=1,linetype=5)+ ••#no legend ••opts(legend.position = "none") •return(base.chart) }

• •physics<-function(){ #Plot of WT/ v. FP - Weighted OLS p2<-ggplot(data=fleet, aes(y=I(fleet$Curb.Weight), x=fleet$Footprint, size=Volume.2021, weight=fleet$Weight, shape=1))+ •geom_point(aes(shape=1))+ •labs(x="Footprint", y="WT", colour="C/T", size="2021 Sales")+ •geom_smooth(method=lm, formula= y~ poly(x,1, raw=TRUE), se=FALSE)+ •geom_smooth(span=1,colour="red")+ •facet_wrap(~NHTSA.Defined.New.NHTSA.Car.Truck)+ •opts(title="WT v. FP - Weighted OLS and Loess Fit")+ •opts(legend.position = "none")

#Plot of WT/FP v. FP - Weighted OLS p1<-ggplot(data=fleet, aes(y=I(fleet$Curb.Weight/fleet$Footprint), x=fleet$Footprint, size=Volume.2021, weight=fleet$Weight))+ •geom_point(aes(shape=1))+ •labs(x="Footprint", y="WT/FP", colour="C/T", size="2021 Sales")+ •geom_smooth(method=lm, formula= y~ poly(x,1, raw=TRUE), se=FALSE)+ •geom_smooth(span=1,colour="red")+ •facet_wrap(~NHTSA.Defined.New.NHTSA.Car.Truck)+ •opts(title="WT/FP v. FP - Weighted OLS and Loess Fit")+ •opts(legend.position = "none")

• # Plot of HP/WT v. FP - Weighted OLS p4<-ggplot(data=fleet, aes(y=I(fleet$Horsepower/fleet$Curb.Weight), x=fleet$Footprint, size=Volume.2021, weight=fleet$Weight))+ •geom_point(aes(shape=1))+ •geom_smooth(method=lm, formula= y~ poly(x,1, raw=TRUE), se=FALSE)+ •facet_wrap(~NHTSA.Defined.New.NHTSA.Car.Truck)+ •labs(x="Footprint", y="HP/WT", colour="C/T", size="2021 Sales")+ •opts(title="HP/WT v. FP - Weighted OLS")+ •opts(legend.position = "none")

return(list(p1,p2,p4)) }

#Footprint Histogram• fphist<-ggplot(data=fleet,aes(x=Footprint, weight=Volume.2021))+ ••geom_bar(color="black", fill="white", binwidth=1)+ ••facet_wrap(~NHTSA.Defined.New.NHTSA.Car.Truck,ncol=1)+ ••labs(x="Footprint",y="MY 2021 Projected Sales")+ ••opts(title=paste("Footprint Distribution by Car and Truck"))+ ••geom_vline(xintercept=41, linetype=2)+ ••geom_vline(xintercept=56, linetype=2)+ ••geom_vline(xintercept=74, linetype=6)+ ••geom_vline(xintercept=41)•• #Plot by vehicle class vcplot<-function(){ man.sales<-aggregate((fleet$Volume.2021), by=list(fleet$Our.Class), sum) colnames(man.sales)<- c("Our.Class", "Man.2021.Sales")

man.footprint<-stack(by(fleet,list(fleet$Our.Class),function(subset)weighted.mean(subset$F ootprint, subset$Volume.2021), simplify=TRUE)) colnames(man.footprint)<- c("Avg.Footprint","Our.Class")

•tyu2<-merge(man.sales,fleet)• •tyu2$man.proportion<-tyu2$Volume.2021/tyu2$Man.2021.Sales •tyu2$wt.fp.proportion<-tyu2$Curb.Weight/tyu2$Footprint*tyu2$man.proportion •manwtfp<-aggregate((tyu2$wt.fp.proportion), by=list(tyu2$Our.Class), sum) •colnames(manwtfp) <- c("Our.Class", "Avg.Density") •manwtfp<- transform(manwtfp, Our.Class=reorder(Our.Class,Avg.Density)) •testmerge<-merge(manwtfp,man.sales) •manwtfp<-merge(testmerge, man.footprint) •#wt/fp averages

• ct<-signif(sum(cars.egr[[1]]$Curb.Weight/cars.egr[[1]]$Footprint*cars.egr[[1]]$Weight),dig its=3) dt<-signif(sum(trucks.egr[[1]]$Curb.Weight/trucks.egr[[1]]$Footprint*trucks.egr[[1]]$Weigh t), digits=3)

•ggplot(data=manwtfp,aes(x=Avg.Footprint, y=Avg.Density,label=Our.Class))+ ••geom_point(size=1)+ ••geom_text(hjust=-.05, angle=30, size=3)+ ••labs(x="Footprint",y="WT/FP")+ ••opts(title=paste("WT/FP by Vehicle Class"))+ ••opts(axis.text.x=theme_text(hjust=1))+ ••geom_hline(yintercept=ct, linetype=2, colour="red")+ ••annotate(geom="text", x = 65, y= 72, colour="red",label=paste("Car fleet avg.:",ct), size=3)+ ••geom_hline(yintercept=dt, linetype=2, colour="blue")+ ••annotate(geom="text", x = 65, y= 84, colour="blue",label=paste("Truck fleet avg.:",dt), size=3)+ ••scale_x_continuous(limits=c(40,70))+ ••scale_y_continuous(limits=c(65,100)) ••}

tester3<-function(df){lm(Curb.Weight ~ Footprint, weights=Volume.2021, data=df)} phys1a<-dlply(fleet4,.(NHTSA.Defined.New.NHTSA.Car.Truck),tester3)[[1]] phys1b<-dlply(fleet4,.(NHTSA.Defined.New.NHTSA.Car.Truck),tester3)[[2]] tester2<-function(df){lm(Curb.Weight/Footprint ~ Footprint, weights=Volume.2021, data=df)} phys2a<-dlply(fleet4,.(NHTSA.Defined.New.NHTSA.Car.Truck),tester2)[[1]] phys2b<-dlply(fleet4,.(NHTSA.Defined.New.NHTSA.Car.Truck),tester2)[[2]] tester<-function(df){lm(Horsepower/Curb.Weight ~ Footprint, weights=Volume.2021, data=df)} phys3a<-dlply(fleet4,.(NHTSA.Defined.New.NHTSA.Car.Truck),tester)[[1]] phys3b<-dlply(fleet4,.(NHTSA.Defined.New.NHTSA.Car.Truck),tester)[[2]]

lapply(list(phys1a,phys1b,phys2a,phys2b,phys3a,phys3b),summary)

pdf(paste("2010_curve_analysis-",Sys.Date( ),".pdf")) textplot(all_regressions,cex=0.5,halign=c("left")) fphist dchart("2010","CO2",0)• dchart("No.Tech","No.Tech.CO2",1) dchart("Tech-Normalized","CO2.Package.1",2) dchart("HP/WT-Tech-Normalized","hp.wt.CO2",3) dchart("WT/FP-Tech-Normalized","crbwt.norm.CO2",4) dchart("HP/WT&WT/FP-Tech-Normalized","hpwt.crbwt.norm.CO2",5) physics() vcplot() dev.off()