#Set up •rm(list=ls(all=TRUE)) •library(ggplot2) •library(quantreg) •library(gplots) •library(xlsReadWrite) •theme_set(theme_bw()) •setwd("I:/Project/2017 LD GHG Rule/Footprint_analysis/Outputs") •fleetorig <- xlsReadWrite::read.xls("I:/Project/2017 LD GHG Rule/Footprint_analysis/fleet/2008_20120509_fleet.xls")

#Drop Electrics and Diesels -Leave Hybrids per NHTSA 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$Footprint..PU.Average, weights=fleet1$Weight) •#HP/WT ~ Footprint Squared •lm.2<-lm(fleet1$Horsepower/fleet1$Curb.Weight ~ poly(fleet1$Footprint..PU.Average,2,raw=TRUE), weights=fleet1$Weight) •#WT/FP ~ FP. •lm.12<-lm(I(fleet1$Curb.Weight/fleet1$Footprint..PU.Average) ~ fleet1$Footprint..PU.Average, weights = fleet1$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..PU.Average, 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..PU.Average*fleet1$Weight) •fleet1$crbwt.norm.CO2<-(fleet1$CO2.Package.1-coef(lm.8)[3]*(fleet1$Curb.Weight-fleet1$crb .wt.fp.avg*fleet1$Footprint..PU.Average)) •#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..PU.Average))

•#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$Footprint..PU.Average,weights = datasetb$Weight) •••unweighted.ols•<-lm(dsb~datasetb$Footprint..PU.Average,weights = NULL) •••weighted.mad•<-rq(dsb~datasetb$Footprint..PU.Average, tau=.5, weights = datasetb$Weight) •••unweighted.mad•<-rq(dsb~datasetb$Footprint..PU.Average, 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("2008",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){
•#Base CO2•fleet4$RCO2<-fleet4[,jj] •base.chart<-ggplot(data=fleet4, aes(y=RCO2, x=Footprint..PU.Average, size=Volume.2021, weight=Weight))+ ••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_y_continuous(limits=c(0,800))+ ••scale_x_continuous(limits=c(35,80))+ ••#weighted lines ••geom_smooth(data = subset(fleet4, NHTSA.Defined.New.NHTSA.Car.Truck =="C"),method=lm, formula= y~ poly(x,1, raw=TRUE), se=FALSE) + ••geom_smooth(data = subset(fleet4, NHTSA.Defined.New.NHTSA.Car.Truck =="T"),method=lm, formula= y~ poly(x,1, raw=TRUE), se=FALSE) + ••geom_quantile(data = subset(fleet4, NHTSA.Defined.New.NHTSA.Car.Truck =="C"),quantiles=.5, colour="red")+ ••geom_quantile(data = subset(fleet4, NHTSA.Defined.New.NHTSA.Car.Truck =="T"),quantiles=.5, colour="red")+ ••#unweighted lines ••geom_smooth(data = subset(fleet4, NHTSA.Defined.New.NHTSA.Car.Truck =="C"),method=lm, formula= y~ poly(x,1, raw=TRUE), se=FALSE, weight=1,linetype=5) + ••geom_smooth(data = subset(fleet4, NHTSA.Defined.New.NHTSA.Car.Truck =="T"),method=lm, formula= y~ poly(x,1, raw=TRUE), se=FALSE,weight=1,linetype=5) + ••geom_quantile(data = subset(fleet4, NHTSA.Defined.New.NHTSA.Car.Truck =="C"),quantiles=.5, colour="red",weight=1,linetype=5)+ ••geom_quantile(data = subset(fleet4, NHTSA.Defined.New.NHTSA.Car.Truck =="T"),quantiles=.5, colour="red",weight=1,linetype=5)+ ••#no legend ••opts(legend.position = "none") ••#add equations ••#annotate(geom="text",x=40,y=700, colour="black", data = subset(fleet4, NHTSA.Defined.New.NHTSA.Car.Truck =="C"), ••#•••label= paste(all_regressions[1+(mult*4),2],all_regressions[1+(mult*4),3]) , size=2.75,hjust=0, vjust=0 ) •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..PU.Average, 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..PU.Average), x=fleet$Footprint..PU.Average, size=Volume.2021, weight=fleet$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$Footprint..PU.Average, size=Volume.2021, weight=fleet$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..PU.Average, 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)

••

tester3<-function(df){lm(Curb.Weight ~ Footprint..PU.Average, 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..PU.Average ~ Footprint..PU.Average, 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..PU.Average, 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("2008_curve_analysis-",Sys.Date( ),".pdf")) textplot(all_regressions,cex=0.5,halign=c("left")) fphist dchart("2008","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() dev.off()