What Factors May Affect Carbon Emissions of Cars
Liang Zhao
October 11, 2016 V1
1.Setting
System Under Test
We find data from the link in data.gov in the 100+ interesting datasets, a dataset of automobile(model 2017) fuel economy is tested. The motivation of this analysis is that the problem of global warming has attracted much more attention since the beginning of this century. Some scientists believe that global warming is caused by the increase of greenhouse gases, and the volume of vehicle exhaust, which is a contributor to greenhouse effect, needs to be largely reduced.
In this study, a four-factor, multi-level experiment is performed to test whether factors of Cyl, Japanese, SmartWay, and Veh.Class may affect the emission level of CO2. The four factors are listed as below:
Cyl: number of cylinders.
Japanese: whether it is a Japanese car.
SmartWay: whether have an energy-saving system.
Veh.Class:the type of car.
# Read the data downloaded from website, and assign it to "car"
car <- read.csv("C:/Users/zhao/Desktop/alpha_2017.csv")
# Then, display "head"" and "tail"" of the dataset-"car"
head(car)## Japanese Make Model Displ Cyl Trans Drive Fuel Cert.Region
## 1 Yes ACURA ACURA ILX 2.4 4 AMS-8 2WD Gasoline CA
## 2 Yes ACURA ACURA ILX 2.4 4 AMS-8 2WD Gasoline FA
## 3 Yes ACURA ACURA MDX 3.5 6 SemiAuto-9 2WD Gasoline CA
## 4 Yes ACURA ACURA MDX 3.5 6 SemiAuto-9 2WD Gasoline CA
## 5 Yes ACURA ACURA MDX 3.5 6 SemiAuto-9 2WD Gasoline FA
## 6 Yes ACURA ACURA MDX 3.5 6 SemiAuto-9 2WD Gasoline FA
## Stnd Stnd.Description Underhood.ID Veh.Class
## 1 L3ULEV125 California LEV-III ULEV125 HHNXV02.4SH3 small car
## 2 T3B125 Federal Tier 3 Bin 125 HHNXV02.4SH3 small car
## 3 L3ULEV125 California LEV-III ULEV125 HHNXV03.5VH3 small SUV
## 4 L3ULEV125 California LEV-III ULEV125 HHNXV03.5VH3 small SUV
## 5 T3B125 Federal Tier 3 Bin 125 HHNXV03.5VH3 small SUV
## 6 T3B125 Federal Tier 3 Bin 125 HHNXV03.5VH3 small SUV
## Air.Pollution.Score City.MPG Hwy.MPG Cmb.MPG Greenhouse.Gas.Score
## 1 6 25 35 29 7
## 2 6 25 35 29 7
## 3 6 19 27 22 5
## 4 6 20 27 23 5
## 5 6 19 27 22 5
## 6 6 20 27 23 5
## SmartWay Comb.CO2
## 1 Yes 309
## 2 Yes 309
## 3 No 404
## 4 No 391
## 5 No 404
## 6 No 391tail(car)## Japanese Make Model Displ Cyl Trans Drive
## 1185 No VOLVO VOLVO XC 90 2 4 SemiAuto-8 4WD
## 1186 No VOLVO VOLVO XC 90 2 4 SemiAuto-8 4WD
## 1187 No VOLVO VOLVO XC 90 2 4 SemiAuto-8 4WD
## 1188 No VOLVO VOLVO XC 90 2 4 SemiAuto-8 4WD
## 1189 No VOLVO VOLVO XC 90 2 4 SemiAuto-8 4WD
## 1190 No VOLVO VOLVO XC 90 2 4 SemiAuto-8 4WD
## Fuel Cert.Region Stnd
## 1185 Gasoline CA L3ULEV125
## 1186 Gasoline CA L3ULEV125
## 1187 Gasoline FA T3B125
## 1188 Gasoline FA T3B125
## 1189 Gasoline/Electricity CA L3SULEV30/PZEV
## 1190 Gasoline/Electricity FA T3B30
## Stnd.Description Underhood.ID Veh.Class
## 1185 California LEV-III ULEV125 HVVXT02.0U3T standard SUV
## 1186 California LEV-III ULEV125 HVVXT02.0U3T standard SUV
## 1187 Federal Tier 3 Bin 125 HVVXT02.0U3T standard SUV
## 1188 Federal Tier 3 Bin 125 HVVXT02.0U3T standard SUV
## 1189 California LEV-III SULEV30/PZEV HVVXT02.0P3T standard SUV
## 1190 Federal Tier 3 Bin 30 HVVXT02.0P3T standard SUV
## Air.Pollution.Score City.MPG Hwy.MPG Cmb.MPG Greenhouse.Gas.Score
## 1185 6 20 25 22 5
## 1186 6 22 25 23 5
## 1187 6 20 25 22 5
## 1188 6 22 25 23 5
## 1189 9 22 25 23 8
## 1190 8 22 25 23 8
## SmartWay Comb.CO2
## 1185 No 399
## 1186 No 384
## 1187 No 399
## 1188 No 384
## 1189 Yes 238
## 1190 Yes 238Factors and Levels
In this study, each experiment contains four different factors, each with multiple levels. We include Cyl, Japanese, SmartWay, and Veh.Class. The factor ‘Cly’ has 2 levels, the factor ‘Japanese’ has 2 levels, the factor ‘SmartWay’ has 2 levels and the factor ‘Veh.Class’ has 5 levels. The factors are selected based on our best guess. For ‘Cylinder’, ‘SmartWay’, and ‘Veh.Class’, it is reasonable to think of that these factors with different levels will affect the vehicle exhaust. For factor ‘Japanese’, we test this factor because many people argues that Japanese cars are more efficient and environmental-friendly. The summay and the structure are listed below:
#Display the summary statistics of "car".
summary(car)## Japanese Make Model Displ
## No :976 BMW :136 HONDA Accord : 19 Min. :1.400
## Yes:214 HYUNDAI : 83 JEEP Cherokee : 14 1st Qu.:2.000
## CHEVROLET: 72 JEEP Compass : 14 Median :2.400
## KIA : 69 JEEP Patriot : 14 Mean :2.514
## PORSCHE : 69 CADILLAC ATS : 12 3rd Qu.:3.000
## FORD : 61 CHEVROLET Equinox: 12 Max. :3.800
## (Other) :700 (Other) :1105
## Cyl Trans Drive Fuel
## Min. :4.000 SemiAuto-6:307 2WD:719 Diesel : 8
## 1st Qu.:4.000 SemiAuto-8:252 4WD:471 Ethanol : 1
## Median :4.000 Man-6 :140 Ethanol/Gas : 32
## Mean :4.802 Auto-6 : 78 Gasoline :1131
## 3rd Qu.:6.000 AMS-7 : 59 Gasoline/Electricity: 18
## Max. :6.000 CVT : 52
## (Other) :302
## Cert.Region Stnd
## CA:597 T3B125 :251
## FA:593 T3B110 :171
## U2 :161
## L3ULEV125 :117
## T3B30 :101
## L3SULEV30/PZEV: 71
## (Other) :318
## Stnd.Description Underhood.ID
## Federal Tier 3 Bin 125 :251 HPRXV03.0C91: 40
## Federal Tier 3 Transitional Bin 110:171 HBMXV02.0B4X: 30
## California LEV-II ULEV :161 HBMXV03.0B58: 30
## California LEV-III ULEV125 :117 HGMXJ03.6165: 30
## Federal Tier 3 Bin 30 :101 HJLXJ03.0FSP: 30
## California LEV-III SULEV30/PZEV : 71 HBMXV03.0F10: 20
## (Other) :318 (Other) :1010
## Veh.Class Air.Pollution.Score City.MPG Hwy.MPG
## large car : 88 Min. :5.000 Min. :13.00 Min. :17.00
## midsize car :214 1st Qu.:6.000 1st Qu.:19.00 1st Qu.:26.00
## small car :507 Median :6.000 Median :21.00 Median :29.00
## small SUV :281 Mean :6.399 Mean :22.07 Mean :29.64
## standard SUV:100 3rd Qu.:7.000 3rd Qu.:24.00 3rd Qu.:33.00
## Max. :9.000 Max. :58.00 Max. :53.00
##
## Cmb.MPG Greenhouse.Gas.Score SmartWay Comb.CO2
## Min. :14.00 Min. : 2.000 No :976 Min. : 51.0
## 1st Qu.:22.00 1st Qu.: 5.000 Yes:214 1st Qu.:324.0
## Median :24.00 Median : 5.000 Median :369.0
## Mean :24.93 Mean : 5.373 Mean :366.6
## 3rd Qu.:27.00 3rd Qu.: 6.000 3rd Qu.:406.0
## Max. :71.00 Max. :10.000 Max. :546.0
## #Display the names found in "car".
names(car)## [1] "Japanese" "Make" "Model"
## [4] "Displ" "Cyl" "Trans"
## [7] "Drive" "Fuel" "Cert.Region"
## [10] "Stnd" "Stnd.Description" "Underhood.ID"
## [13] "Veh.Class" "Air.Pollution.Score" "City.MPG"
## [16] "Hwy.MPG" "Cmb.MPG" "Greenhouse.Gas.Score"
## [19] "SmartWay" "Comb.CO2"#Display the structure of "car" and set 'Cyl' as factor.
car$Make<-as.character(car$Make)
car$Model<-as.character(car$Model)
car$Trans<-as.character(car$Trans)
car$Drive<-as.character(car$Drive)
car$Fuel<-as.character(car$Fuel)
car$Cert.Region<-as.character(car$Cert.Region)
car$Stnd<-as.character(car$Stnd)
car$Stnd.Descrption<-as.character(car$Stnd.Description)
car$Underhood.ID <-as.character(car$Underhood.ID )
car$Cyl=as.factor(car$Cyl)
str(car)## 'data.frame': 1190 obs. of 21 variables:
## $ Japanese : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 2 2 2 2 2 ...
## $ Make : chr "ACURA" "ACURA" "ACURA" "ACURA" ...
## $ Model : chr "ACURA ILX" "ACURA ILX" "ACURA MDX" "ACURA MDX" ...
## $ Displ : num 2.4 2.4 3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5 ...
## $ Cyl : Factor w/ 2 levels "4","6": 1 1 2 2 2 2 2 2 2 2 ...
## $ Trans : chr "AMS-8" "AMS-8" "SemiAuto-9" "SemiAuto-9" ...
## $ Drive : chr "2WD" "2WD" "2WD" "2WD" ...
## $ Fuel : chr "Gasoline" "Gasoline" "Gasoline" "Gasoline" ...
## $ Cert.Region : chr "CA" "FA" "CA" "CA" ...
## $ Stnd : chr "L3ULEV125" "T3B125" "L3ULEV125" "L3ULEV125" ...
## $ Stnd.Description : Factor w/ 18 levels "California LEV-II LEV",..: 9 13 9 9 13 13 9 9 13 13 ...
## $ Underhood.ID : chr "HHNXV02.4SH3" "HHNXV02.4SH3" "HHNXV03.5VH3" "HHNXV03.5VH3" ...
## $ Veh.Class : Factor w/ 5 levels "large car","midsize car",..: 3 3 4 4 4 4 4 4 4 4 ...
## $ Air.Pollution.Score : int 6 6 6 6 6 6 6 6 6 6 ...
## $ City.MPG : int 25 25 19 20 19 20 18 19 18 19 ...
## $ Hwy.MPG : int 35 35 27 27 27 27 26 26 26 26 ...
## $ Cmb.MPG : int 29 29 22 23 22 23 21 22 21 22 ...
## $ Greenhouse.Gas.Score: int 7 7 5 5 5 5 4 5 4 5 ...
## $ SmartWay : Factor w/ 2 levels "No","Yes": 2 2 1 1 1 1 1 1 1 1 ...
## $ Comb.CO2 : int 309 309 404 391 404 391 424 404 424 404 ...
## $ Stnd.Descrption : chr "California LEV-III ULEV125" "Federal Tier 3 Bin 125" "California LEV-III ULEV125" "California LEV-III ULEV125" ...Continuous variables (if any)
In this dataset, the controllable variables cannot be considered as continuous variables. A continuous variable is the variable that has infinite numbers of possible values. [1] The factors chosen in our model such as ‘Cyl’, ‘Japanese’, ‘SmartWay’, and ‘Veh.Class’ are not numeric variables, and they have a discrete values, so they cannot be considered as continuous variables. The response variable-‘Comb.CO2’, is kind of tricky. The response variable may be rounded to single digit. Even though the variables are integers, we tend to think that this variable should be continuous variables, because the emission of CO2 can be infinite numbers of possible values.
Response variables
In this analysis, we consider only one response variable, ‘Comb.CO2’, which denotes the average emission volume of CO2 in each model. If the ‘Comb.CO2’ is large, the car is not comparatively environment-friendly.
The Data: How is it organized and what does it look like?
This dataset contains the preliminary fuel economy values for 2017 model year vehicles from the Environmental Protection Agency’s National Vehicle and Fuel Emissions Laboratory in Ann Arbor, Michigan. The fuel economy data and fuel costs are updated weekly. 19 values are stored in the original table, and they are ‘Japanese’, ‘Make’, ‘Displ’, ‘Cyl’, ‘Trans’, ‘Drive’, ‘Fuel’, ‘Cert Region’, ‘Stnd’, ‘Stnd Discription’, ‘Veh Class’, ‘Air Pollution Score’, ‘City MPG’, ‘Hwy MPG’, ‘Cmb MPG’, ‘Greenhouse Gas Score’, ‘SmartWay’, and ‘Comb CO2’. In our analysis, we take ‘Japanese’, ‘Veh Class’, ‘Cyl’, and ‘SmartWay’ as our main factors, and ‘Comb CO2’ as the response factor.
2. (Experimental) Design
How will the experiment be organized and conducted to test the hypothesis?
In this experimental design, we would like to test whether the variation of our response factor can be explained by the four factors and the interaction term. So the null hypothesis in our experiment is that ‘Cyl’, ‘Japanese’, ‘SmartWay’, ‘Veh.Class’ and the interaction term do not have significant effects on ‘Comb CO2’ (i.e. the means between different levels are equal). In order to test the hypothesis, we perform an analysis of variance (ANOVA) to see if there is any difference in the means for ‘Comb CO2’ among the levels.
What is the rationale for this design?
The rationale for this study is that we are trying to see if the ‘Cyl’, ‘Japanese’, ‘SmartWay’, ‘Veh.Class’ and the interaction term have effects on the ejection of CO2. Because we believe the factor ‘Cyl’, ‘Japanese’, ‘SmartWay’ and ‘Veh.Class’ have effects on the emission of CO2 based on Best Guess. In this design, a four factor- multi level experiment is introduced to test whether the effects of different factors may affect the CO2 emission.
Randomize: What is the Randomization Scheme?
“Randomization is the use of a known, understood probabilistic mechanism for the assignment of treatments to units.”[2]
In order to reduce the nuisance effect, (1) subjects can be picked randomly, (2)subjects can be randomly assigned to each treatments, and (3) oreders of each units can also be randomized. Since fuel economy data are the result of vehicle testing, the cars in each model should be randomly picked under a known probabilistic mechanism to generate the data in our dataset. In our study we do not include the randomization scheme because we are analyzing the dataset.
Replicate: Are there replicates and/or repeated measures?
“Replication means an independent repeat run of each factor combination.Replication reflects sources of variability both between runs and (potentially) within runs”[3]
In this experiment, we analyze the data observed with different car model, so we do not have any replicates or repeated measures present.
Block: Did you use blocking in the design?
“Blocking is a design technique used to improve the precision with which comparisons among the factors of interest are made.Generally, a block is a set of relatively homogeneous experimental conditions.”[4]
In our analysis, blocking is not involved in our design, because in this data, we do not find a controllable nuisance factor that affect our results.
3. (Statistical) Analysis
(Exploratory Data Analysis) Graphics and descriptive summary
In this section, we list the summary of our dataset. Meanwhile, we also show the boxplot and interaction plot to reflect the mean effects and the interaction effects of four factors.
#Create a boxplot of'Comb.CO2'by 'Japanese'.
boxplot(car$Comb.CO2~car$Japanese, xlab="Japanese Car", ylab="Comb.CO2")
# Calculate the mean of 'Comb.CO2' by 'Japanese'.
tapply(car$Comb.CO2,car$Make,mean)## ACURA AUDI BMW BUCK CADILLAC
## 374.0769 371.4000 369.6912 379.4375 403.5455
## CHEVROLET CHRYSLER DODGE FIAT FORD
## 327.9444 365.0000 437.4000 301.7500 397.9180
## GENESIS GMC HONDA HYUNDAI INFINITI
## 443.0000 426.3636 325.4211 335.5181 393.3125
## JAGUAR JEEP KIA LAND ROVER LEXUS
## 393.6000 384.8269 353.8986 389.6667 315.5000
## LINCOLN LOTUS MASERATI MAZDA MERCEDES-BENZ
## 437.6667 459.5000 474.6000 289.2857 383.5652
## MINI MITSUBISHI NISSAN PORSCHE SUBARU
## 318.9444 320.0000 386.5833 392.0725 356.0625
## TOYOTA VOLVO VW
## 290.6531 348.6875 353.1500#Create a boxplot of'Comb.CO2'by 'SmartWay').
boxplot(car$Comb.CO2~car$SmartWay, xlab="Smartway", ylab="Comb.CO2")
# Calculate the mean of 'Comb.CO2' by 'SmartWay'.
tapply(car$Comb.CO2,car$SmartWay,mean)## No Yes
## 388.0953 268.6262#Create a boxplot of'Comb.CO2'by vehacle 'Veh.Class'.
boxplot(car$Comb.CO2~car$Veh.Class, xlab="Vehicle Class", ylab="Comb.CO2")
# Calculate the mean of 'Comb.CO2' by 'Veh.Class'.
tapply(car$Comb.CO2,car$Veh.Class,mean)## large car midsize car small car small SUV standard SUV
## 388.5114 326.3224 352.6529 387.6441 445.2200#Create a boxplot of'Comb.CO2'by 'Cyl'.
boxplot(car$Comb.CO2~car$Cyl, xlab="Clynder", ylab="Comb.CO2")
# Calculate the mean of 'Comb.CO2' by 'Cyl'.
tapply(car$Comb.CO2,car$Cyl,mean)## 4 6
## 331.5638 418.9979From the boxplot and the list of means above, we can intuitively deduce that Japanese cars are comparatively eject less CO2 , and the cars which install the SmartWay system are more likely be environmental-friendly. Surprisingly, we find that midsized cars comparatively have lowest emission level of CO2, and small cars are not in the lowest level. Finally, cars with 6 cylinders emit more CO2 than with 4 cylinder.
interaction.plot(car$Japanese, car$SmartWay, car$Comb.CO2)
interaction.plot(car$Japanese, car$Veh.Class, car$Comb.CO2)
interaction.plot(car$Japanese, car$Cyl, car$Comb.CO2)
interaction.plot(car$SmartWay, car$Veh.Class, car$Comb.CO2)
interaction.plot(car$SmartWay, car$Cyl, car$Comb.CO2)
interaction.plot(car$Cyl, car$Veh.Class, car$Comb.CO2)
From the interaction analysis above, we found that factor ‘SmartWay’ and ‘Japanese’ have substitution effects. The reason behind this may be that the Japanese cars themselves eject less CO2 than non-Japanese cars, so the SmartWay system has less effect on these cars. For other interaction plots, the two-way interactions seem to be in the same direction.
Testing
In this section, in order to test whether the variation of ‘Comb.CO2’ can be explained by the treatments we take into consideration. We use the analysis of variance (ANOVA) to test if factors ‘Japanese’, ‘Veh Class’, ‘Cyl’, ‘SmartWay’, and interaction term can explain the variation of ‘Comb.CO2’. In this study, the null hypothesis is tested. If we reject the null hypothesis, we are intended to believe that the mean differences in ‘Com.Co2’ for each ‘Japanese’, ‘Veh.Class’, ‘Cyl’, and ‘SmartWay’ are not caused by randomization, and the mean differences can be explained by these different factor levels. If we cannot reject the null hypothesis, we tend to believe it may be caused by randomization.
anova1= aov(car$Comb.CO2~car$Japanese)
summary(anova1)## Df Sum Sq Mean Sq F value Pr(>F)
## car$Japanese 1 159423 159423 36.48 2.06e-09 ***
## Residuals 1188 5192344 4371
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova2= aov(car$Comb.CO2~car$Cyl)
summary(anova2)## Df Sum Sq Mean Sq F value Pr(>F)
## car$Cyl 1 2184855 2184855 819.6 <2e-16 ***
## Residuals 1188 3166912 2666
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova3= aov(car$Comb.CO2~car$Veh.Class)
summary(anova3)## Df Sum Sq Mean Sq F value Pr(>F)
## car$Veh.Class 4 1230594 307648 88.46 <2e-16 ***
## Residuals 1185 4121173 3478
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova4= aov(car$Comb.CO2~car$SmartWay)
summary(anova4)## Df Sum Sq Mean Sq F value Pr(>F)
## car$SmartWay 1 2505117 2505117 1045 <2e-16 ***
## Residuals 1188 2846650 2396
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova5= aov(car$Comb.CO2~car$Japanese*car$Cyl)
summary(anova5)## Df Sum Sq Mean Sq F value Pr(>F)
## car$Japanese 1 159423 159423 62.473 6.14e-15 ***
## car$Cyl 1 2165596 2165596 848.625 < 2e-16 ***
## car$Japanese:car$Cyl 1 209 209 0.082 0.775
## Residuals 1186 3026538 2552
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova6= aov(car$Comb.CO2~car$Japanese*car$Veh.Class)
summary(anova6)## Df Sum Sq Mean Sq F value Pr(>F)
## car$Japanese 1 159423 159423 46.473 1.48e-11 ***
## car$Veh.Class 4 1101109 275277 80.245 < 2e-16 ***
## car$Japanese:car$Veh.Class 3 39849 13283 3.872 0.00904 **
## Residuals 1181 4051386 3430
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova7= aov(car$Comb.CO2~car$Japanese*car$SmartWay)
summary(anova7)## Df Sum Sq Mean Sq F value Pr(>F)
## car$Japanese 1 159423 159423 66.830 7.54e-16 ***
## car$SmartWay 1 2349589 2349589 984.950 < 2e-16 ***
## car$Japanese:car$SmartWay 1 13564 13564 5.686 0.0173 *
## Residuals 1186 2829191 2385
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova8= aov(car$Comb.CO2~car$Cyl*car$Veh.Class)
summary(anova8)## Df Sum Sq Mean Sq F value Pr(>F)
## car$Cyl 1 2184855 2184855 1079.654 < 2e-16 ***
## car$Veh.Class 4 731173 182793 90.328 < 2e-16 ***
## car$Cyl:car$Veh.Class 4 47817 11954 5.907 0.000105 ***
## Residuals 1180 2387922 2024
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova9= aov(car$Comb.CO2~car$Cyl*car$SmartWay)
summary(anova9)## Df Sum Sq Mean Sq F value Pr(>F)
## car$Cyl 1 2184855 2184855 1379.720 < 2e-16 ***
## car$SmartWay 1 1277761 1277761 806.897 < 2e-16 ***
## car$Cyl:car$SmartWay 1 11062 11062 6.985 0.00833 **
## Residuals 1186 1878090 1584
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova10= aov(car$Comb.CO2~car$Veh.Class*car$SmartWay)
summary(anova10)## Df Sum Sq Mean Sq F value Pr(>F)
## car$Veh.Class 4 1230594 307648 165.454 < 2e-16 ***
## car$SmartWay 1 1855117 1855117 997.683 < 2e-16 ***
## car$Veh.Class:car$SmartWay 4 71936 17984 9.672 1.07e-07 ***
## Residuals 1180 2194120 1859
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1According to the results of the analyses of varianceabove, We can reject the null hypothesis that the main factor ‘Japanese’, ‘Cyl’, ‘SmartWay’ and ‘Veh.Class’ have no effect on the ejection of CO2, with each p-value < 0.001. For the interactions,‘Japanese x Veh.Class’(p-value<0.01),‘Japanese x SmartWay’(p-value<0.05), ‘Cyl x Veh.Class’(p-value<0.001),‘Cyl x SmartWay’(p-value<0.01) and ‘Veh.Class x Smartway’(p-value<0.001) are statistically significant. The interaction factor ‘Japanese x Cyl’(p-value = 0.775) are not statistically significant.
Estimation
Diagnostics / Model Adequacy Checking
4. References to the literature
[1]. Definition of continuous variable. http://www.statisticshowto.com/continuous-variable/
[2]. Gary W. Oehlert. A First Course in Design and Analysis of Experiments (p.6).
[3]. Montgomery, Douglas C.. Design and Analysis of Experiments, 8th Edition (p.13). Wiley. Kindle Edition.
[4]. Montgomery, Douglas C.. Design and Analysis of Experiments, 8th Edition (p.13). Wiley. Kindle Edition.
5. Appendices
A summary of, or pointer to, the raw data
http://www.fueleconomy.gov/feg/EPAGreenGuide/pdf/all_alpha_17.pdf