cars
Yadu
July 23, 2015
First we have to install the package ggplot2:
#install.packages("ggplot2")Next, we have to load the following packages (ggplot2 to generate scatterplots, plyr to change the column names, and datasets so that we can obtain the mtcars dataset):
library(ggplot2)
library(plyr)
library(datasets)Next, we change the names of the columns as follows:
colnames(mtcars) <- c("Mileage (miles/gallon)", "Number of Cylinders", "Displacement (cubic inches)", "Gross Horsepower", "Rear Axle Ratio", "Weight (lb/1000)","Quarter Mile Time (Seconds)", "Engine Shape (V or Straight)", "Manual or Automatic Transmission", "Number of Forward Gears", "Number of Carburettors")
mtcars## Mileage (miles/gallon) Number of Cylinders
## Mazda RX4 21.0 6
## Mazda RX4 Wag 21.0 6
## Datsun 710 22.8 4
## Hornet 4 Drive 21.4 6
## Hornet Sportabout 18.7 8
## Valiant 18.1 6
## Duster 360 14.3 8
## Merc 240D 24.4 4
## Merc 230 22.8 4
## Merc 280 19.2 6
## Merc 280C 17.8 6
## Merc 450SE 16.4 8
## Merc 450SL 17.3 8
## Merc 450SLC 15.2 8
## Cadillac Fleetwood 10.4 8
## Lincoln Continental 10.4 8
## Chrysler Imperial 14.7 8
## Fiat 128 32.4 4
## Honda Civic 30.4 4
## Toyota Corolla 33.9 4
## Toyota Corona 21.5 4
## Dodge Challenger 15.5 8
## AMC Javelin 15.2 8
## Camaro Z28 13.3 8
## Pontiac Firebird 19.2 8
## Fiat X1-9 27.3 4
## Porsche 914-2 26.0 4
## Lotus Europa 30.4 4
## Ford Pantera L 15.8 8
## Ferrari Dino 19.7 6
## Maserati Bora 15.0 8
## Volvo 142E 21.4 4
## Displacement (cubic inches) Gross Horsepower
## Mazda RX4 160.0 110
## Mazda RX4 Wag 160.0 110
## Datsun 710 108.0 93
## Hornet 4 Drive 258.0 110
## Hornet Sportabout 360.0 175
## Valiant 225.0 105
## Duster 360 360.0 245
## Merc 240D 146.7 62
## Merc 230 140.8 95
## Merc 280 167.6 123
## Merc 280C 167.6 123
## Merc 450SE 275.8 180
## Merc 450SL 275.8 180
## Merc 450SLC 275.8 180
## Cadillac Fleetwood 472.0 205
## Lincoln Continental 460.0 215
## Chrysler Imperial 440.0 230
## Fiat 128 78.7 66
## Honda Civic 75.7 52
## Toyota Corolla 71.1 65
## Toyota Corona 120.1 97
## Dodge Challenger 318.0 150
## AMC Javelin 304.0 150
## Camaro Z28 350.0 245
## Pontiac Firebird 400.0 175
## Fiat X1-9 79.0 66
## Porsche 914-2 120.3 91
## Lotus Europa 95.1 113
## Ford Pantera L 351.0 264
## Ferrari Dino 145.0 175
## Maserati Bora 301.0 335
## Volvo 142E 121.0 109
## Rear Axle Ratio Weight (lb/1000)
## Mazda RX4 3.90 2.620
## Mazda RX4 Wag 3.90 2.875
## Datsun 710 3.85 2.320
## Hornet 4 Drive 3.08 3.215
## Hornet Sportabout 3.15 3.440
## Valiant 2.76 3.460
## Duster 360 3.21 3.570
## Merc 240D 3.69 3.190
## Merc 230 3.92 3.150
## Merc 280 3.92 3.440
## Merc 280C 3.92 3.440
## Merc 450SE 3.07 4.070
## Merc 450SL 3.07 3.730
## Merc 450SLC 3.07 3.780
## Cadillac Fleetwood 2.93 5.250
## Lincoln Continental 3.00 5.424
## Chrysler Imperial 3.23 5.345
## Fiat 128 4.08 2.200
## Honda Civic 4.93 1.615
## Toyota Corolla 4.22 1.835
## Toyota Corona 3.70 2.465
## Dodge Challenger 2.76 3.520
## AMC Javelin 3.15 3.435
## Camaro Z28 3.73 3.840
## Pontiac Firebird 3.08 3.845
## Fiat X1-9 4.08 1.935
## Porsche 914-2 4.43 2.140
## Lotus Europa 3.77 1.513
## Ford Pantera L 4.22 3.170
## Ferrari Dino 3.62 2.770
## Maserati Bora 3.54 3.570
## Volvo 142E 4.11 2.780
## Quarter Mile Time (Seconds)
## Mazda RX4 16.46
## Mazda RX4 Wag 17.02
## Datsun 710 18.61
## Hornet 4 Drive 19.44
## Hornet Sportabout 17.02
## Valiant 20.22
## Duster 360 15.84
## Merc 240D 20.00
## Merc 230 22.90
## Merc 280 18.30
## Merc 280C 18.90
## Merc 450SE 17.40
## Merc 450SL 17.60
## Merc 450SLC 18.00
## Cadillac Fleetwood 17.98
## Lincoln Continental 17.82
## Chrysler Imperial 17.42
## Fiat 128 19.47
## Honda Civic 18.52
## Toyota Corolla 19.90
## Toyota Corona 20.01
## Dodge Challenger 16.87
## AMC Javelin 17.30
## Camaro Z28 15.41
## Pontiac Firebird 17.05
## Fiat X1-9 18.90
## Porsche 914-2 16.70
## Lotus Europa 16.90
## Ford Pantera L 14.50
## Ferrari Dino 15.50
## Maserati Bora 14.60
## Volvo 142E 18.60
## Engine Shape (V or Straight)
## Mazda RX4 0
## Mazda RX4 Wag 0
## Datsun 710 1
## Hornet 4 Drive 1
## Hornet Sportabout 0
## Valiant 1
## Duster 360 0
## Merc 240D 1
## Merc 230 1
## Merc 280 1
## Merc 280C 1
## Merc 450SE 0
## Merc 450SL 0
## Merc 450SLC 0
## Cadillac Fleetwood 0
## Lincoln Continental 0
## Chrysler Imperial 0
## Fiat 128 1
## Honda Civic 1
## Toyota Corolla 1
## Toyota Corona 1
## Dodge Challenger 0
## AMC Javelin 0
## Camaro Z28 0
## Pontiac Firebird 0
## Fiat X1-9 1
## Porsche 914-2 0
## Lotus Europa 1
## Ford Pantera L 0
## Ferrari Dino 0
## Maserati Bora 0
## Volvo 142E 1
## Manual or Automatic Transmission
## Mazda RX4 1
## Mazda RX4 Wag 1
## Datsun 710 1
## Hornet 4 Drive 0
## Hornet Sportabout 0
## Valiant 0
## Duster 360 0
## Merc 240D 0
## Merc 230 0
## Merc 280 0
## Merc 280C 0
## Merc 450SE 0
## Merc 450SL 0
## Merc 450SLC 0
## Cadillac Fleetwood 0
## Lincoln Continental 0
## Chrysler Imperial 0
## Fiat 128 1
## Honda Civic 1
## Toyota Corolla 1
## Toyota Corona 0
## Dodge Challenger 0
## AMC Javelin 0
## Camaro Z28 0
## Pontiac Firebird 0
## Fiat X1-9 1
## Porsche 914-2 1
## Lotus Europa 1
## Ford Pantera L 1
## Ferrari Dino 1
## Maserati Bora 1
## Volvo 142E 1
## Number of Forward Gears Number of Carburettors
## Mazda RX4 4 4
## Mazda RX4 Wag 4 4
## Datsun 710 4 1
## Hornet 4 Drive 3 1
## Hornet Sportabout 3 2
## Valiant 3 1
## Duster 360 3 4
## Merc 240D 4 2
## Merc 230 4 2
## Merc 280 4 4
## Merc 280C 4 4
## Merc 450SE 3 3
## Merc 450SL 3 3
## Merc 450SLC 3 3
## Cadillac Fleetwood 3 4
## Lincoln Continental 3 4
## Chrysler Imperial 3 4
## Fiat 128 4 1
## Honda Civic 4 2
## Toyota Corolla 4 1
## Toyota Corona 3 1
## Dodge Challenger 3 2
## AMC Javelin 3 2
## Camaro Z28 3 4
## Pontiac Firebird 3 2
## Fiat X1-9 4 1
## Porsche 914-2 5 2
## Lotus Europa 5 2
## Ford Pantera L 5 4
## Ferrari Dino 5 6
## Maserati Bora 5 8
## Volvo 142E 4 2Next, we have to substitute some of the quantitative data with qualitative data:
mtcars$`Engine Shape (V or Straight)` <- gsub("0", "V", mtcars$`Engine Shape (V or Straight)`)
mtcars$`Engine Shape (V or Straight)` <- gsub("1", "Straight", mtcars$`Engine Shape (V or Straight)`)
mtcars$`Manual or Automatic Transmission` <- gsub("0", "Automatic", mtcars$`Manual or Automatic Transmission`)
mtcars$`Manual or Automatic Transmission` <- gsub("1", "Manual", mtcars$`Manual or Automatic Transmission`)
mtcars## Mileage (miles/gallon) Number of Cylinders
## Mazda RX4 21.0 6
## Mazda RX4 Wag 21.0 6
## Datsun 710 22.8 4
## Hornet 4 Drive 21.4 6
## Hornet Sportabout 18.7 8
## Valiant 18.1 6
## Duster 360 14.3 8
## Merc 240D 24.4 4
## Merc 230 22.8 4
## Merc 280 19.2 6
## Merc 280C 17.8 6
## Merc 450SE 16.4 8
## Merc 450SL 17.3 8
## Merc 450SLC 15.2 8
## Cadillac Fleetwood 10.4 8
## Lincoln Continental 10.4 8
## Chrysler Imperial 14.7 8
## Fiat 128 32.4 4
## Honda Civic 30.4 4
## Toyota Corolla 33.9 4
## Toyota Corona 21.5 4
## Dodge Challenger 15.5 8
## AMC Javelin 15.2 8
## Camaro Z28 13.3 8
## Pontiac Firebird 19.2 8
## Fiat X1-9 27.3 4
## Porsche 914-2 26.0 4
## Lotus Europa 30.4 4
## Ford Pantera L 15.8 8
## Ferrari Dino 19.7 6
## Maserati Bora 15.0 8
## Volvo 142E 21.4 4
## Displacement (cubic inches) Gross Horsepower
## Mazda RX4 160.0 110
## Mazda RX4 Wag 160.0 110
## Datsun 710 108.0 93
## Hornet 4 Drive 258.0 110
## Hornet Sportabout 360.0 175
## Valiant 225.0 105
## Duster 360 360.0 245
## Merc 240D 146.7 62
## Merc 230 140.8 95
## Merc 280 167.6 123
## Merc 280C 167.6 123
## Merc 450SE 275.8 180
## Merc 450SL 275.8 180
## Merc 450SLC 275.8 180
## Cadillac Fleetwood 472.0 205
## Lincoln Continental 460.0 215
## Chrysler Imperial 440.0 230
## Fiat 128 78.7 66
## Honda Civic 75.7 52
## Toyota Corolla 71.1 65
## Toyota Corona 120.1 97
## Dodge Challenger 318.0 150
## AMC Javelin 304.0 150
## Camaro Z28 350.0 245
## Pontiac Firebird 400.0 175
## Fiat X1-9 79.0 66
## Porsche 914-2 120.3 91
## Lotus Europa 95.1 113
## Ford Pantera L 351.0 264
## Ferrari Dino 145.0 175
## Maserati Bora 301.0 335
## Volvo 142E 121.0 109
## Rear Axle Ratio Weight (lb/1000)
## Mazda RX4 3.90 2.620
## Mazda RX4 Wag 3.90 2.875
## Datsun 710 3.85 2.320
## Hornet 4 Drive 3.08 3.215
## Hornet Sportabout 3.15 3.440
## Valiant 2.76 3.460
## Duster 360 3.21 3.570
## Merc 240D 3.69 3.190
## Merc 230 3.92 3.150
## Merc 280 3.92 3.440
## Merc 280C 3.92 3.440
## Merc 450SE 3.07 4.070
## Merc 450SL 3.07 3.730
## Merc 450SLC 3.07 3.780
## Cadillac Fleetwood 2.93 5.250
## Lincoln Continental 3.00 5.424
## Chrysler Imperial 3.23 5.345
## Fiat 128 4.08 2.200
## Honda Civic 4.93 1.615
## Toyota Corolla 4.22 1.835
## Toyota Corona 3.70 2.465
## Dodge Challenger 2.76 3.520
## AMC Javelin 3.15 3.435
## Camaro Z28 3.73 3.840
## Pontiac Firebird 3.08 3.845
## Fiat X1-9 4.08 1.935
## Porsche 914-2 4.43 2.140
## Lotus Europa 3.77 1.513
## Ford Pantera L 4.22 3.170
## Ferrari Dino 3.62 2.770
## Maserati Bora 3.54 3.570
## Volvo 142E 4.11 2.780
## Quarter Mile Time (Seconds)
## Mazda RX4 16.46
## Mazda RX4 Wag 17.02
## Datsun 710 18.61
## Hornet 4 Drive 19.44
## Hornet Sportabout 17.02
## Valiant 20.22
## Duster 360 15.84
## Merc 240D 20.00
## Merc 230 22.90
## Merc 280 18.30
## Merc 280C 18.90
## Merc 450SE 17.40
## Merc 450SL 17.60
## Merc 450SLC 18.00
## Cadillac Fleetwood 17.98
## Lincoln Continental 17.82
## Chrysler Imperial 17.42
## Fiat 128 19.47
## Honda Civic 18.52
## Toyota Corolla 19.90
## Toyota Corona 20.01
## Dodge Challenger 16.87
## AMC Javelin 17.30
## Camaro Z28 15.41
## Pontiac Firebird 17.05
## Fiat X1-9 18.90
## Porsche 914-2 16.70
## Lotus Europa 16.90
## Ford Pantera L 14.50
## Ferrari Dino 15.50
## Maserati Bora 14.60
## Volvo 142E 18.60
## Engine Shape (V or Straight)
## Mazda RX4 V
## Mazda RX4 Wag V
## Datsun 710 Straight
## Hornet 4 Drive Straight
## Hornet Sportabout V
## Valiant Straight
## Duster 360 V
## Merc 240D Straight
## Merc 230 Straight
## Merc 280 Straight
## Merc 280C Straight
## Merc 450SE V
## Merc 450SL V
## Merc 450SLC V
## Cadillac Fleetwood V
## Lincoln Continental V
## Chrysler Imperial V
## Fiat 128 Straight
## Honda Civic Straight
## Toyota Corolla Straight
## Toyota Corona Straight
## Dodge Challenger V
## AMC Javelin V
## Camaro Z28 V
## Pontiac Firebird V
## Fiat X1-9 Straight
## Porsche 914-2 V
## Lotus Europa Straight
## Ford Pantera L V
## Ferrari Dino V
## Maserati Bora V
## Volvo 142E Straight
## Manual or Automatic Transmission
## Mazda RX4 Manual
## Mazda RX4 Wag Manual
## Datsun 710 Manual
## Hornet 4 Drive Automatic
## Hornet Sportabout Automatic
## Valiant Automatic
## Duster 360 Automatic
## Merc 240D Automatic
## Merc 230 Automatic
## Merc 280 Automatic
## Merc 280C Automatic
## Merc 450SE Automatic
## Merc 450SL Automatic
## Merc 450SLC Automatic
## Cadillac Fleetwood Automatic
## Lincoln Continental Automatic
## Chrysler Imperial Automatic
## Fiat 128 Manual
## Honda Civic Manual
## Toyota Corolla Manual
## Toyota Corona Automatic
## Dodge Challenger Automatic
## AMC Javelin Automatic
## Camaro Z28 Automatic
## Pontiac Firebird Automatic
## Fiat X1-9 Manual
## Porsche 914-2 Manual
## Lotus Europa Manual
## Ford Pantera L Manual
## Ferrari Dino Manual
## Maserati Bora Manual
## Volvo 142E Manual
## Number of Forward Gears Number of Carburettors
## Mazda RX4 4 4
## Mazda RX4 Wag 4 4
## Datsun 710 4 1
## Hornet 4 Drive 3 1
## Hornet Sportabout 3 2
## Valiant 3 1
## Duster 360 3 4
## Merc 240D 4 2
## Merc 230 4 2
## Merc 280 4 4
## Merc 280C 4 4
## Merc 450SE 3 3
## Merc 450SL 3 3
## Merc 450SLC 3 3
## Cadillac Fleetwood 3 4
## Lincoln Continental 3 4
## Chrysler Imperial 3 4
## Fiat 128 4 1
## Honda Civic 4 2
## Toyota Corolla 4 1
## Toyota Corona 3 1
## Dodge Challenger 3 2
## AMC Javelin 3 2
## Camaro Z28 3 4
## Pontiac Firebird 3 2
## Fiat X1-9 4 1
## Porsche 914-2 5 2
## Lotus Europa 5 2
## Ford Pantera L 5 4
## Ferrari Dino 5 6
## Maserati Bora 5 8
## Volvo 142E 4 2Next, we obtain data regarding the internal structure of the data:
str(mtcars)## 'data.frame': 32 obs. of 11 variables:
## $ Mileage (miles/gallon) : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ Number of Cylinders : num 6 6 4 6 8 6 8 4 4 6 ...
## $ Displacement (cubic inches) : num 160 160 108 258 360 ...
## $ Gross Horsepower : num 110 110 93 110 175 105 245 62 95 123 ...
## $ Rear Axle Ratio : num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ Weight (lb/1000) : num 2.62 2.88 2.32 3.21 3.44 ...
## $ Quarter Mile Time (Seconds) : num 16.5 17 18.6 19.4 17 ...
## $ Engine Shape (V or Straight) : chr "V" "V" "Straight" "Straight" ...
## $ Manual or Automatic Transmission: chr "Manual" "Manual" "Manual" "Automatic" ...
## $ Number of Forward Gears : num 4 4 4 3 3 3 3 4 4 4 ...
## $ Number of Carburettors : num 4 4 1 1 2 1 4 2 2 4 ...summary(mtcars)## Mileage (miles/gallon) Number of Cylinders Displacement (cubic inches)
## Min. :10.40 Min. :4.000 Min. : 71.1
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8
## Median :19.20 Median :6.000 Median :196.3
## Mean :20.09 Mean :6.188 Mean :230.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0
## Max. :33.90 Max. :8.000 Max. :472.0
## Gross Horsepower Rear Axle Ratio Weight (lb/1000)
## Min. : 52.0 Min. :2.760 Min. :1.513
## 1st Qu.: 96.5 1st Qu.:3.080 1st Qu.:2.581
## Median :123.0 Median :3.695 Median :3.325
## Mean :146.7 Mean :3.597 Mean :3.217
## 3rd Qu.:180.0 3rd Qu.:3.920 3rd Qu.:3.610
## Max. :335.0 Max. :4.930 Max. :5.424
## Quarter Mile Time (Seconds) Engine Shape (V or Straight)
## Min. :14.50 Length:32
## 1st Qu.:16.89 Class :character
## Median :17.71 Mode :character
## Mean :17.85
## 3rd Qu.:18.90
## Max. :22.90
## Manual or Automatic Transmission Number of Forward Gears
## Length:32 Min. :3.000
## Class :character 1st Qu.:3.000
## Mode :character Median :4.000
## Mean :3.688
## 3rd Qu.:4.000
## Max. :5.000
## Number of Carburettors
## Min. :1.000
## 1st Qu.:2.000
## Median :2.000
## Mean :2.812
## 3rd Qu.:4.000
## Max. :8.000Next, we calculate the amount of time required to travel a full mile as follows:
mtcars$`Full Mile Time (Seconds)` <- (mtcars$`Quarter Mile Time (Seconds)`)*4The result is an entire new column consisting of quantitative data:
mtcars$`Full Mile Time (Seconds)`## [1] 65.84 68.08 74.44 77.76 68.08 80.88 63.36 80.00 91.60 73.20 75.60
## [12] 69.60 70.40 72.00 71.92 71.28 69.68 77.88 74.08 79.60 80.04 67.48
## [23] 69.20 61.64 68.20 75.60 66.80 67.60 58.00 62.00 58.40 74.40Next, we take the inverse of the quantity previously calculated to obtain the maximum speed of the vehicle:
mtcars$`Speed (Miles Per Second)` <- 1/(mtcars$`Full Mile Time (Seconds)`)Here also, we obtain an entire new column consisting of quantitative data:
mtcars$`Speed (Miles Per Second)`## [1] 0.01518834 0.01468860 0.01343364 0.01286008 0.01468860 0.01236400
## [7] 0.01578283 0.01250000 0.01091703 0.01366120 0.01322751 0.01436782
## [13] 0.01420455 0.01388889 0.01390434 0.01402918 0.01435132 0.01284027
## [19] 0.01349892 0.01256281 0.01249375 0.01481921 0.01445087 0.01622323
## [25] 0.01466276 0.01322751 0.01497006 0.01479290 0.01724138 0.01612903
## [31] 0.01712329 0.01344086Next, we calculate the number of revolutions per minute as follows:
mtcars$`Revolutions Per Minute` <- (mtcars$`Speed (Miles Per Second)`)*2112*(mtcars$`Rear Axle Ratio`)Like the previous two data sets, this is also a column consisting of quantitative data:
mtcars$`Revolutions Per Minute`## [1] 125.10328 120.98707 109.23160 83.65432 97.72033 72.07122 107.00000
## [8] 97.41600 90.38253 113.10164 109.51111 93.15862 92.10000 90.05333
## [15] 86.04227 88.88889 97.90126 110.64407 140.55292 111.96784 97.63118
## [22] 86.38293 96.13873 127.80273 95.38065 113.98095 140.06228 117.78462
## [29] 153.66621 123.31355 128.02192 116.67097Next, we calculate torque as follows:
mtcars$`Torque` <- ((mtcars$`Gross Horsepower`)*5252)/(mtcars$`Revolutions Per Minute`)Again, we have another column consisting of quantitative data:
mtcars$`Torque`## [1] 4617.944 4775.056 4471.563 6906.039 9405.412 7651.598 12025.607
## [8] 3342.613 5520.314 5711.641 5898.908 10147.853 10264.495 10497.779
## [15] 12513.152 12703.275 12338.554 3132.857 1943.069 3048.911 5218.046
## [22] 9119.858 8194.408 10068.173 9636.127 3041.140 3412.282 5038.655
## [29] 9022.986 7453.358 13743.115 4906.688Next, we take two subsets of the newly updated dataset:
cardata1 <- mtcars[c(15,4)]
cardata1## Torque Gross Horsepower
## Mazda RX4 4617.944 110
## Mazda RX4 Wag 4775.056 110
## Datsun 710 4471.563 93
## Hornet 4 Drive 6906.039 110
## Hornet Sportabout 9405.412 175
## Valiant 7651.598 105
## Duster 360 12025.607 245
## Merc 240D 3342.613 62
## Merc 230 5520.314 95
## Merc 280 5711.641 123
## Merc 280C 5898.908 123
## Merc 450SE 10147.853 180
## Merc 450SL 10264.495 180
## Merc 450SLC 10497.779 180
## Cadillac Fleetwood 12513.152 205
## Lincoln Continental 12703.275 215
## Chrysler Imperial 12338.554 230
## Fiat 128 3132.857 66
## Honda Civic 1943.069 52
## Toyota Corolla 3048.911 65
## Toyota Corona 5218.046 97
## Dodge Challenger 9119.858 150
## AMC Javelin 8194.408 150
## Camaro Z28 10068.173 245
## Pontiac Firebird 9636.127 175
## Fiat X1-9 3041.140 66
## Porsche 914-2 3412.282 91
## Lotus Europa 5038.655 113
## Ford Pantera L 9022.986 264
## Ferrari Dino 7453.358 175
## Maserati Bora 13743.115 335
## Volvo 142E 4906.688 109cardata2 <- mtcars[c(14,4)]
cardata2## Revolutions Per Minute Gross Horsepower
## Mazda RX4 125.10328 110
## Mazda RX4 Wag 120.98707 110
## Datsun 710 109.23160 93
## Hornet 4 Drive 83.65432 110
## Hornet Sportabout 97.72033 175
## Valiant 72.07122 105
## Duster 360 107.00000 245
## Merc 240D 97.41600 62
## Merc 230 90.38253 95
## Merc 280 113.10164 123
## Merc 280C 109.51111 123
## Merc 450SE 93.15862 180
## Merc 450SL 92.10000 180
## Merc 450SLC 90.05333 180
## Cadillac Fleetwood 86.04227 205
## Lincoln Continental 88.88889 215
## Chrysler Imperial 97.90126 230
## Fiat 128 110.64407 66
## Honda Civic 140.55292 52
## Toyota Corolla 111.96784 65
## Toyota Corona 97.63118 97
## Dodge Challenger 86.38293 150
## AMC Javelin 96.13873 150
## Camaro Z28 127.80273 245
## Pontiac Firebird 95.38065 175
## Fiat X1-9 113.98095 66
## Porsche 914-2 140.06228 91
## Lotus Europa 117.78462 113
## Ford Pantera L 153.66621 264
## Ferrari Dino 123.31355 175
## Maserati Bora 128.02192 335
## Volvo 142E 116.67097 109We want to find out if horsepower have a linear correlation with any of the calculated quantities. We answer the question by generating scatterplots, lines of best fit, and loess curves of best fit as follows:
require(ggplot2)
ggplot(data = cardata1, aes(x = cardata1$`Torque`, y = cardata1$`Gross Horsepower`))+
geom_point(shape = 1)+
geom_smooth(method = lm)+
xlab("Torque")+
ylab("Gross Horsepower")+
ggtitle("Correlation between Gross Horsepower and Torque")
ggplot(data = cardata1, aes(x = cardata1$`Torque`, y =
cardata1$`Gross Horsepower`))+
geom_point(shape = 1)+
geom_smooth()+
xlab("Torque")+
ylab("Gross Horsepower")+
ggtitle("Correlation between Gross Horsepower and Torque")## geom_smooth: method="auto" and size of largest group is <1000, so using loess. Use 'method = x' to change the smoothing method.
ggplot(data = cardata2, aes(x = cardata2$`Revolutions Per Minute`, y = cardata2$`Gross Horsepower`))+
geom_point(shape = 1)+
geom_smooth(method = lm)+
xlab("Revolutions Per Minute")+
ylab("Gross Horsepower")+
ggtitle("Correlation between Gross Horsepower and Revolutions Per Minute")
ggplot(data = cardata2, aes(x = cardata2$`Revolutions Per Minute`, y = cardata2$`Gross Horsepower`))+
geom_point(shape = 1)+
geom_smooth()+
xlab("Revolutions Per Minute")+
ylab("Gross Horsepower")+
ggtitle("Correlation between Gross Horsepower and Revolutions Per Minute")## geom_smooth: method="auto" and size of largest group is <1000, so using loess. Use 'method = x' to change the smoothing method.
Then, we calculate the correlation coefficients for both sets of data as follows:
cor(cardata1$`Gross Horsepower`, cardata1$`Torque`)## [1] 0.9100991cor(cardata2$`Gross Horsepower`, cardata2$`Revolutions Per Minute`)## [1] 0.06119933#Horsepower has an almost-linear correlation with torque but not with the number of revolutions per minute. A line of best fit does exist in the scatter plot. The correlation coefficient with torque is 0.91 which is close to 1 which indicates that the correlation is almost linear. The correlation coefficient with the number of revolutions per minute is 0.06 which is close to 0 which indicates that there is almost no linear correlation with the number of revolutions per minute. It is almost impossible for a line of best fit to exist. However, it is possible for a loess smothed fit curve to exist for both relations.