data(Cars93,package="MASS")
View(Cars93)
str(Cars93)## 'data.frame': 93 obs. of 27 variables:
## $ Manufacturer : Factor w/ 32 levels "Acura","Audi",..: 1 1 2 2 3 4 4 4 4 5 ...
## $ Model : Factor w/ 93 levels "100","190E","240",..: 49 56 9 1 6 24 54 74 73 35 ...
## $ Type : Factor w/ 6 levels "Compact","Large",..: 4 3 1 3 3 3 2 2 3 2 ...
## $ Min.Price : num 12.9 29.2 25.9 30.8 23.7 14.2 19.9 22.6 26.3 33 ...
## $ Price : num 15.9 33.9 29.1 37.7 30 15.7 20.8 23.7 26.3 34.7 ...
## $ Max.Price : num 18.8 38.7 32.3 44.6 36.2 17.3 21.7 24.9 26.3 36.3 ...
## $ MPG.city : int 25 18 20 19 22 22 19 16 19 16 ...
## $ MPG.highway : int 31 25 26 26 30 31 28 25 27 25 ...
## $ AirBags : Factor w/ 3 levels "Driver & Passenger",..: 3 1 2 1 2 2 2 2 2 2 ...
## $ DriveTrain : Factor w/ 3 levels "4WD","Front",..: 2 2 2 2 3 2 2 3 2 2 ...
## $ Cylinders : Factor w/ 6 levels "3","4","5","6",..: 2 4 4 4 2 2 4 4 4 5 ...
## $ EngineSize : num 1.8 3.2 2.8 2.8 3.5 2.2 3.8 5.7 3.8 4.9 ...
## $ Horsepower : int 140 200 172 172 208 110 170 180 170 200 ...
## $ RPM : int 6300 5500 5500 5500 5700 5200 4800 4000 4800 4100 ...
## $ Rev.per.mile : int 2890 2335 2280 2535 2545 2565 1570 1320 1690 1510 ...
## $ Man.trans.avail : Factor w/ 2 levels "No","Yes": 2 2 2 2 2 1 1 1 1 1 ...
## $ Fuel.tank.capacity: num 13.2 18 16.9 21.1 21.1 16.4 18 23 18.8 18 ...
## $ Passengers : int 5 5 5 6 4 6 6 6 5 6 ...
## $ Length : int 177 195 180 193 186 189 200 216 198 206 ...
## $ Wheelbase : int 102 115 102 106 109 105 111 116 108 114 ...
## $ Width : int 68 71 67 70 69 69 74 78 73 73 ...
## $ Turn.circle : int 37 38 37 37 39 41 42 45 41 43 ...
## $ Rear.seat.room : num 26.5 30 28 31 27 28 30.5 30.5 26.5 35 ...
## $ Luggage.room : int 11 15 14 17 13 16 17 21 14 18 ...
## $ Weight : int 2705 3560 3375 3405 3640 2880 3470 4105 3495 3620 ...
## $ Origin : Factor w/ 2 levels "USA","non-USA": 2 2 2 2 2 1 1 1 1 1 ...
## $ Make : Factor w/ 93 levels "Acura Integra",..: 1 2 4 3 5 6 7 9 8 10 ...x<-data.frame(Cars93$Horsepower,Cars93$Wheelbase) #creates Data frame
cor(x)## Cars93.Horsepower Cars93.Wheelbase
## Cars93.Horsepower 1.0000000 0.4868542
## Cars93.Wheelbase 0.4868542 1.0000000plot(x)
Regression Analysis on Cars93 dataset
names(Cars93)## [1] "Manufacturer" "Model" "Type"
## [4] "Min.Price" "Price" "Max.Price"
## [7] "MPG.city" "MPG.highway" "AirBags"
## [10] "DriveTrain" "Cylinders" "EngineSize"
## [13] "Horsepower" "RPM" "Rev.per.mile"
## [16] "Man.trans.avail" "Fuel.tank.capacity" "Passengers"
## [19] "Length" "Wheelbase" "Width"
## [22] "Turn.circle" "Rear.seat.room" "Luggage.room"
## [25] "Weight" "Origin" "Make"fit<-lm(Price~.,data=Cars93)
fit##
## Call:
## lm(formula = Price ~ ., data = Cars93)
##
## Coefficients:
## (Intercept) ManufacturerAudi
## 33.9 3.8
## ManufacturerBMW ManufacturerBuick
## -3.9 -10.2
## ManufacturerCadillac ManufacturerChevrolet
## 6.2 -18.0
## ManufacturerChrylser ManufacturerChrysler
## -15.5 -18.1
## ManufacturerDodge ManufacturerEagle
## -8.1 -14.6
## ManufacturerFord ManufacturerGeo
## -22.6 -21.4
## ManufacturerHonda ManufacturerHyundai
## -14.1 -20.0
## ManufacturerInfiniti ManufacturerLexus
## 14.0 1.3
## ManufacturerLincoln ManufacturerMazda
## 2.2 -22.3
## ManufacturerMercedes-Benz ManufacturerMercury
## 28.0 -19.0
## ManufacturerMitsubishi ManufacturerNissan
## -23.6 -22.1
## ManufacturerOldsmobile ManufacturerPlymouth
## -13.2 -19.5
## ManufacturerPontiac ManufacturerSaab
## -22.8 -5.2
## ManufacturerSaturn ManufacturerSubaru
## -22.8 -23.0
## ManufacturerSuzuki ManufacturerToyota
## -25.3 -24.1
## ManufacturerVolkswagen ManufacturerVolvo
## -13.9 -7.2
## Model190E Model240
## -30.0 -4.0
## Model300E Model323
## NA -3.3
## Model535i Model626
## NA 4.9
## Model850 Model90
## NA -8.6
## Model900 ModelAccord
## NA -2.3
## ModelAchieva ModelAltima
## -7.2 3.9
## ModelBonneville ModelCamaro
## 13.3 -0.8
## ModelCamry ModelCapri
## 8.4 -0.8
## ModelCaprice ModelCavalier
## 2.9 -2.5
## ModelCelica ModelCentury
## 8.6 -8.0
## ModelCivic ModelColt
## -7.7 -16.6
## ModelConcorde ModelContinental
## NA -1.8
## ModelCorrado ModelCorsica
## 3.3 -4.5
## ModelCougar ModelCrown_Victoria
## NA 9.6
## ModelCutlass_Ciera ModelDeVille
## -4.4 -5.4
## ModelDiamante ModelDynasty
## 15.8 -10.2
## ModelES300 ModelEighty-Eight
## -7.2 NA
## ModelElantra ModelEscort
## -3.9 -1.2
## ModelExcel ModelFestiva
## -5.9 -3.9
## ModelFirebird ModelFox
## 6.6 -10.9
## ModelGrand_Prix ModelImperial
## 7.4 13.7
## ModelIntegra ModelJusty
## -18.0 -2.5
## ModelLaser ModelLeBaron
## NA NA
## ModelLeMans ModelLeSabre
## -2.1 -2.9
## ModelLegacy ModelLegend
## 8.6 NA
## ModelLoyale ModelLumina
## NA NA
## ModelMaxima ModelMetro
## 9.7 -4.1
## ModelMirage ModelMustang
## NA 4.6
## ModelPassat ModelPrelude
## NA NA
## ModelProbe ModelProtege
## 2.7 NA
## ModelQ45 ModelRiviera
## NA 2.6
## ModelRoadmaster ModelSC300
## NA NA
## ModelSL ModelScoupe
## NA -3.9
## ModelSentra ModelSeville
## NA NA
## ModelShadow ModelSonata
## -14.5 NA
## ModelSpirit ModelStealth
## -12.5 NA
## ModelStorm ModelSummit
## NA -7.1
## ModelSunbird ModelSwift
## NA NA
## ModelTaurus ModelTempo
## 8.9 NA
## ModelTercel ModelTown_Car
## NA NA
## ModelVision TypeLarge
## NA NA
## TypeMidsize TypeSmall
## NA NA
## TypeSporty Min.Price
## NA NA
## Max.Price MPG.city
## NA NA
## MPG.highway AirBagsDriver only
## NA NA
## AirBagsNone DriveTrainFront
## NA NA
## DriveTrainRear Cylinders4
## NA NA
## Cylinders5 Cylinders6
## NA NA
## Cylinders8 EngineSize
## NA NA
## Horsepower RPM
## NA NA
## Rev.per.mile Man.trans.availYes
## NA NA
## Fuel.tank.capacity Passengers
## NA NA
## Length Wheelbase
## NA NA
## Width Turn.circle
## NA NA
## Rear.seat.room Luggage.room
## NA NA
## Weight Originnon-USA
## NA NA
## MakeAcura Legend MakeAudi 100
## NA NA
## MakeAudi 90 MakeBMW 535i
## NA NA
## MakeBuick Century MakeBuick LeSabre
## NA NA
## MakeBuick Riviera MakeBuick Roadmaster
## NA NA
## MakeCadillac DeVille MakeCadillac Seville
## NA NA
## MakeChevrolet Camaro MakeChevrolet Caprice
## NA NA
## MakeChevrolet Cavalier MakeChevrolet Corsica
## NA NA
## MakeChevrolet Lumina MakeChrylser Concorde
## NA NA
## MakeChrysler Imperial MakeChrysler LeBaron
## NA NA
## MakeDodge Colt MakeDodge Dynasty
## NA NA
## MakeDodge Shadow MakeDodge Spirit
## NA NA
## MakeDodge Stealth MakeEagle Summit
## NA NA
## MakeEagle Vision MakeFord Crown_Victoria
## NA NA
## MakeFord Escort MakeFord Festiva
## NA NA
## MakeFord Mustang MakeFord Probe
## NA NA
## MakeFord Taurus MakeFord Tempo
## NA NA
## MakeGeo Metro MakeGeo Storm
## NA NA
## MakeHonda Accord MakeHonda Civic
## NA NA
## MakeHonda Prelude MakeHyundai Elantra
## NA NA
## MakeHyundai Excel MakeHyundai Scoupe
## NA NA
## MakeHyundai Sonata MakeInfiniti Q45
## NA NA
## MakeLexus ES300 MakeLexus SC300
## NA NA
## MakeLincoln Continental MakeLincoln Town_Car
## NA NA
## MakeMazda 323 MakeMazda 626
## NA NA
## MakeMazda Protege MakeMercedes-Benz 190E
## NA NA
## MakeMercedes-Benz 300E MakeMercury Capri
## NA NA
## MakeMercury Cougar MakeMitsubishi Diamante
## NA NA
## MakeMitsubishi Mirage MakeNissan Altima
## NA NA
## MakeNissan Maxima MakeNissan Sentra
## NA NA
## MakeOldsmobile Achieva MakeOldsmobile Cutlass_Ciera
## NA NA
## MakeOldsmobile Eighty-Eight MakePlymouth Laser
## NA NA
## MakePontiac Bonneville MakePontiac Firebird
## NA NA
## MakePontiac Grand_Prix MakePontiac LeMans
## NA NA
## MakePontiac Sunbird MakeSaab 900
## NA NA
## MakeSaturn SL MakeSubaru Justy
## NA NA
## MakeSubaru Legacy MakeSubaru Loyale
## NA NA
## MakeSuzuki Swift MakeToyota Camry
## NA NA
## MakeToyota Celica MakeToyota Tercel
## NA NA
## MakeVolkswagen Corrado MakeVolkswagen Fox
## NA NA
## MakeVolkswagen Passat MakeVolvo 240
## NA NA
## MakeVolvo 850
## NAsummary(fit)##
## Call:
## lm(formula = Price ~ ., data = Cars93)
##
## Residuals:
## ALL 82 residuals are 0: no residual degrees of freedom!
##
## Coefficients: (143 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.9 NA NA NA
## ManufacturerAudi 3.8 NA NA NA
## ManufacturerBMW -3.9 NA NA NA
## ManufacturerBuick -10.2 NA NA NA
## ManufacturerCadillac 6.2 NA NA NA
## ManufacturerChevrolet -18.0 NA NA NA
## ManufacturerChrylser -15.5 NA NA NA
## ManufacturerChrysler -18.1 NA NA NA
## ManufacturerDodge -8.1 NA NA NA
## ManufacturerEagle -14.6 NA NA NA
## ManufacturerFord -22.6 NA NA NA
## ManufacturerGeo -21.4 NA NA NA
## ManufacturerHonda -14.1 NA NA NA
## ManufacturerHyundai -20.0 NA NA NA
## ManufacturerInfiniti 14.0 NA NA NA
## ManufacturerLexus 1.3 NA NA NA
## ManufacturerLincoln 2.2 NA NA NA
## ManufacturerMazda -22.3 NA NA NA
## ManufacturerMercedes-Benz 28.0 NA NA NA
## ManufacturerMercury -19.0 NA NA NA
## ManufacturerMitsubishi -23.6 NA NA NA
## ManufacturerNissan -22.1 NA NA NA
## ManufacturerOldsmobile -13.2 NA NA NA
## ManufacturerPlymouth -19.5 NA NA NA
## ManufacturerPontiac -22.8 NA NA NA
## ManufacturerSaab -5.2 NA NA NA
## ManufacturerSaturn -22.8 NA NA NA
## ManufacturerSubaru -23.0 NA NA NA
## ManufacturerSuzuki -25.3 NA NA NA
## ManufacturerToyota -24.1 NA NA NA
## ManufacturerVolkswagen -13.9 NA NA NA
## ManufacturerVolvo -7.2 NA NA NA
## Model190E -30.0 NA NA NA
## Model240 -4.0 NA NA NA
## Model300E NA NA NA NA
## Model323 -3.3 NA NA NA
## Model535i NA NA NA NA
## Model626 4.9 NA NA NA
## Model850 NA NA NA NA
## Model90 -8.6 NA NA NA
## Model900 NA NA NA NA
## ModelAccord -2.3 NA NA NA
## ModelAchieva -7.2 NA NA NA
## ModelAltima 3.9 NA NA NA
## ModelBonneville 13.3 NA NA NA
## ModelCamaro -0.8 NA NA NA
## ModelCamry 8.4 NA NA NA
## ModelCapri -0.8 NA NA NA
## ModelCaprice 2.9 NA NA NA
## ModelCavalier -2.5 NA NA NA
## ModelCelica 8.6 NA NA NA
## ModelCentury -8.0 NA NA NA
## ModelCivic -7.7 NA NA NA
## ModelColt -16.6 NA NA NA
## ModelConcorde NA NA NA NA
## ModelContinental -1.8 NA NA NA
## ModelCorrado 3.3 NA NA NA
## ModelCorsica -4.5 NA NA NA
## ModelCougar NA NA NA NA
## ModelCrown_Victoria 9.6 NA NA NA
## ModelCutlass_Ciera -4.4 NA NA NA
## ModelDeVille -5.4 NA NA NA
## ModelDiamante 15.8 NA NA NA
## ModelDynasty -10.2 NA NA NA
## ModelES300 -7.2 NA NA NA
## ModelEighty-Eight NA NA NA NA
## ModelElantra -3.9 NA NA NA
## ModelEscort -1.2 NA NA NA
## ModelExcel -5.9 NA NA NA
## ModelFestiva -3.9 NA NA NA
## ModelFirebird 6.6 NA NA NA
## ModelFox -10.9 NA NA NA
## ModelGrand_Prix 7.4 NA NA NA
## ModelImperial 13.7 NA NA NA
## ModelIntegra -18.0 NA NA NA
## ModelJusty -2.5 NA NA NA
## ModelLaser NA NA NA NA
## ModelLeBaron NA NA NA NA
## ModelLeMans -2.1 NA NA NA
## ModelLeSabre -2.9 NA NA NA
## ModelLegacy 8.6 NA NA NA
## ModelLegend NA NA NA NA
## ModelLoyale NA NA NA NA
## ModelLumina NA NA NA NA
## ModelMaxima 9.7 NA NA NA
## ModelMetro -4.1 NA NA NA
## ModelMirage NA NA NA NA
## ModelMustang 4.6 NA NA NA
## ModelPassat NA NA NA NA
## ModelPrelude NA NA NA NA
## ModelProbe 2.7 NA NA NA
## ModelProtege NA NA NA NA
## ModelQ45 NA NA NA NA
## ModelRiviera 2.6 NA NA NA
## ModelRoadmaster NA NA NA NA
## ModelSC300 NA NA NA NA
## ModelSL NA NA NA NA
## ModelScoupe -3.9 NA NA NA
## ModelSentra NA NA NA NA
## ModelSeville NA NA NA NA
## ModelShadow -14.5 NA NA NA
## ModelSonata NA NA NA NA
## ModelSpirit -12.5 NA NA NA
## ModelStealth NA NA NA NA
## ModelStorm NA NA NA NA
## ModelSummit -7.1 NA NA NA
## ModelSunbird NA NA NA NA
## ModelSwift NA NA NA NA
## ModelTaurus 8.9 NA NA NA
## ModelTempo NA NA NA NA
## ModelTercel NA NA NA NA
## ModelTown_Car NA NA NA NA
## ModelVision NA NA NA NA
## TypeLarge NA NA NA NA
## TypeMidsize NA NA NA NA
## TypeSmall NA NA NA NA
## TypeSporty NA NA NA NA
## Min.Price NA NA NA NA
## Max.Price NA NA NA NA
## MPG.city NA NA NA NA
## MPG.highway NA NA NA NA
## AirBagsDriver only NA NA NA NA
## AirBagsNone NA NA NA NA
## DriveTrainFront NA NA NA NA
## DriveTrainRear NA NA NA NA
## Cylinders4 NA NA NA NA
## Cylinders5 NA NA NA NA
## Cylinders6 NA NA NA NA
## Cylinders8 NA NA NA NA
## EngineSize NA NA NA NA
## Horsepower NA NA NA NA
## RPM NA NA NA NA
## Rev.per.mile NA NA NA NA
## Man.trans.availYes NA NA NA NA
## Fuel.tank.capacity NA NA NA NA
## Passengers NA NA NA NA
## Length NA NA NA NA
## Wheelbase NA NA NA NA
## Width NA NA NA NA
## Turn.circle NA NA NA NA
## Rear.seat.room NA NA NA NA
## Luggage.room NA NA NA NA
## Weight NA NA NA NA
## Originnon-USA NA NA NA NA
## MakeAcura Legend NA NA NA NA
## MakeAudi 100 NA NA NA NA
## MakeAudi 90 NA NA NA NA
## MakeBMW 535i NA NA NA NA
## MakeBuick Century NA NA NA NA
## MakeBuick LeSabre NA NA NA NA
## MakeBuick Riviera NA NA NA NA
## MakeBuick Roadmaster NA NA NA NA
## MakeCadillac DeVille NA NA NA NA
## MakeCadillac Seville NA NA NA NA
## MakeChevrolet Camaro NA NA NA NA
## MakeChevrolet Caprice NA NA NA NA
## MakeChevrolet Cavalier NA NA NA NA
## MakeChevrolet Corsica NA NA NA NA
## MakeChevrolet Lumina NA NA NA NA
## MakeChrylser Concorde NA NA NA NA
## MakeChrysler Imperial NA NA NA NA
## MakeChrysler LeBaron NA NA NA NA
## MakeDodge Colt NA NA NA NA
## MakeDodge Dynasty NA NA NA NA
## MakeDodge Shadow NA NA NA NA
## MakeDodge Spirit NA NA NA NA
## MakeDodge Stealth NA NA NA NA
## MakeEagle Summit NA NA NA NA
## MakeEagle Vision NA NA NA NA
## MakeFord Crown_Victoria NA NA NA NA
## MakeFord Escort NA NA NA NA
## MakeFord Festiva NA NA NA NA
## MakeFord Mustang NA NA NA NA
## MakeFord Probe NA NA NA NA
## MakeFord Taurus NA NA NA NA
## MakeFord Tempo NA NA NA NA
## MakeGeo Metro NA NA NA NA
## MakeGeo Storm NA NA NA NA
## MakeHonda Accord NA NA NA NA
## MakeHonda Civic NA NA NA NA
## MakeHonda Prelude NA NA NA NA
## MakeHyundai Elantra NA NA NA NA
## MakeHyundai Excel NA NA NA NA
## MakeHyundai Scoupe NA NA NA NA
## MakeHyundai Sonata NA NA NA NA
## MakeInfiniti Q45 NA NA NA NA
## MakeLexus ES300 NA NA NA NA
## MakeLexus SC300 NA NA NA NA
## MakeLincoln Continental NA NA NA NA
## MakeLincoln Town_Car NA NA NA NA
## MakeMazda 323 NA NA NA NA
## MakeMazda 626 NA NA NA NA
## MakeMazda Protege NA NA NA NA
## MakeMercedes-Benz 190E NA NA NA NA
## MakeMercedes-Benz 300E NA NA NA NA
## MakeMercury Capri NA NA NA NA
## MakeMercury Cougar NA NA NA NA
## MakeMitsubishi Diamante NA NA NA NA
## MakeMitsubishi Mirage NA NA NA NA
## MakeNissan Altima NA NA NA NA
## MakeNissan Maxima NA NA NA NA
## MakeNissan Sentra NA NA NA NA
## MakeOldsmobile Achieva NA NA NA NA
## MakeOldsmobile Cutlass_Ciera NA NA NA NA
## MakeOldsmobile Eighty-Eight NA NA NA NA
## MakePlymouth Laser NA NA NA NA
## MakePontiac Bonneville NA NA NA NA
## MakePontiac Firebird NA NA NA NA
## MakePontiac Grand_Prix NA NA NA NA
## MakePontiac LeMans NA NA NA NA
## MakePontiac Sunbird NA NA NA NA
## MakeSaab 900 NA NA NA NA
## MakeSaturn SL NA NA NA NA
## MakeSubaru Justy NA NA NA NA
## MakeSubaru Legacy NA NA NA NA
## MakeSubaru Loyale NA NA NA NA
## MakeSuzuki Swift NA NA NA NA
## MakeToyota Camry NA NA NA NA
## MakeToyota Celica NA NA NA NA
## MakeToyota Tercel NA NA NA NA
## MakeVolkswagen Corrado NA NA NA NA
## MakeVolkswagen Fox NA NA NA NA
## MakeVolkswagen Passat NA NA NA NA
## MakeVolvo 240 NA NA NA NA
## MakeVolvo 850 NA NA NA NA
##
## Residual standard error: NaN on 0 degrees of freedom
## (11 observations deleted due to missingness)
## Multiple R-squared: 1, Adjusted R-squared: NaN
## F-statistic: NaN on 81 and 0 DF, p-value: NARegression on numeric data
names(Cars93)## [1] "Manufacturer" "Model" "Type"
## [4] "Min.Price" "Price" "Max.Price"
## [7] "MPG.city" "MPG.highway" "AirBags"
## [10] "DriveTrain" "Cylinders" "EngineSize"
## [13] "Horsepower" "RPM" "Rev.per.mile"
## [16] "Man.trans.avail" "Fuel.tank.capacity" "Passengers"
## [19] "Length" "Wheelbase" "Width"
## [22] "Turn.circle" "Rear.seat.room" "Luggage.room"
## [25] "Weight" "Origin" "Make"Cars_new = Cars93[,c(4,5,6,7,8,13,14)]
fit<-lm(Price~.,data=Cars_new)
fit##
## Call:
## lm(formula = Price ~ ., data = Cars_new)
##
## Coefficients:
## (Intercept) Min.Price Max.Price MPG.city MPG.highway
## -2.424e-02 5.010e-01 4.999e-01 -1.366e-04 8.368e-04
## Horsepower RPM
## -9.402e-05 -1.293e-07summary(fit)##
## Call:
## lm(formula = Price ~ ., data = Cars_new)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.059180 -0.004209 0.002749 0.005789 0.056644
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -2.424e-02 3.521e-02 -0.689 0.493
## Min.Price 5.010e-01 9.555e-04 524.319 <2e-16 ***
## Max.Price 4.999e-01 6.702e-04 745.820 <2e-16 ***
## MPG.city -1.366e-04 1.891e-03 -0.072 0.943
## MPG.highway 8.368e-04 1.768e-03 0.473 0.637
## Horsepower -9.402e-05 1.127e-04 -0.834 0.407
## RPM -1.293e-07 6.132e-06 -0.021 0.983
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02942 on 86 degrees of freedom
## Multiple R-squared: 1, Adjusted R-squared: 1
## F-statistic: 1.653e+06 on 6 and 86 DF, p-value: < 2.2e-16step(fit) ###tells you the significant vars## Start: AIC=-649.16
## Price ~ Min.Price + Max.Price + MPG.city + MPG.highway + Horsepower +
## RPM
##
## Df Sum of Sq RSS AIC
## - RPM 1 0.00 0.07 -651.16
## - MPG.city 1 0.00 0.07 -651.15
## - MPG.highway 1 0.00 0.07 -650.92
## - Horsepower 1 0.00 0.08 -650.41
## <none> 0.07 -649.16
## - Min.Price 1 237.87 237.94 99.37
## - Max.Price 1 481.30 481.37 164.90
##
## Step: AIC=-651.16
## Price ~ Min.Price + Max.Price + MPG.city + MPG.highway + Horsepower
##
## Df Sum of Sq RSS AIC
## - MPG.city 1 0.00 0.07 -653.15
## - MPG.highway 1 0.00 0.07 -652.91
## - Horsepower 1 0.00 0.08 -652.30
## <none> 0.07 -651.16
## - Min.Price 1 240.37 240.45 98.34
## - Max.Price 1 486.96 487.03 163.98
##
## Step: AIC=-653.15
## Price ~ Min.Price + Max.Price + MPG.highway + Horsepower
##
## Df Sum of Sq RSS AIC
## - Horsepower 1 0.00 0.08 -654.29
## - MPG.highway 1 0.00 0.08 -654.18
## <none> 0.07 -653.15
## - Min.Price 1 245.00 245.07 98.11
## - Max.Price 1 494.54 494.62 163.42
##
## Step: AIC=-654.29
## Price ~ Min.Price + Max.Price + MPG.highway
##
## Df Sum of Sq RSS AIC
## - MPG.highway 1 0.00 0.08 -654.49
## <none> 0.08 -654.29
## - Min.Price 1 286.32 286.40 110.61
## - Max.Price 1 497.16 497.23 161.91
##
## Step: AIC=-654.49
## Price ~ Min.Price + Max.Price
##
## Df Sum of Sq RSS AIC
## <none> 0.08 -654.49
## - Min.Price 1 313.24 313.32 116.96
## - Max.Price 1 497.22 497.30 159.92##
## Call:
## lm(formula = Price ~ Min.Price + Max.Price, data = Cars_new)
##
## Coefficients:
## (Intercept) Min.Price Max.Price
## -0.005201 0.500354 0.499838cor(Cars_new)###show the correlations among the values in the variables## Min.Price Price Max.Price MPG.city MPG.highway
## Min.Price 1.00000000 0.970601402 0.90675608 -0.6228754 -0.5799658
## Price 0.97060140 1.000000000 0.98158027 -0.5945622 -0.5606804
## Max.Price 0.90675608 0.981580272 1.00000000 -0.5478109 -0.5225607
## MPG.city -0.62287544 -0.594562163 -0.54781090 1.0000000 0.9439358
## MPG.highway -0.57996581 -0.560680362 -0.52256074 0.9439358 1.0000000
## Horsepower 0.80244412 0.788217578 0.74444475 -0.6726362 -0.6190437
## RPM -0.04259816 -0.004954931 0.02501478 0.3630451 0.3134687
## Horsepower RPM
## Min.Price 0.80244412 -0.042598158
## Price 0.78821758 -0.004954931
## Max.Price 0.74444475 0.025014782
## MPG.city -0.67263615 0.363045129
## MPG.highway -0.61904368 0.313468728
## Horsepower 1.00000000 0.036688212
## RPM 0.03668821 1.000000000cov(Cars_new) ###using ## Min.Price Price Max.Price MPG.city MPG.highway
## Min.Price 76.49302 81.99801 87.47720 -30.61497 -27.04464
## Price 81.99801 93.30458 104.58534 -32.27532 -28.87584
## Max.Price 87.47720 104.58534 121.67098 -33.95830 -30.73252
## MPG.city -30.61497 -32.27532 -33.95830 31.58228 28.28343
## MPG.highway -27.04464 -28.87584 -30.73252 28.28343 28.42730
## Horsepower 367.57405 398.76473 430.07590 -197.97990 -172.86547
## RPM -222.32118 -28.56066 164.65288 1217.47896 997.33520
## Horsepower RPM
## Min.Price 367.5741 -222.32118
## Price 398.7647 -28.56066
## Max.Price 430.0759 164.65288
## MPG.city -197.9799 1217.47896
## MPG.highway -172.8655 997.33520
## Horsepower 2743.0788 1146.63394
## RPM 1146.6339 356088.70968Cars_new$predicted_price <- predict(fit,Cars_new)
View(Cars_new)
Test <-cbind(Cars_new$Price, Cars_new$predicted_price)
View(Test)
Test1<-cbind(Cars_new$Price, Cars_new$predicted_price, Cars_new$Price-Cars_new$predicted_price)
View(Test1)
summary(Test1)## V1 V2 V3
## Min. : 7.40 Min. : 7.399 Min. :-0.059180
## 1st Qu.:12.20 1st Qu.:12.196 1st Qu.:-0.004209
## Median :17.70 Median :17.692 Median : 0.002749
## Mean :19.51 Mean :19.510 Mean : 0.000000
## 3rd Qu.:23.30 3rd Qu.:23.297 3rd Qu.: 0.005789
## Max. :61.90 Max. :61.907 Max. : 0.056644####where v1 - price, v2 - predicted-price, v3- is error (difference between v1,v3)
fit1<-lm(formula=log(Price)~.,data=Cars_new)#transformation
fit1##
## Call:
## lm(formula = log(Price) ~ ., data = Cars_new)
##
## Coefficients:
## (Intercept) Min.Price Max.Price MPG.city
## 2.345e+00 2.104e-02 1.665e-02 -2.098e-02
## MPG.highway Horsepower RPM predicted_price
## 6.128e-03 6.014e-04 1.234e-08 NAsummary(fit1)##
## Call:
## lm(formula = log(Price) ~ ., data = Cars_new)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.35811 -0.04295 0.02385 0.06746 0.24633
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.345e+00 1.240e-01 18.917 < 2e-16 ***
## Min.Price 2.104e-02 3.364e-03 6.254 1.49e-08 ***
## Max.Price 1.665e-02 2.360e-03 7.056 4.11e-10 ***
## MPG.city -2.098e-02 6.657e-03 -3.152 0.00223 **
## MPG.highway 6.128e-03 6.226e-03 0.984 0.32772
## Horsepower 6.014e-04 3.969e-04 1.515 0.13337
## RPM 1.234e-08 2.159e-05 0.001 0.99955
## predicted_price NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1036 on 86 degrees of freedom
## Multiple R-squared: 0.9515, Adjusted R-squared: 0.9481
## F-statistic: 281.2 on 6 and 86 DF, p-value: < 2.2e-16hist(Cars_new$Price-Cars_new$predicted_price)
plot(Cars_new$Price-Cars_new$predicted_price,Cars_new$predicted_price)
cor(Cars_new$Price-Cars_new$predicted_price,Cars_new$predicted_price)## [1] 3.188682e-13Prediction process in Regression Model
Sample data for Train and Test
to find the number of observations we use nrow(Cars93)
data(Cars93)## Warning in data(Cars93): data set 'Cars93' not foundsamp_size<-floor(0.75 * nrow(Cars93))
data(Adult)## Warning in data(Adult): data set 'Adult' not found