Analysis of mtcars
Data Dudes
October 10, 2016
Abstract:
As climate change becomes an ever more real threat to the Earth in the minds of leaders across the world, many governments are taking action to mitigate greenhouse gas emissions. The automobile industry in particular is targeted for regulations and in many instances fuel economy standards are set in place for car manufacturers to meet. If manufacturers continue to produce cars with poor gas mileage in spite of the standard, they are often made to pay a tax. In order to meet these standards and avoid excess taxation, engineers and businesses must come up with creative solutions so as to reduce fuel consumption without compromising on performance.
Since this issue is so relevant to today's engineering challenges and protecting the environment, our team has decided to analyze data in order to explore which avenues may be considered by engineering teams when attempting to meet fuel economy standards. To do this, we have used the MTcars data set, which has data on the design, performance and fuel economy for 32 automobiles from 1973 - 1974. All of the data therein was extracted from the 1974 Motor Trend US magazine.
Our exploratory analysis will be useful as it will delve into the various factors which may have some sort of influence on fuel economy (miles per gallon). The variables we have chosen to compare to the MPG are horsepower, displacement, number of cylinders, and number of carburetors. We hypothesize that these variables will have a strong relationship to a cars fuel economy. Our hope is that the analysis will provide findings that will identify which components of cars are the biggest perpetrators in minimizing fuel economy.
In order to execute the analysis, we will use both Python and R. Our analysis will begin with describing the data and then will proceed into displaying different relationships between design of the car and the miles per gallon it is able to achieve. A detailed report, including our code and methods, can be viewed below. Analysis of mtcars
Our question is an exploratory one: Which data field correlates most closely with mpg out of no. of cylinders and transmission type (manual or automatic)? We want to understand how each correlates with the miles per gallon data.
Source Data
We used the mtcars data set that is built-in to the R distribution. mtcars data comes from the 1974 Motor Trend magazine. The data includes fuel consumption data, and ten aspects of car design for then-current car models.
First we look at the structure of the data set
str(mtcars)## 'data.frame': 32 obs. of 11 variables:
## $ mpg : num 21 21 22.8 21.4 18.7 18.1 14.3 24.4 22.8 19.2 ...
## $ cyl : num 6 6 4 6 8 6 8 4 4 6 ...
## $ disp: num 160 160 108 258 360 ...
## $ hp : num 110 110 93 110 175 105 245 62 95 123 ...
## $ drat: num 3.9 3.9 3.85 3.08 3.15 2.76 3.21 3.69 3.92 3.92 ...
## $ wt : num 2.62 2.88 2.32 3.21 3.44 ...
## $ qsec: num 16.5 17 18.6 19.4 17 ...
## $ vs : num 0 0 1 1 0 1 0 1 1 1 ...
## $ am : num 1 1 1 0 0 0 0 0 0 0 ...
## $ gear: num 4 4 4 3 3 3 3 4 4 4 ...
## $ carb: num 4 4 1 1 2 1 4 2 2 4 ...names(mtcars)## [1] "mpg" "cyl" "disp" "hp" "drat" "wt" "qsec" "vs" "am" "gear"
## [11] "carb"We find that it contains 32 rows and 11 variables. Now we look at some of the actual data - first few rows and last few rows.
head(mtcars)## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1tail(mtcars)## mpg cyl disp hp drat wt qsec vs am gear carb
## Porsche 914-2 26.0 4 120.3 91 4.43 2.140 16.7 0 1 5 2
## Lotus Europa 30.4 4 95.1 113 3.77 1.513 16.9 1 1 5 2
## Ford Pantera L 15.8 8 351.0 264 4.22 3.170 14.5 0 1 5 4
## Ferrari Dino 19.7 6 145.0 175 3.62 2.770 15.5 0 1 5 6
## Maserati Bora 15.0 8 301.0 335 3.54 3.570 14.6 0 1 5 8
## Volvo 142E 21.4 4 121.0 109 4.11 2.780 18.6 1 1 4 2We see that the data appears tidy. Now we look at the desriptive statistics for each field - (min, 1st Q, Median, Mean, 3rd Q, max)
summary(mtcars)## mpg cyl disp hp
## Min. :10.40 Min. :4.000 Min. : 71.1 Min. : 52.0
## 1st Qu.:15.43 1st Qu.:4.000 1st Qu.:120.8 1st Qu.: 96.5
## Median :19.20 Median :6.000 Median :196.3 Median :123.0
## Mean :20.09 Mean :6.188 Mean :230.7 Mean :146.7
## 3rd Qu.:22.80 3rd Qu.:8.000 3rd Qu.:326.0 3rd Qu.:180.0
## Max. :33.90 Max. :8.000 Max. :472.0 Max. :335.0
## drat wt qsec vs
## Min. :2.760 Min. :1.513 Min. :14.50 Min. :0.0000
## 1st Qu.:3.080 1st Qu.:2.581 1st Qu.:16.89 1st Qu.:0.0000
## Median :3.695 Median :3.325 Median :17.71 Median :0.0000
## Mean :3.597 Mean :3.217 Mean :17.85 Mean :0.4375
## 3rd Qu.:3.920 3rd Qu.:3.610 3rd Qu.:18.90 3rd Qu.:1.0000
## Max. :4.930 Max. :5.424 Max. :22.90 Max. :1.0000
## am gear carb
## Min. :0.0000 Min. :3.000 Min. :1.000
## 1st Qu.:0.0000 1st Qu.:3.000 1st Qu.:2.000
## Median :0.0000 Median :4.000 Median :2.000
## Mean :0.4062 Mean :3.688 Mean :2.812
## 3rd Qu.:1.0000 3rd Qu.:4.000 3rd Qu.:4.000
## Max. :1.0000 Max. :5.000 Max. :8.000Since mode is not a built-in R function, we calculate it for each.
mode_mpg <- names(sort(-table(mtcars$mpg)))[1]
mode_cyl <- names(sort(-table(mtcars$cyl)))[1]
mode_disp <- names(sort(-table(mtcars$disp)))[1]
mode_hp <- names(sort(-table(mtcars$hp)))[1]
mode_drat <- names(sort(-table(mtcars$drat)))[1]
mode_wt <- names(sort(-table(mtcars$wt)))[1]
mode_qsec <- names(sort(-table(mtcars$qsec)))[1]
mode_vs <- names(sort(-table(mtcars$vs)))[1]
mode_am <- names(sort(-table(mtcars$am)))[1]
mode_gear <- names(sort(-table(mtcars$gear)))[1]
mode_carb <- names(sort(-table(mtcars$carb)))[1]Then we print it.
paste("The mode of the miles per gallon data is", mode_mpg)## [1] "The mode of the miles per gallon data is 10.4"paste("The mode of the number of cylinders data is", mode_cyl)## [1] "The mode of the number of cylinders data is 8"paste("The mode of the displacement data is", mode_disp)## [1] "The mode of the displacement data is 275.8"paste("The mode of the horsepower data is", mode_hp)## [1] "The mode of the horsepower data is 110"paste("The mode of the rear axle ratio data is", mode_drat)## [1] "The mode of the rear axle ratio data is 3.07"paste("The mode of the weight (1000 lbs) data is", mode_wt)## [1] "The mode of the weight (1000 lbs) data is 3.44"paste("The mode of the quarter mile time data is", mode_qsec)## [1] "The mode of the quarter mile time data is 17.02"paste("The mode of the V/S data is", mode_vs)## [1] "The mode of the V/S data is 0"paste("The mode of the transmission data is", mode_am)## [1] "The mode of the transmission data is 0"paste("The mode of the number of forward gears data is", mode_gear)## [1] "The mode of the number of forward gears data is 3"paste("The mode of the number of carburetors data is", mode_carb)## [1] "The mode of the number of carburetors data is 2"Now we look at correlation of hp and mpg.
cor(mtcars$mpg, mtcars$hp)## [1] -0.7761684We find a fairly strong negative correlation.
Plotting the data - HP vs MPG
Below is the effect that number of horsepower on mpg.
Fitting the Data - HP vs. MPG
We then apply linear regression to fit the data to a line. We use geom_smooth with the linear model method.
ggplot(mtcars, aes(hp, mpg)) + geom_point() +
geom_smooth(method = "lm", se = FALSE)
Since the mpg is unlikely to hit zero as the hp increases, we would expect a more asymptotic line. So let’s apply stat_smooth to get a better fit.
#apply smoothing since mpg unlikely to hit zero
ggplot(mtcars, aes(hp, mpg)) +
stat_smooth() + geom_point()
Effect on Number of Cylinders on MPG
Now we do a similar analysis as above, but instead by looking at the number of cylinders and its effect on miles per gallon.
The correlation of mpg and cyl is shown below.
cor(mtcars$mpg, mtcars$cyl)## [1] -0.852162This gives an even stronger negative correlation of -0.85
Doing a quick scatter plot yields the following.
qplot(cyl, mpg, data = mtcars, colour = cyl, geom = "point") 
Fitting the Data - Cyl vs. MPG
We then apply linear regression to fit the data to a line. We use geom_smooth with the linear model method.
ggplot(mtcars, aes(cyl, mpg)) + geom_point() +
geom_smooth(method = "lm", se = FALSE)
Summary
Our analysis shows a strong negative correlation for both number of horsepower as well as number of cylinders on miles per gallon. As both horsepower and/or cylinders increase, we see miles per gallon decreasing.
References:
Motor Trend Car Road Tests. October 7th, 2016. https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/mtcars.html
Energy Policy and Conservation Act. October, 7th, 2016. http://legcounsel.house.gov/Comps/EPCA.pdf
For calculating the mode:
[R] find the mode of a dataset; T Lumley, December 24, 1999 https://stat.ethz.ch/pipermail/r-help/1999-December/005668.html
For ggplot2 suggestions:
ggplot2 - An implementation of the grammar of graphics; Hadley Wickham, 2007 http://ggplot2.org/resources/2007-vanderbilt.pdf
Blog: 10 Reasons to switch to ggplot. Mandy Mejia; Nov 13, 2013 https://mandymejia.wordpress.com/2013/11/13/10-reasons-to-switch-to-ggplot-7/
Package ‘ggplot2’, August 29, 2016 https://cran.r-project.org/web/packages/ggplot2/ggplot2.pdf
Data Visualization with ggplot2 Cheat Sheet; March 2015 https://www.rstudio.com/wp-content/uploads/2015/03/ggplot2-cheatsheet.pdf
For ggplot fitting and smoothing
Add a smoother. ggplot2 help documents http://docs.ggplot2.org/0.9.3.1/stat_smooth.html
Lines: horizontal, vertical, and specified by slope and intercept. ggplot2 help documents http://docs.ggplot2.org/current/geom_abline.html