In this report, we will look at the mtcars dataset, which is used as a demo dataset in Rstudio. The data was gathered from “Motor Trend” magazine issues in 1974. Eleven characteristics were recorded for 32 different types of automobiles manufactured between 1973 and 1974. We will analyze the relationships between cyl (number of cylinders), gear (number of forward gears) and hp (gross horsepower).
We will look at the data and describe what we see:
data(mtcars)
dim(mtcars)## [1] 32 11The dataset contains 32 observations, or types of cars listed in rows, and 11 variables, or car characteristics listed in columns. A description of each variable follows:
We will look at the structure of the data and look at the first 6 rows to get a general sense of what type of data we are working with:
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 ...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 1First, we will provide a summary of all variables. Second, we will explore how to generate summary statistics by grouping variables. We will focus on three variables: cyl, gear, and hp.
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. :8.000library(Hmisc)## Loading required package: lattice## Loading required package: survival## Loading required package: Formula## Loading required package: ggplot2##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:base':
##
## format.pval, unitslibrary(psych)##
## Attaching package: 'psych'## The following object is masked from 'package:Hmisc':
##
## describe## The following objects are masked from 'package:ggplot2':
##
## %+%, alphalibrary(doBy)
summaryBy(gear + cyl ~ hp, data = mtcars,FUN = function(x) { c(m = mean(x), s = sd(x)) } )## hp gear.m gear.s cyl.m cyl.s
## 1 52 4.000000 NA 4.000000 NA
## 2 62 4.000000 NA 4.000000 NA
## 3 65 4.000000 NA 4.000000 NA
## 4 66 4.000000 0.0000000 4.000000 0.000000
## 5 91 5.000000 NA 4.000000 NA
## 6 93 4.000000 NA 4.000000 NA
## 7 95 4.000000 NA 4.000000 NA
## 8 97 3.000000 NA 4.000000 NA
## 9 105 3.000000 NA 6.000000 NA
## 10 109 4.000000 NA 4.000000 NA
## 11 110 3.666667 0.5773503 6.000000 0.000000
## 12 113 5.000000 NA 4.000000 NA
## 13 123 4.000000 0.0000000 6.000000 0.000000
## 14 150 3.000000 0.0000000 8.000000 0.000000
## 15 175 3.666667 1.1547005 7.333333 1.154701
## 16 180 3.000000 0.0000000 8.000000 0.000000
## 17 205 3.000000 NA 8.000000 NA
## 18 215 3.000000 NA 8.000000 NA
## 19 230 3.000000 NA 8.000000 NA
## 20 245 3.000000 0.0000000 8.000000 0.000000
## 21 264 5.000000 NA 8.000000 NA
## 22 335 5.000000 NA 8.000000 NAGiven this data, we can see the average horsepower is 123. Our results show that number of forward gears at the average horsepower is 4 and number of cylinders at the average horsepower is 6.
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