FX Jollois

All the following code can be executed into R console, without any additional packages installation or data laoding, except when indicated.

Introduction to R language

Some useful things

Basic commands

1 + 2
## [1] 3
a = 1
a + 2
## [1] 3
c(1, 2)
## [1] 1 2
c(1, 2) + 3
## [1] 4 5
1:5
## [1] 1 2 3 4 5
seq(1, 5)
## [1] 1 2 3 4 5
seq(1, 5, by = .5)
## [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
seq(1, 5, length = 9)
## [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
rep(1, 5)
## [1] 1 1 1 1 1
rep(c(1, 3), times = 5)
##  [1] 1 3 1 3 1 3 1 3 1 3
rep(c(1, 3), each = 5)
##  [1] 1 1 1 1 1 3 3 3 3 3
rep(c(1, 3), times = 2, each = 5)
##  [1] 1 1 1 1 1 3 3 3 3 3 1 1 1 1 1 3 3 3 3 3
rep(c(1, 3), times = 2, each = 5, length = 11)
##  [1] 1 1 1 1 1 3 3 3 3 3 1
ifelse(1 > 2, "sup", "inf")
## [1] "inf"
for(v in 1:5) print(v**2)
## [1] 1
## [1] 4
## [1] 9
## [1] 16
## [1] 25
sample(1:10)
##  [1]  4  3  5  1  9  6 10  2  8  7
paste("good", "morning")
## [1] "good morning"
paste("good", "morning", sep = "-")
## [1] "good-morning"
paste0("good", "morning")
## [1] "goodmorning"
paste("good", c("morning", "afternoon"))
## [1] "good morning"   "good afternoon"

Working directory

# this code is not executed
getwd()
setwd("path/to/your/working/directory")
getwd() # if no change, problem with previous line

Packages

Packages directory

# this code is not executed
.libPaths()
.libPaths("path/to/your/packages/directory")
.libPaths() # if no change, problem with previous line

Package installation

# this code is not executed
install.packages("packagename") # one or more packages name
library(package) # without any quote

Functions

f <- function(a, b) {
    return(a ** b)
}
f(2, 5)
## [1] 32
f(a = 2, b = 5)
## [1] 32
f(a = 2, 5)
## [1] 32
f(b = 2, a = 5)
## [1] 25
f(b = 2, 5)
## [1] 25
f <- function(a, b = 1) {
    return(a ** b)
}
f(2, 5)
## [1] 32
f(2)
## [1] 2
f <- function(a, b = 1, ...) {
    s = sum(a, ...)
    return(s ** b)
}
f(2, 5)
## [1] 32
f(c(1, 2, 3), 5)
## [1] 7776
f(c(1, NA, 3), 5)
## [1] NA
sum(c(1, NA, 3))
## [1] NA
sum(c(1, NA, 3), na.rm = TRUE)
## [1] 4
f(c(1, NA, 3), 5, na.rm = TRUE)
## [1] 1024

Import data from text files

We present here different files, with specific needs to correctly import data into R. We use the read.table() command, with options.

heart.txt
  • Tabulated separated variables (default value)
  • attriutes names in the first line (header = T)
heart = read.table("donnees/heart.txt", header = T)
head(heart)
##   age     sexe type_douleur pression cholester sucre electro taux_max
## 1  70 masculin            D      130       322     A       C      109
## 2  67  feminin            C      115       564     A       C      160
## 3  57 masculin            B      124       261     A       A      141
## 4  64 masculin            D      128       263     A       A      105
## 5  74  feminin            B      120       269     A       C      121
## 6  65 masculin            D      120       177     A       A      140
##   angine depression pic vaisseau    coeur
## 1    non        2.4   2        D presence
## 2    non        1.6   2        A  absence
## 3    non        0.3   1        A presence
## 4    oui        0.2   2        B  absence
## 5    oui        0.2   1        B  absence
## 6    non        0.4   1        A  absence
hepatitis.TXT
  • Tabulated separated variables
  • attributes names in the first line (header = T)
  • missing value indicated with "?" (na.strings = "?")
hep = read.table("donnees/hepatitis.TXT", header = T, na.strings = "?")
head(hep)
##   AGE    SEX STEROID ANTIVIRALS FATIGUE MALAISE ANOREXIA LIVER_BIG
## 1  30   male      no         no      no      no       no        no
## 2  50 female      no         no     yes      no       no        no
## 3  78 female     yes         no     yes      no       no       yes
## 4  31 female    <NA>        yes      no      no       no       yes
## 5  34 female     yes         no      no      no       no       yes
## 6  34 female     yes         no      no      no       no       yes
##   LIVER_FIRM SPLEEN_PALPABLE SPIDERS ASCITES VARICES BILIRUBIN
## 1         no              no      no      no      no       1.0
## 2         no              no      no      no      no       0.9
## 3         no              no      no      no      no       0.7
## 4         no              no      no      no      no       0.7
## 5         no              no      no      no      no       1.0
## 6         no              no      no      no      no       0.9
##   ALK_PHOSPHATE SGOT ALBUMIN PROTIME HISTOLOGY Class
## 1         85.00   18     4.0   61.85        no  LIVE
## 2        135.00   42     3.5   61.85        no  LIVE
## 3         96.00   32     4.0   61.85        no  LIVE
## 4         46.00   52     4.0   80.00        no  LIVE
## 5        105.33  200     4.0   61.85        no  LIVE
## 6         95.00   28     4.0   75.00        no  LIVE
Iris_bis.txx
  • delimited variables with "%" (sep = "%")
  • attributes names in the first line (header = T)
  • specific decimal separator (dec = ".")
ir = read.table("donnees/Iris_bis.txt", header = T, sep = "%", dec = ",")
Detroit_homicide.txt
  • attributes names in the first line (header = T)
  • 35 first rows useless (skip = 35)
dh = read.table("donnees/Detroit_homicide.txt", skip = 35, header = T)
head(dh)
##      FTP UEMP   MAN    LIC     GR CLEAR     WM  NMAN   GOV   HE     WE
## 1 260.35 11.0 455.5 178.15 215.98  93.4 558724 538.1 133.9 2.98 117.18
## 2 269.80  7.0 480.2 156.41 180.48  88.5 538584 547.6 137.6 3.09 134.02
## 3 272.04  5.2 506.1 198.02 209.57  94.4 519171 562.8 143.6 3.23 141.68
## 4 272.96  4.3 535.8 222.10 231.67  92.0 500457 591.0 150.3 3.33 147.98
## 5 272.51  3.5 576.0 301.92 297.65  91.0 482418 626.1 164.3 3.46 159.85
## 6 261.34  3.2 601.7 391.22 367.62  87.4 465029 659.8 179.5 3.60 157.19
##     HOM   ACC    ASR
## 1  8.60 39.17 306.18
## 2  8.90 40.27 315.16
## 3  8.52 45.31 277.53
## 4  8.89 49.51 234.07
## 5 13.07 55.05 230.84
## 6 14.57 53.90 217.99

Working with data.frame

About data.frame (basic manipulation)

head(iris)
##   Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1          5.1         3.5          1.4         0.2  setosa
## 2          4.9         3.0          1.4         0.2  setosa
## 3          4.7         3.2          1.3         0.2  setosa
## 4          4.6         3.1          1.5         0.2  setosa
## 5          5.0         3.6          1.4         0.2  setosa
## 6          5.4         3.9          1.7         0.4  setosa
class(iris)
## [1] "data.frame"
names(iris)
## [1] "Sepal.Length" "Sepal.Width"  "Petal.Length" "Petal.Width" 
## [5] "Species"
dim(iris)
## [1] 150   5
nrow(iris)
## [1] 150
ncol(iris)
## [1] 5
str(iris)
## 'data.frame':    150 obs. of  5 variables:
##  $ Sepal.Length: num  5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
##  $ Sepal.Width : num  3.5 3 3.2 3.1 3.6 3.9 3.4 3.4 2.9 3.1 ...
##  $ Petal.Length: num  1.4 1.4 1.3 1.5 1.4 1.7 1.4 1.5 1.4 1.5 ...
##  $ Petal.Width : num  0.2 0.2 0.2 0.2 0.2 0.4 0.3 0.2 0.2 0.1 ...
##  $ Species     : Factor w/ 3 levels "setosa","versicolor",..: 1 1 1 1 1 1 1 1 1 1 ...

For illustration, we extract 20 random rows from iris.

iris = head(iris[sample(seq(nrow(iris))),], 20)

Get one column from a data.frame

iris$Sepal.Length
##  [1] 5.0 7.9 4.5 6.6 6.4 6.2 4.7 6.4 5.8 6.7 6.6 5.1 6.4 7.1 4.9 5.1 6.3
## [18] 7.7 6.3 5.5
iris[,1]
##  [1] 5.0 7.9 4.5 6.6 6.4 6.2 4.7 6.4 5.8 6.7 6.6 5.1 6.4 7.1 4.9 5.1 6.3
## [18] 7.7 6.3 5.5
iris[,"Sepal.Length"]
##  [1] 5.0 7.9 4.5 6.6 6.4 6.2 4.7 6.4 5.8 6.7 6.6 5.1 6.4 7.1 4.9 5.1 6.3
## [18] 7.7 6.3 5.5
iris[1]
##     Sepal.Length
## 94           5.0
## 132          7.9
## 42           4.5
## 59           6.6
## 112          6.4
## 98           6.2
## 30           4.7
## 52           6.4
## 143          5.8
## 145          6.7
## 76           6.6
## 99           5.1
## 75           6.4
## 103          7.1
## 58           4.9
## 24           5.1
## 104          6.3
## 118          7.7
## 73           6.3
## 37           5.5
iris["Sepal.Length"]
##     Sepal.Length
## 94           5.0
## 132          7.9
## 42           4.5
## 59           6.6
## 112          6.4
## 98           6.2
## 30           4.7
## 52           6.4
## 143          5.8
## 145          6.7
## 76           6.6
## 99           5.1
## 75           6.4
## 103          7.1
## 58           4.9
## 24           5.1
## 104          6.3
## 118          7.7
## 73           6.3
## 37           5.5

Get more than one column

iris[,c(1,3)]
##     Sepal.Length Petal.Length
## 94           5.0          3.3
## 132          7.9          6.4
## 42           4.5          1.3
## 59           6.6          4.6
## 112          6.4          5.3
## 98           6.2          4.3
## 30           4.7          1.6
## 52           6.4          4.5
## 143          5.8          5.1
## 145          6.7          5.7
## 76           6.6          4.4
## 99           5.1          3.0
## 75           6.4          4.3
## 103          7.1          5.9
## 58           4.9          3.3
## 24           5.1          1.7
## 104          6.3          5.6
## 118          7.7          6.7
## 73           6.3          4.9
## 37           5.5          1.3
iris[,c("Sepal.Length", "Petal.Length")]
##     Sepal.Length Petal.Length
## 94           5.0          3.3
## 132          7.9          6.4
## 42           4.5          1.3
## 59           6.6          4.6
## 112          6.4          5.3
## 98           6.2          4.3
## 30           4.7          1.6
## 52           6.4          4.5
## 143          5.8          5.1
## 145          6.7          5.7
## 76           6.6          4.4
## 99           5.1          3.0
## 75           6.4          4.3
## 103          7.1          5.9
## 58           4.9          3.3
## 24           5.1          1.7
## 104          6.3          5.6
## 118          7.7          6.7
## 73           6.3          4.9
## 37           5.5          1.3
iris[c(1,3)]
##     Sepal.Length Petal.Length
## 94           5.0          3.3
## 132          7.9          6.4
## 42           4.5          1.3
## 59           6.6          4.6
## 112          6.4          5.3
## 98           6.2          4.3
## 30           4.7          1.6
## 52           6.4          4.5
## 143          5.8          5.1
## 145          6.7          5.7
## 76           6.6          4.4
## 99           5.1          3.0
## 75           6.4          4.3
## 103          7.1          5.9
## 58           4.9          3.3
## 24           5.1          1.7
## 104          6.3          5.6
## 118          7.7          6.7
## 73           6.3          4.9
## 37           5.5          1.3
iris[c("Sepal.Length", "Petal.Length")]
##     Sepal.Length Petal.Length
## 94           5.0          3.3
## 132          7.9          6.4
## 42           4.5          1.3
## 59           6.6          4.6
## 112          6.4          5.3
## 98           6.2          4.3
## 30           4.7          1.6
## 52           6.4          4.5
## 143          5.8          5.1
## 145          6.7          5.7
## 76           6.6          4.4
## 99           5.1          3.0
## 75           6.4          4.3
## 103          7.1          5.9
## 58           4.9          3.3
## 24           5.1          1.7
## 104          6.3          5.6
## 118          7.7          6.7
## 73           6.3          4.9
## 37           5.5          1.3
iris[-c(2, 4, 5)]
##     Sepal.Length Petal.Length
## 94           5.0          3.3
## 132          7.9          6.4
## 42           4.5          1.3
## 59           6.6          4.6
## 112          6.4          5.3
## 98           6.2          4.3
## 30           4.7          1.6
## 52           6.4          4.5
## 143          5.8          5.1
## 145          6.7          5.7
## 76           6.6          4.4
## 99           5.1          3.0
## 75           6.4          4.3
## 103          7.1          5.9
## 58           4.9          3.3
## 24           5.1          1.7
## 104          6.3          5.6
## 118          7.7          6.7
## 73           6.3          4.9
## 37           5.5          1.3

Get one row from a data.frame

iris[1,]
##    Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
## 94            5         2.3          3.3           1 versicolor
iris[c(1,3),]
##    Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
## 94          5.0         2.3          3.3         1.0 versicolor
## 42          4.5         2.3          1.3         0.3     setosa
iris[iris$Sepal.Length > 6,]
##     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
## 132          7.9         3.8          6.4         2.0  virginica
## 59           6.6         2.9          4.6         1.3 versicolor
## 112          6.4         2.7          5.3         1.9  virginica
## 98           6.2         2.9          4.3         1.3 versicolor
## 52           6.4         3.2          4.5         1.5 versicolor
## 145          6.7         3.3          5.7         2.5  virginica
## 76           6.6         3.0          4.4         1.4 versicolor
## 75           6.4         2.9          4.3         1.3 versicolor
## 103          7.1         3.0          5.9         2.1  virginica
## 104          6.3         2.9          5.6         1.8  virginica
## 118          7.7         3.8          6.7         2.2  virginica
## 73           6.3         2.5          4.9         1.5 versicolor

Data types

class(names(iris))
## [1] "character"
class(iris$Sepal.Length)
## [1] "numeric"
class(iris$Species)
## [1] "factor"
head(iris$Species)
## [1] versicolor virginica  setosa     versicolor virginica  versicolor
## Levels: setosa versicolor virginica

Group two data.frame together

cbind(iris[,1], iris[,4:5])
##     iris[, 1] Petal.Width    Species
## 94        5.0         1.0 versicolor
## 132       7.9         2.0  virginica
## 42        4.5         0.3     setosa
## 59        6.6         1.3 versicolor
## 112       6.4         1.9  virginica
## 98        6.2         1.3 versicolor
## 30        4.7         0.2     setosa
## 52        6.4         1.5 versicolor
## 143       5.8         1.9  virginica
## 145       6.7         2.5  virginica
## 76        6.6         1.4 versicolor
## 99        5.1         1.1 versicolor
## 75        6.4         1.3 versicolor
## 103       7.1         2.1  virginica
## 58        4.9         1.0 versicolor
## 24        5.1         0.5     setosa
## 104       6.3         1.8  virginica
## 118       7.7         2.2  virginica
## 73        6.3         1.5 versicolor
## 37        5.5         0.2     setosa
rbind(iris[1:3,], iris[8:10,])
##     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
## 94           5.0         2.3          3.3         1.0 versicolor
## 132          7.9         3.8          6.4         2.0  virginica
## 42           4.5         2.3          1.3         0.3     setosa
## 52           6.4         3.2          4.5         1.5 versicolor
## 143          5.8         2.7          5.1         1.9  virginica
## 145          6.7         3.3          5.7         2.5  virginica

Univariate statistics

We now work on the complete iris dataset.

Quantitative

Numerical statistics
mean(iris$Sepal.Length)
## [1] 5.843333
sd(iris$Sepal.Length)
## [1] 0.8280661
var(iris$Sepal.Length)
## [1] 0.6856935
median(iris$Sepal.Length)
## [1] 5.8
min(iris$Sepal.Length)
## [1] 4.3
max(iris$Sepal.Length)
## [1] 7.9
range(iris$Sepal.Length)
## [1] 4.3 7.9
quantile(iris$Sepal.Length)
##   0%  25%  50%  75% 100% 
##  4.3  5.1  5.8  6.4  7.9
quantile(iris$Sepal.Length, .1)
## 10% 
## 4.8
quantile(iris$Sepal.Length, c(.01, .1, .9, .99))
##  1% 10% 90% 99% 
## 4.4 4.8 6.9 7.7
summary(iris$Sepal.Length)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   4.300   5.100   5.800   5.843   6.400   7.900
shapiro.test(iris$Sepal.Length)
## 
##  Shapiro-Wilk normality test
## 
## data:  iris$Sepal.Length
## W = 0.97609, p-value = 0.01018
Basic graphics
hist(iris$Sepal.Length)

boxplot(iris$Sepal.Length)

qqnorm(iris$Sepal.Length)
qqline(iris$Sepal.Length)

plot(ecdf(iris$Sepal.Length))

Qualitative

factor

Numerical statistics
t = table(iris$Species)
prop.table(t)
## 
##     setosa versicolor  virginica 
##  0.3333333  0.3333333  0.3333333
chisq.test(t)
## 
##  Chi-squared test for given probabilities
## 
## data:  t
## X-squared = 0, df = 2, p-value = 1
chisq.test(t, p = c(.2, .3, .5))
## 
##  Chi-squared test for given probabilities
## 
## data:  t
## X-squared = 22.222, df = 2, p-value = 1.495e-05
Basic graphics
barplot(table(iris$Species))
plot(iris$Species) # work only because Species is declared as factor

pie(table(iris$Species))

Bivariate statistics

Two quantitatives

Numerical
cov(iris$Sepal.Length, iris$Sepal.Width)
## [1] -0.042434
cor(iris$Sepal.Length, iris$Sepal.Width)
## [1] -0.1175698
cor.test(iris$Sepal.Length, iris$Sepal.Width)
## 
##  Pearson's product-moment correlation
## 
## data:  iris$Sepal.Length and iris$Sepal.Width
## t = -1.4403, df = 148, p-value = 0.1519
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.27269325  0.04351158
## sample estimates:
##        cor 
## -0.1175698
m = lm(Sepal.Length ~ Sepal.Width, data = iris)
m
## 
## Call:
## lm(formula = Sepal.Length ~ Sepal.Width, data = iris)
## 
## Coefficients:
## (Intercept)  Sepal.Width  
##      6.5262      -0.2234
summary(m)
## 
## Call:
## lm(formula = Sepal.Length ~ Sepal.Width, data = iris)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5561 -0.6333 -0.1120  0.5579  2.2226 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   6.5262     0.4789   13.63   <2e-16 ***
## Sepal.Width  -0.2234     0.1551   -1.44    0.152    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8251 on 148 degrees of freedom
## Multiple R-squared:  0.01382,    Adjusted R-squared:  0.007159 
## F-statistic: 2.074 on 1 and 148 DF,  p-value: 0.1519
Graphics
plot(iris$Sepal.Length, iris$Sepal.Width)

plot(iris$Sepal.Length ~ iris$Sepal.Width)

plot(Sepal.Length ~ Sepal.Width, data = iris)
abline(m, col = "red")

Two qualitatives

Create a new ordinal attribute from Sepal.Length, with 5 values for instance.

iris$Sepal.Length.ord = cut(iris$Sepal.Length, 5)
table(iris$Sepal.Length.ord)
## 
##  (4.3,5.02] (5.02,5.74] (5.74,6.46] (6.46,7.18]  (7.18,7.9] 
##          32          41          42          24          11
diff(range(iris$Sepal.Length)) / 5
## [1] 0.72
Numerical statistics
t = table(iris$Species, iris$Sepal.Length.ord)
t
##             
##              (4.3,5.02] (5.02,5.74] (5.74,6.46] (6.46,7.18] (7.18,7.9]
##   setosa             28          21           1           0          0
##   versicolor          3          18          20           9          0
##   virginica           1           2          21          15         11
prop.table(t)
##             
##               (4.3,5.02] (5.02,5.74] (5.74,6.46] (6.46,7.18]  (7.18,7.9]
##   setosa     0.186666667 0.140000000 0.006666667 0.000000000 0.000000000
##   versicolor 0.020000000 0.120000000 0.133333333 0.060000000 0.000000000
##   virginica  0.006666667 0.013333333 0.140000000 0.100000000 0.073333333
prop.table(t, margin = 1)
##             
##              (4.3,5.02] (5.02,5.74] (5.74,6.46] (6.46,7.18] (7.18,7.9]
##   setosa           0.56        0.42        0.02        0.00       0.00
##   versicolor       0.06        0.36        0.40        0.18       0.00
##   virginica        0.02        0.04        0.42        0.30       0.22
prop.table(t, margin = 2)
##             
##              (4.3,5.02] (5.02,5.74] (5.74,6.46] (6.46,7.18] (7.18,7.9]
##   setosa     0.87500000  0.51219512  0.02380952  0.00000000 0.00000000
##   versicolor 0.09375000  0.43902439  0.47619048  0.37500000 0.00000000
##   virginica  0.03125000  0.04878049  0.50000000  0.62500000 1.00000000
chisq.test(t)
## Warning in chisq.test(t): Chi-squared approximation may be incorrect
## 
##  Pearson's Chi-squared test
## 
## data:  t
## X-squared = 112.1, df = 8, p-value < 2.2e-16
Graphics
barplot(t)

barplot(t, beside = TRUE)

barplot(prop.table(t, margin = 2))

assocplot(t)

mosaicplot(t)

One quantitative vs. one qualitative

Numerical statistics
tapply(iris$Sepal.Length, iris$Species, mean)
##     setosa versicolor  virginica 
##      5.006      5.936      6.588
tapply(iris$Sepal.Length, iris$Species, summary)
## $setosa
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   4.300   4.800   5.000   5.006   5.200   5.800 
## 
## $versicolor
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   4.900   5.600   5.900   5.936   6.300   7.000 
## 
## $virginica
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   4.900   6.225   6.500   6.588   6.900   7.900
anova(lm(Sepal.Length ~ Species, data = iris))
## Analysis of Variance Table
## 
## Response: Sepal.Length
##            Df Sum Sq Mean Sq F value    Pr(>F)    
## Species     2 63.212  31.606  119.26 < 2.2e-16 ***
## Residuals 147 38.956   0.265                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
m = aov(Sepal.Length ~ Species, data = iris)
m
## Call:
##    aov(formula = Sepal.Length ~ Species, data = iris)
## 
## Terms:
##                  Species Residuals
## Sum of Squares  63.21213  38.95620
## Deg. of Freedom        2       147
## 
## Residual standard error: 0.5147894
## Estimated effects may be unbalanced
summary(m)
##              Df Sum Sq Mean Sq F value Pr(>F)    
## Species       2  63.21  31.606   119.3 <2e-16 ***
## Residuals   147  38.96   0.265                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Graphics
boxplot(Sepal.Length ~ Species, data = iris)

par(mfrow = c(3, 1), mar = c(2, 2, 0, 0) + .1)
x = iris$Sepal.Length
for (v in levels(iris$Species)) {
    hist(x[iris$Species == v], 
         freq = FALSE,
         xlim = range(x),
         breaks = seq(min(x), max(x), length = 10),
         main = NULL)
}

Multivariate statistics (basic)

on data.frame

summary(iris)
##   Sepal.Length    Sepal.Width     Petal.Length    Petal.Width   
##  Min.   :4.300   Min.   :2.000   Min.   :1.000   Min.   :0.100  
##  1st Qu.:5.100   1st Qu.:2.800   1st Qu.:1.600   1st Qu.:0.300  
##  Median :5.800   Median :3.000   Median :4.350   Median :1.300  
##  Mean   :5.843   Mean   :3.057   Mean   :3.758   Mean   :1.199  
##  3rd Qu.:6.400   3rd Qu.:3.300   3rd Qu.:5.100   3rd Qu.:1.800  
##  Max.   :7.900   Max.   :4.400   Max.   :6.900   Max.   :2.500  
##        Species      Sepal.Length.ord
##  setosa    :50   (4.3,5.02] :32     
##  versicolor:50   (5.02,5.74]:41     
##  virginica :50   (5.74,6.46]:42     
##                  (6.46,7.18]:24     
##                  (7.18,7.9] :11     
## 
apply(iris[1:4], 2, mean)
## Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
##     5.843333     3.057333     3.758000     1.199333
apply(iris[1:4], 2, summary)
##         Sepal.Length Sepal.Width Petal.Length Petal.Width
## Min.        4.300000    2.000000        1.000    0.100000
## 1st Qu.     5.100000    2.800000        1.600    0.300000
## Median      5.800000    3.000000        4.350    1.300000
## Mean        5.843333    3.057333        3.758    1.199333
## 3rd Qu.     6.400000    3.300000        5.100    1.800000
## Max.        7.900000    4.400000        6.900    2.500000
apply(iris[1:4], 2, tapply, iris$Species, mean)
##            Sepal.Length Sepal.Width Petal.Length Petal.Width
## setosa            5.006       3.428        1.462       0.246
## versicolor        5.936       2.770        4.260       1.326
## virginica         6.588       2.974        5.552       2.026
cor(iris[1:4])
##              Sepal.Length Sepal.Width Petal.Length Petal.Width
## Sepal.Length    1.0000000  -0.1175698    0.8717538   0.8179411
## Sepal.Width    -0.1175698   1.0000000   -0.4284401  -0.3661259
## Petal.Length    0.8717538  -0.4284401    1.0000000   0.9628654
## Petal.Width     0.8179411  -0.3661259    0.9628654   1.0000000
plot(Sepal.Length ~ Sepal.Width, data = iris, 
     col = rainbow(3)[iris$Species], pch = 19)
legend("topright", 
       pch = 19, col = rainbow(3), 
       legend = levels(iris$Species))

pairs(iris[-5])

pairs(iris[-5], col = rainbow(3)[iris$Species], pch = 19, upper.panel = NULL)

Advanced manipulation, using basic R code

subset()

subset(iris, subset = Species == "setosa")
##    Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 1           5.1         3.5          1.4         0.2  setosa
## 2           4.9         3.0          1.4         0.2  setosa
## 3           4.7         3.2          1.3         0.2  setosa
## 4           4.6         3.1          1.5         0.2  setosa
## 5           5.0         3.6          1.4         0.2  setosa
## 6           5.4         3.9          1.7         0.4  setosa
## 7           4.6         3.4          1.4         0.3  setosa
## 8           5.0         3.4          1.5         0.2  setosa
## 9           4.4         2.9          1.4         0.2  setosa
## 10          4.9         3.1          1.5         0.1  setosa
## 11          5.4         3.7          1.5         0.2  setosa
## 12          4.8         3.4          1.6         0.2  setosa
## 13          4.8         3.0          1.4         0.1  setosa
## 14          4.3         3.0          1.1         0.1  setosa
## 15          5.8         4.0          1.2         0.2  setosa
## 16          5.7         4.4          1.5         0.4  setosa
## 17          5.4         3.9          1.3         0.4  setosa
## 18          5.1         3.5          1.4         0.3  setosa
## 19          5.7         3.8          1.7         0.3  setosa
## 20          5.1         3.8          1.5         0.3  setosa
## 21          5.4         3.4          1.7         0.2  setosa
## 22          5.1         3.7          1.5         0.4  setosa
## 23          4.6         3.6          1.0         0.2  setosa
## 24          5.1         3.3          1.7         0.5  setosa
## 25          4.8         3.4          1.9         0.2  setosa
## 26          5.0         3.0          1.6         0.2  setosa
## 27          5.0         3.4          1.6         0.4  setosa
## 28          5.2         3.5          1.5         0.2  setosa
## 29          5.2         3.4          1.4         0.2  setosa
## 30          4.7         3.2          1.6         0.2  setosa
## 31          4.8         3.1          1.6         0.2  setosa
## 32          5.4         3.4          1.5         0.4  setosa
## 33          5.2         4.1          1.5         0.1  setosa
## 34          5.5         4.2          1.4         0.2  setosa
## 35          4.9         3.1          1.5         0.2  setosa
## 36          5.0         3.2          1.2         0.2  setosa
## 37          5.5         3.5          1.3         0.2  setosa
## 38          4.9         3.6          1.4         0.1  setosa
## 39          4.4         3.0          1.3         0.2  setosa
## 40          5.1         3.4          1.5         0.2  setosa
## 41          5.0         3.5          1.3         0.3  setosa
## 42          4.5         2.3          1.3         0.3  setosa
## 43          4.4         3.2          1.3         0.2  setosa
## 44          5.0         3.5          1.6         0.6  setosa
## 45          5.1         3.8          1.9         0.4  setosa
## 46          4.8         3.0          1.4         0.3  setosa
## 47          5.1         3.8          1.6         0.2  setosa
## 48          4.6         3.2          1.4         0.2  setosa
## 49          5.3         3.7          1.5         0.2  setosa
## 50          5.0         3.3          1.4         0.2  setosa
##    Sepal.Length.ord
## 1       (5.02,5.74]
## 2        (4.3,5.02]
## 3        (4.3,5.02]
## 4        (4.3,5.02]
## 5        (4.3,5.02]
## 6       (5.02,5.74]
## 7        (4.3,5.02]
## 8        (4.3,5.02]
## 9        (4.3,5.02]
## 10       (4.3,5.02]
## 11      (5.02,5.74]
## 12       (4.3,5.02]
## 13       (4.3,5.02]
## 14       (4.3,5.02]
## 15      (5.74,6.46]
## 16      (5.02,5.74]
## 17      (5.02,5.74]
## 18      (5.02,5.74]
## 19      (5.02,5.74]
## 20      (5.02,5.74]
## 21      (5.02,5.74]
## 22      (5.02,5.74]
## 23       (4.3,5.02]
## 24      (5.02,5.74]
## 25       (4.3,5.02]
## 26       (4.3,5.02]
## 27       (4.3,5.02]
## 28      (5.02,5.74]
## 29      (5.02,5.74]
## 30       (4.3,5.02]
## 31       (4.3,5.02]
## 32      (5.02,5.74]
## 33      (5.02,5.74]
## 34      (5.02,5.74]
## 35       (4.3,5.02]
## 36       (4.3,5.02]
## 37      (5.02,5.74]
## 38       (4.3,5.02]
## 39       (4.3,5.02]
## 40      (5.02,5.74]
## 41       (4.3,5.02]
## 42       (4.3,5.02]
## 43       (4.3,5.02]
## 44       (4.3,5.02]
## 45      (5.02,5.74]
## 46       (4.3,5.02]
## 47      (5.02,5.74]
## 48       (4.3,5.02]
## 49      (5.02,5.74]
## 50       (4.3,5.02]
subset(iris, subset = Species == "setosa" & Sepal.Length > 5.5)
##    Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 15          5.8         4.0          1.2         0.2  setosa
## 16          5.7         4.4          1.5         0.4  setosa
## 19          5.7         3.8          1.7         0.3  setosa
##    Sepal.Length.ord
## 15      (5.74,6.46]
## 16      (5.02,5.74]
## 19      (5.02,5.74]
subset(iris, select = c(Sepal.Length, Species))
##     Sepal.Length    Species
## 1            5.1     setosa
## 2            4.9     setosa
## 3            4.7     setosa
## 4            4.6     setosa
## 5            5.0     setosa
## 6            5.4     setosa
## 7            4.6     setosa
## 8            5.0     setosa
## 9            4.4     setosa
## 10           4.9     setosa
## 11           5.4     setosa
## 12           4.8     setosa
## 13           4.8     setosa
## 14           4.3     setosa
## 15           5.8     setosa
## 16           5.7     setosa
## 17           5.4     setosa
## 18           5.1     setosa
## 19           5.7     setosa
## 20           5.1     setosa
## 21           5.4     setosa
## 22           5.1     setosa
## 23           4.6     setosa
## 24           5.1     setosa
## 25           4.8     setosa
## 26           5.0     setosa
## 27           5.0     setosa
## 28           5.2     setosa
## 29           5.2     setosa
## 30           4.7     setosa
## 31           4.8     setosa
## 32           5.4     setosa
## 33           5.2     setosa
## 34           5.5     setosa
## 35           4.9     setosa
## 36           5.0     setosa
## 37           5.5     setosa
## 38           4.9     setosa
## 39           4.4     setosa
## 40           5.1     setosa
## 41           5.0     setosa
## 42           4.5     setosa
## 43           4.4     setosa
## 44           5.0     setosa
## 45           5.1     setosa
## 46           4.8     setosa
## 47           5.1     setosa
## 48           4.6     setosa
## 49           5.3     setosa
## 50           5.0     setosa
## 51           7.0 versicolor
## 52           6.4 versicolor
## 53           6.9 versicolor
## 54           5.5 versicolor
## 55           6.5 versicolor
## 56           5.7 versicolor
## 57           6.3 versicolor
## 58           4.9 versicolor
## 59           6.6 versicolor
## 60           5.2 versicolor
## 61           5.0 versicolor
## 62           5.9 versicolor
## 63           6.0 versicolor
## 64           6.1 versicolor
## 65           5.6 versicolor
## 66           6.7 versicolor
## 67           5.6 versicolor
## 68           5.8 versicolor
## 69           6.2 versicolor
## 70           5.6 versicolor
## 71           5.9 versicolor
## 72           6.1 versicolor
## 73           6.3 versicolor
## 74           6.1 versicolor
## 75           6.4 versicolor
## 76           6.6 versicolor
## 77           6.8 versicolor
## 78           6.7 versicolor
## 79           6.0 versicolor
## 80           5.7 versicolor
## 81           5.5 versicolor
## 82           5.5 versicolor
## 83           5.8 versicolor
## 84           6.0 versicolor
## 85           5.4 versicolor
## 86           6.0 versicolor
## 87           6.7 versicolor
## 88           6.3 versicolor
## 89           5.6 versicolor
## 90           5.5 versicolor
## 91           5.5 versicolor
## 92           6.1 versicolor
## 93           5.8 versicolor
## 94           5.0 versicolor
## 95           5.6 versicolor
## 96           5.7 versicolor
## 97           5.7 versicolor
## 98           6.2 versicolor
## 99           5.1 versicolor
## 100          5.7 versicolor
## 101          6.3  virginica
## 102          5.8  virginica
## 103          7.1  virginica
## 104          6.3  virginica
## 105          6.5  virginica
## 106          7.6  virginica
## 107          4.9  virginica
## 108          7.3  virginica
## 109          6.7  virginica
## 110          7.2  virginica
## 111          6.5  virginica
## 112          6.4  virginica
## 113          6.8  virginica
## 114          5.7  virginica
## 115          5.8  virginica
## 116          6.4  virginica
## 117          6.5  virginica
## 118          7.7  virginica
## 119          7.7  virginica
## 120          6.0  virginica
## 121          6.9  virginica
## 122          5.6  virginica
## 123          7.7  virginica
## 124          6.3  virginica
## 125          6.7  virginica
## 126          7.2  virginica
## 127          6.2  virginica
## 128          6.1  virginica
## 129          6.4  virginica
## 130          7.2  virginica
## 131          7.4  virginica
## 132          7.9  virginica
## 133          6.4  virginica
## 134          6.3  virginica
## 135          6.1  virginica
## 136          7.7  virginica
## 137          6.3  virginica
## 138          6.4  virginica
## 139          6.0  virginica
## 140          6.9  virginica
## 141          6.7  virginica
## 142          6.9  virginica
## 143          5.8  virginica
## 144          6.8  virginica
## 145          6.7  virginica
## 146          6.7  virginica
## 147          6.3  virginica
## 148          6.5  virginica
## 149          6.2  virginica
## 150          5.9  virginica
subset(iris, 
       subset = Species == "setosa" & Sepal.Length > 5.5, 
       select = c(Sepal.Length, Species))
##    Sepal.Length Species
## 15          5.8  setosa
## 16          5.7  setosa
## 19          5.7  setosa

transform()

transform(iris, Sepal.Length.ord = cut(Sepal.Length, 5))
##     Sepal.Length Sepal.Width Petal.Length Petal.Width    Species
## 1            5.1         3.5          1.4         0.2     setosa
## 2            4.9         3.0          1.4         0.2     setosa
## 3            4.7         3.2          1.3         0.2     setosa
## 4            4.6         3.1          1.5         0.2     setosa
## 5            5.0         3.6          1.4         0.2     setosa
## 6            5.4         3.9          1.7         0.4     setosa
## 7            4.6         3.4          1.4         0.3     setosa
## 8            5.0         3.4          1.5         0.2     setosa
## 9            4.4         2.9          1.4         0.2     setosa
## 10           4.9         3.1          1.5         0.1     setosa
## 11           5.4         3.7          1.5         0.2     setosa
## 12           4.8         3.4          1.6         0.2     setosa
## 13           4.8         3.0          1.4         0.1     setosa
## 14           4.3         3.0          1.1         0.1     setosa
## 15           5.8         4.0          1.2         0.2     setosa
## 16           5.7         4.4          1.5         0.4     setosa
## 17           5.4         3.9          1.3         0.4     setosa
## 18           5.1         3.5          1.4         0.3     setosa
## 19           5.7         3.8          1.7         0.3     setosa
## 20           5.1         3.8          1.5         0.3     setosa
## 21           5.4         3.4          1.7         0.2     setosa
## 22           5.1         3.7          1.5         0.4     setosa
## 23           4.6         3.6          1.0         0.2     setosa
## 24           5.1         3.3          1.7         0.5     setosa
## 25           4.8         3.4          1.9         0.2     setosa
## 26           5.0         3.0          1.6         0.2     setosa
## 27           5.0         3.4          1.6         0.4     setosa
## 28           5.2         3.5          1.5         0.2     setosa
## 29           5.2         3.4          1.4         0.2     setosa
## 30           4.7         3.2          1.6         0.2     setosa
## 31           4.8         3.1          1.6         0.2     setosa
## 32           5.4         3.4          1.5         0.4     setosa
## 33           5.2         4.1          1.5         0.1     setosa
## 34           5.5         4.2          1.4         0.2     setosa
## 35           4.9         3.1          1.5         0.2     setosa
## 36           5.0         3.2          1.2         0.2     setosa
## 37           5.5         3.5          1.3         0.2     setosa
## 38           4.9         3.6          1.4         0.1     setosa
## 39           4.4         3.0          1.3         0.2     setosa
## 40           5.1         3.4          1.5         0.2     setosa
## 41           5.0         3.5          1.3         0.3     setosa
## 42           4.5         2.3          1.3         0.3     setosa
## 43           4.4         3.2          1.3         0.2     setosa
## 44           5.0         3.5          1.6         0.6     setosa
## 45           5.1         3.8          1.9         0.4     setosa
## 46           4.8         3.0          1.4         0.3     setosa
## 47           5.1         3.8          1.6         0.2     setosa
## 48           4.6         3.2          1.4         0.2     setosa
## 49           5.3         3.7          1.5         0.2     setosa
## 50           5.0         3.3          1.4         0.2     setosa
## 51           7.0         3.2          4.7         1.4 versicolor
## 52           6.4         3.2          4.5         1.5 versicolor
## 53           6.9         3.1          4.9         1.5 versicolor
## 54           5.5         2.3          4.0         1.3 versicolor
## 55           6.5         2.8          4.6         1.5 versicolor
## 56           5.7         2.8          4.5         1.3 versicolor
## 57           6.3         3.3          4.7         1.6 versicolor
## 58           4.9         2.4          3.3         1.0 versicolor
## 59           6.6         2.9          4.6         1.3 versicolor
## 60           5.2         2.7          3.9         1.4 versicolor
## 61           5.0         2.0          3.5         1.0 versicolor
## 62           5.9         3.0          4.2         1.5 versicolor
## 63           6.0         2.2          4.0         1.0 versicolor
## 64           6.1         2.9          4.7         1.4 versicolor
## 65           5.6         2.9          3.6         1.3 versicolor
## 66           6.7         3.1          4.4         1.4 versicolor
## 67           5.6         3.0          4.5         1.5 versicolor
## 68           5.8         2.7          4.1         1.0 versicolor
## 69           6.2         2.2          4.5         1.5 versicolor
## 70           5.6         2.5          3.9         1.1 versicolor
## 71           5.9         3.2          4.8         1.8 versicolor
## 72           6.1         2.8          4.0         1.3 versicolor
## 73           6.3         2.5          4.9         1.5 versicolor
## 74           6.1         2.8          4.7         1.2 versicolor
## 75           6.4         2.9          4.3         1.3 versicolor
## 76           6.6         3.0          4.4         1.4 versicolor
## 77           6.8         2.8          4.8         1.4 versicolor
## 78           6.7         3.0          5.0         1.7 versicolor
## 79           6.0         2.9          4.5         1.5 versicolor
## 80           5.7         2.6          3.5         1.0 versicolor
## 81           5.5         2.4          3.8         1.1 versicolor
## 82           5.5         2.4          3.7         1.0 versicolor
## 83           5.8         2.7          3.9         1.2 versicolor
## 84           6.0         2.7          5.1         1.6 versicolor
## 85           5.4         3.0          4.5         1.5 versicolor
## 86           6.0         3.4          4.5         1.6 versicolor
## 87           6.7         3.1          4.7         1.5 versicolor
## 88           6.3         2.3          4.4         1.3 versicolor
## 89           5.6         3.0          4.1         1.3 versicolor
## 90           5.5         2.5          4.0         1.3 versicolor
## 91           5.5         2.6          4.4         1.2 versicolor
## 92           6.1         3.0          4.6         1.4 versicolor
## 93           5.8         2.6          4.0         1.2 versicolor
## 94           5.0         2.3          3.3         1.0 versicolor
## 95           5.6         2.7          4.2         1.3 versicolor
## 96           5.7         3.0          4.2         1.2 versicolor
## 97           5.7         2.9          4.2         1.3 versicolor
## 98           6.2         2.9          4.3         1.3 versicolor
## 99           5.1         2.5          3.0         1.1 versicolor
## 100          5.7         2.8          4.1         1.3 versicolor
## 101          6.3         3.3          6.0         2.5  virginica
## 102          5.8         2.7          5.1         1.9  virginica
## 103          7.1         3.0          5.9         2.1  virginica
## 104          6.3         2.9          5.6         1.8  virginica
## 105          6.5         3.0          5.8         2.2  virginica
## 106          7.6         3.0          6.6         2.1  virginica
## 107          4.9         2.5          4.5         1.7  virginica
## 108          7.3         2.9          6.3         1.8  virginica
## 109          6.7         2.5          5.8         1.8  virginica
## 110          7.2         3.6          6.1         2.5  virginica
## 111          6.5         3.2          5.1         2.0  virginica
## 112          6.4         2.7          5.3         1.9  virginica
## 113          6.8         3.0          5.5         2.1  virginica
## 114          5.7         2.5          5.0         2.0  virginica
## 115          5.8         2.8          5.1         2.4  virginica
## 116          6.4         3.2          5.3         2.3  virginica
## 117          6.5         3.0          5.5         1.8  virginica
## 118          7.7         3.8          6.7         2.2  virginica
## 119          7.7         2.6          6.9         2.3  virginica
## 120          6.0         2.2          5.0         1.5  virginica
## 121          6.9         3.2          5.7         2.3  virginica
## 122          5.6         2.8          4.9         2.0  virginica
## 123          7.7         2.8          6.7         2.0  virginica
## 124          6.3         2.7          4.9         1.8  virginica
## 125          6.7         3.3          5.7         2.1  virginica
## 126          7.2         3.2          6.0         1.8  virginica
## 127          6.2         2.8          4.8         1.8  virginica
## 128          6.1         3.0          4.9         1.8  virginica
## 129          6.4         2.8          5.6         2.1  virginica
## 130          7.2         3.0          5.8         1.6  virginica
## 131          7.4         2.8          6.1         1.9  virginica
## 132          7.9         3.8          6.4         2.0  virginica
## 133          6.4         2.8          5.6         2.2  virginica
## 134          6.3         2.8          5.1         1.5  virginica
## 135          6.1         2.6          5.6         1.4  virginica
## 136          7.7         3.0          6.1         2.3  virginica
## 137          6.3         3.4          5.6         2.4  virginica
## 138          6.4         3.1          5.5         1.8  virginica
## 139          6.0         3.0          4.8         1.8  virginica
## 140          6.9         3.1          5.4         2.1  virginica
## 141          6.7         3.1          5.6         2.4  virginica
## 142          6.9         3.1          5.1         2.3  virginica
## 143          5.8         2.7          5.1         1.9  virginica
## 144          6.8         3.2          5.9         2.3  virginica
## 145          6.7         3.3          5.7         2.5  virginica
## 146          6.7         3.0          5.2         2.3  virginica
## 147          6.3         2.5          5.0         1.9  virginica
## 148          6.5         3.0          5.2         2.0  virginica
## 149          6.2         3.4          5.4         2.3  virginica
## 150          5.9         3.0          5.1         1.8  virginica
##     Sepal.Length.ord
## 1        (5.02,5.74]
## 2         (4.3,5.02]
## 3         (4.3,5.02]
## 4         (4.3,5.02]
## 5         (4.3,5.02]
## 6        (5.02,5.74]
## 7         (4.3,5.02]
## 8         (4.3,5.02]
## 9         (4.3,5.02]
## 10        (4.3,5.02]
## 11       (5.02,5.74]
## 12        (4.3,5.02]
## 13        (4.3,5.02]
## 14        (4.3,5.02]
## 15       (5.74,6.46]
## 16       (5.02,5.74]
## 17       (5.02,5.74]
## 18       (5.02,5.74]
## 19       (5.02,5.74]
## 20       (5.02,5.74]
## 21       (5.02,5.74]
## 22       (5.02,5.74]
## 23        (4.3,5.02]
## 24       (5.02,5.74]
## 25        (4.3,5.02]
## 26        (4.3,5.02]
## 27        (4.3,5.02]
## 28       (5.02,5.74]
## 29       (5.02,5.74]
## 30        (4.3,5.02]
## 31        (4.3,5.02]
## 32       (5.02,5.74]
## 33       (5.02,5.74]
## 34       (5.02,5.74]
## 35        (4.3,5.02]
## 36        (4.3,5.02]
## 37       (5.02,5.74]
## 38        (4.3,5.02]
## 39        (4.3,5.02]
## 40       (5.02,5.74]
## 41        (4.3,5.02]
## 42        (4.3,5.02]
## 43        (4.3,5.02]
## 44        (4.3,5.02]
## 45       (5.02,5.74]
## 46        (4.3,5.02]
## 47       (5.02,5.74]
## 48        (4.3,5.02]
## 49       (5.02,5.74]
## 50        (4.3,5.02]
## 51       (6.46,7.18]
## 52       (5.74,6.46]
## 53       (6.46,7.18]
## 54       (5.02,5.74]
## 55       (6.46,7.18]
## 56       (5.02,5.74]
## 57       (5.74,6.46]
## 58        (4.3,5.02]
## 59       (6.46,7.18]
## 60       (5.02,5.74]
## 61        (4.3,5.02]
## 62       (5.74,6.46]
## 63       (5.74,6.46]
## 64       (5.74,6.46]
## 65       (5.02,5.74]
## 66       (6.46,7.18]
## 67       (5.02,5.74]
## 68       (5.74,6.46]
## 69       (5.74,6.46]
## 70       (5.02,5.74]
## 71       (5.74,6.46]
## 72       (5.74,6.46]
## 73       (5.74,6.46]
## 74       (5.74,6.46]
## 75       (5.74,6.46]
## 76       (6.46,7.18]
## 77       (6.46,7.18]
## 78       (6.46,7.18]
## 79       (5.74,6.46]
## 80       (5.02,5.74]
## 81       (5.02,5.74]
## 82       (5.02,5.74]
## 83       (5.74,6.46]
## 84       (5.74,6.46]
## 85       (5.02,5.74]
## 86       (5.74,6.46]
## 87       (6.46,7.18]
## 88       (5.74,6.46]
## 89       (5.02,5.74]
## 90       (5.02,5.74]
## 91       (5.02,5.74]
## 92       (5.74,6.46]
## 93       (5.74,6.46]
## 94        (4.3,5.02]
## 95       (5.02,5.74]
## 96       (5.02,5.74]
## 97       (5.02,5.74]
## 98       (5.74,6.46]
## 99       (5.02,5.74]
## 100      (5.02,5.74]
## 101      (5.74,6.46]
## 102      (5.74,6.46]
## 103      (6.46,7.18]
## 104      (5.74,6.46]
## 105      (6.46,7.18]
## 106       (7.18,7.9]
## 107       (4.3,5.02]
## 108       (7.18,7.9]
## 109      (6.46,7.18]
## 110       (7.18,7.9]
## 111      (6.46,7.18]
## 112      (5.74,6.46]
## 113      (6.46,7.18]
## 114      (5.02,5.74]
## 115      (5.74,6.46]
## 116      (5.74,6.46]
## 117      (6.46,7.18]
## 118       (7.18,7.9]
## 119       (7.18,7.9]
## 120      (5.74,6.46]
## 121      (6.46,7.18]
## 122      (5.02,5.74]
## 123       (7.18,7.9]
## 124      (5.74,6.46]
## 125      (6.46,7.18]
## 126       (7.18,7.9]
## 127      (5.74,6.46]
## 128      (5.74,6.46]
## 129      (5.74,6.46]
## 130       (7.18,7.9]
## 131       (7.18,7.9]
## 132       (7.18,7.9]
## 133      (5.74,6.46]
## 134      (5.74,6.46]
## 135      (5.74,6.46]
## 136       (7.18,7.9]
## 137      (5.74,6.46]
## 138      (5.74,6.46]
## 139      (5.74,6.46]
## 140      (6.46,7.18]
## 141      (6.46,7.18]
## 142      (6.46,7.18]
## 143      (5.74,6.46]
## 144      (6.46,7.18]
## 145      (6.46,7.18]
## 146      (6.46,7.18]
## 147      (5.74,6.46]
## 148      (6.46,7.18]
## 149      (5.74,6.46]
## 150      (5.74,6.46]

aggregate()

aggregate(Sepal.Length ~ 0, iris, mean)
##   Sepal.Length
## 1     5.843333
aggregate(Sepal.Length ~ 0, iris, length)
##   Sepal.Length
## 1          150
aggregate(Sepal.Length ~ Species, iris, mean)
##      Species Sepal.Length
## 1     setosa        5.006
## 2 versicolor        5.936
## 3  virginica        6.588
aggregate(Sepal.Length ~ Species, iris, length)
##      Species Sepal.Length
## 1     setosa           50
## 2 versicolor           50
## 3  virginica           50
aggregate(cbind(Sepal.Length, Sepal.Width) ~ Species, iris, mean)
##      Species Sepal.Length Sepal.Width
## 1     setosa        5.006       3.428
## 2 versicolor        5.936       2.770
## 3  virginica        6.588       2.974
aggregate(. ~ Species, iris, mean)
##      Species Sepal.Length Sepal.Width Petal.Length Petal.Width
## 1     setosa        5.006       3.428        1.462       0.246
## 2 versicolor        5.936       2.770        4.260       1.326
## 3  virginica        6.588       2.974        5.552       2.026
##   Sepal.Length.ord
## 1             1.46
## 2             2.70
## 3             3.66
aggregate(Sepal.Length ~ Species, iris, function(v) {
    return(c(mean = mean(v), sd = sd(v)))
    })
##      Species Sepal.Length.mean Sepal.Length.sd
## 1     setosa         5.0060000       0.3524897
## 2 versicolor         5.9360000       0.5161711
## 3  virginica         6.5880000       0.6358796

setNames()

setNames(aggregate(Sepal.Length ~ Species, iris, mean),
         c("Species", "Sepal Length mean"))
##      Species Sepal Length mean
## 1     setosa             5.006
## 2 versicolor             5.936
## 3  virginica             6.588

merge()

a = aggregate(Sepal.Length ~ Species, iris, mean)
a = setNames(a, c("Species", "Sepal Length mean"))
b = aggregate(Sepal.Width ~ Species, iris, min)
b = setNames(b, c("Species", "Sepal Width min"))
merge(a, b)
##      Species Sepal Length mean Sepal Width min
## 1     setosa             5.006             2.3
## 2 versicolor             5.936             2.0
## 3  virginica             6.588             2.2
a = aggregate(Sepal.Length ~ Species, iris, mean)
b = aggregate(Sepal.Width ~ Species, iris, min)
merge(a, b, by = "Species")
##      Species Sepal.Length Sepal.Width
## 1     setosa        5.006         2.3
## 2 versicolor        5.936         2.0
## 3  virginica        6.588         2.2

Data visualization

In the following code, we need two packages:

library ggplot2

library(ggplot2)

Two functions: qplot() and ggplot(). The first one is a simplier version of the second one. We focus here on the ggplot().

Univariate

Quantitative
ggplot(iris, aes(Sepal.Length)) + geom_histogram()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(iris, aes(Sepal.Length)) + geom_density()

ggplot(iris, aes(Sepal.Length)) + 
    geom_histogram(aes(y = ..density..)) + 
    geom_density()
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(iris, aes(sample = Sepal.Length)) + geom_qq()

ggplot(iris, aes(0, Sepal.Length)) + geom_boxplot()

ggplot(iris, aes(Sepal.Length)) + stat_ecdf()

Qualitative
ggplot(iris, aes(Sepal.Length.ord)) + geom_bar()

ggplot(iris, aes(Sepal.Length.ord)) + 
    geom_bar(aes(y = (..count../(sum(..count..))))) 

library(scales)
ggplot(iris, aes(Sepal.Length.ord)) + 
    geom_bar(aes(y = (..count../(sum(..count..))))) +
    scale_y_continuous(labels = percent) 

ggplot(iris, aes("", fill = Sepal.Length.ord)) + 
    geom_bar(aes(y = (..count..)/sum(..count..))) +
    scale_y_continuous(labels = percent)

ggplot(iris, aes("", fill = Sepal.Length.ord)) + 
    geom_bar(aes(y = (..count..)/sum(..count..)), width = 1) +
    scale_y_continuous(labels = percent) +
    coord_polar(theta = "y")

Bivariate

Two Quantitatives
ggplot(iris, aes(Sepal.Length, Sepal.Width)) + geom_point()

ggplot(iris, aes(Sepal.Length, Sepal.Width)) + geom_rug()

ggplot(iris, aes(Sepal.Length, Sepal.Width)) + geom_smooth()
## `geom_smooth()` using method = 'loess'

ggplot(iris, aes(Sepal.Length, Sepal.Width)) + geom_smooth(method = "lm")

ggplot(iris, aes(Sepal.Length, Sepal.Width)) + 
    geom_point() + 
    geom_rug() + 
    geom_smooth(method = "lm")

ggplot(iris, aes(Sepal.Length, Sepal.Width)) + geom_bin2d(bins = 10)

Two qualitatives
ggplot(iris, aes(Sepal.Length.ord)) + geom_bar() + facet_wrap(~ Species)

ggplot(iris, aes(Sepal.Length.ord, fill = Species)) + geom_bar()

ggplot(iris, aes(Sepal.Length.ord, fill = Species)) + 
    geom_bar(position = "fill") +
    scale_y_continuous(labels = percent)

ggplot(iris, aes("", fill = Sepal.Length.ord)) + 
    geom_bar(aes(y = (..count..)/sum(..count..)), width = 1) +
    scale_y_continuous(labels = percent) +
    coord_polar(theta = "y") + 
    facet_wrap(~ Species)

ggplot(iris, aes(Species, Sepal.Length.ord)) + geom_bin2d()

Qualitative vs. Quantitative
ggplot(iris, aes(Sepal.Length)) + geom_histogram() + facet_grid(Species ~.)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(iris, aes(Sepal.Length, fill = Species)) + 
    geom_histogram() + facet_grid(Species ~.)
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

ggplot(iris, aes(Sepal.Length, col = Species)) + geom_density()

ggplot(iris, aes(Species, Sepal.Length)) + geom_boxplot()

ggplot(iris, aes(Species, Sepal.Length, fill = Species)) + geom_boxplot()

ggplot(iris, aes(Sepal.Length, col = Species)) + stat_ecdf()

Multivariate

Some graphics with more than 2 variables

ggplot(iris, aes(Petal.Length, Petal.Width, col = Species)) + 
    geom_point()

ggplot(iris, aes(Petal.Length, Petal.Width, col = Species)) + 
    geom_point() + facet_wrap(~ Sepal.Length.ord)

ggplot(iris, aes(Petal.Length, Petal.Width, col = Species)) + 
    geom_point() + facet_grid(Species ~ Sepal.Length.ord)

library FactoMineR

For data analysis, such as Principle Components Analysis (PCA)

library(FactoMineR)
pca = PCA(iris, quali.sup = c(5, 6)) # since we add Sepal.Length.ord to iris data
summary(pca)
## 
## Call:
## PCA(X = iris, quali.sup = c(5, 6)) 
## 
## 
## Eigenvalues
##                        Dim.1   Dim.2   Dim.3   Dim.4
## Variance               2.918   0.914   0.147   0.021
## % of var.             72.962  22.851   3.669   0.518
## Cumulative % of var.  72.962  95.813  99.482 100.000
## 
## Individuals (the 10 first)
##                  Dist    Dim.1    ctr   cos2    Dim.2    ctr   cos2  
## 1            |  2.319 | -2.265  1.172  0.954 |  0.480  0.168  0.043 |
## 2            |  2.202 | -2.081  0.989  0.893 | -0.674  0.331  0.094 |
## 3            |  2.389 | -2.364  1.277  0.979 | -0.342  0.085  0.020 |
## 4            |  2.378 | -2.299  1.208  0.935 | -0.597  0.260  0.063 |
## 5            |  2.476 | -2.390  1.305  0.932 |  0.647  0.305  0.068 |
## 6            |  2.555 | -2.076  0.984  0.660 |  1.489  1.617  0.340 |
## 7            |  2.468 | -2.444  1.364  0.981 |  0.048  0.002  0.000 |
## 8            |  2.246 | -2.233  1.139  0.988 |  0.223  0.036  0.010 |
## 9            |  2.592 | -2.335  1.245  0.812 | -1.115  0.907  0.185 |
## 10           |  2.249 | -2.184  1.090  0.943 | -0.469  0.160  0.043 |
##               Dim.3    ctr   cos2  
## 1            -0.128  0.074  0.003 |
## 2            -0.235  0.250  0.011 |
## 3             0.044  0.009  0.000 |
## 4             0.091  0.038  0.001 |
## 5             0.016  0.001  0.000 |
## 6             0.027  0.003  0.000 |
## 7             0.335  0.511  0.018 |
## 8            -0.089  0.036  0.002 |
## 9             0.145  0.096  0.003 |
## 10           -0.254  0.293  0.013 |
## 
## Variables
##                 Dim.1    ctr   cos2    Dim.2    ctr   cos2    Dim.3    ctr
## Sepal.Length |  0.890 27.151  0.792 |  0.361 14.244  0.130 | -0.276 51.778
## Sepal.Width  | -0.460  7.255  0.212 |  0.883 85.247  0.779 |  0.094  5.972
## Petal.Length |  0.992 33.688  0.983 |  0.023  0.060  0.001 |  0.054  2.020
## Petal.Width  |  0.965 31.906  0.931 |  0.064  0.448  0.004 |  0.243 40.230
##                cos2  
## Sepal.Length  0.076 |
## Sepal.Width   0.009 |
## Petal.Length  0.003 |
## Petal.Width   0.059 |
## 
## Supplementary categories
##                   Dist     Dim.1    cos2  v.test     Dim.2    cos2  v.test
## setosa       |   2.244 |  -2.225   0.983 -11.240 |   0.289   0.017   2.608
## versicolor   |   0.748 |   0.496   0.441   2.508 |  -0.550   0.541  -4.967
## virginica    |   1.753 |   1.728   0.971   8.732 |   0.261   0.022   2.359
## (4.3,5.02]   |   2.070 |  -2.004   0.937  -7.455 |  -0.516   0.062  -3.433
## (5.02,5.74]  |   0.994 |  -0.990   0.992  -4.340 |   0.079   0.006   0.622
## (5.74,6.46]  |   0.979 |   0.950   0.942   4.235 |  -0.214   0.048  -1.707
## (6.46,7.18]  |   1.631 |   1.562   0.917   4.872 |   0.451   0.077   2.514
## (7.18,7.9]   |   2.738 |   2.482   0.822   4.990 |   1.040   0.144   3.736
##                  Dim.3    cos2  v.test  
## setosa       |  -0.043   0.000  -0.965 |
## versicolor   |  -0.096   0.017  -2.166 |
## virginica    |   0.139   0.006   3.131 |
## (4.3,5.02]   |   0.056   0.001   0.935 |
## (5.02,5.74]  |   0.037   0.001   0.721 |
## (5.74,6.46]  |   0.097   0.010   1.925 |
## (6.46,7.18]  |  -0.082   0.003  -1.136 |
## (7.18,7.9]   |  -0.493   0.032  -4.421 |
dimdesc(pca)
## $Dim.1
## $Dim.1$quanti
##              correlation       p.value
## Petal.Length   0.9915552 3.369916e-133
## Petal.Width    0.9649790  6.609632e-88
## Sepal.Length   0.8901688  2.190813e-52
## Sepal.Width   -0.4601427  3.139724e-09
## 
## $Dim.1$quali
##                         R2      p.value
## Species          0.9346162 8.650956e-88
## Sepal.Length.ord 0.7605984 5.445095e-44
## 
## $Dim.1$category
##               Estimate      p.value
## virginica    1.7283051 8.295665e-25
## (7.18,7.9]   2.0821611 2.066701e-07
## (6.46,7.18]  1.1621035 4.207377e-07
## (5.74,6.46]  0.5501108 1.367268e-05
## versicolor   0.4964480 1.164951e-02
## (5.02,5.74] -1.3905151 8.028009e-06
## (4.3,5.02]  -2.4038602 1.051683e-16
## setosa      -2.2247532 2.073453e-62
## 
## 
## $Dim.2
## $Dim.2$quanti
##              correlation      p.value
## Sepal.Width    0.8827163 2.123801e-50
## Sepal.Length   0.3608299 5.731933e-06
## 
## $Dim.2$quali
##                         R2      p.value
## Sepal.Length.ord 0.2006322 1.382761e-06
## Species          0.1657182 1.646217e-06
## 
## $Dim.2$category
##               Estimate      p.value
## (7.18,7.9]   0.8721703 1.395107e-04
## setosa       0.2889275 8.646553e-03
## (6.46,7.18]  0.2831920 1.144684e-02
## virginica    0.2612430 1.783576e-02
## (4.3,5.02]  -0.6843715 4.893669e-04
## versicolor  -0.5501705 2.374413e-07
## 
## 
## $Dim.3
## $Dim.3$quanti
##              correlation      p.value
## Petal.Width    0.2429827 0.0027349555
## Sepal.Length  -0.2756577 0.0006395628
## 
## $Dim.3$quali
##                          R2      p.value
## Sepal.Length.ord 0.15386335 6.671063e-05
## Species          0.06902197 5.212527e-03
## 
## $Dim.3$category
##               Estimate      p.value
## virginica   0.13896861 1.532356e-03
## versicolor -0.09612951 2.983835e-02
## (7.18,7.9] -0.41623009 5.267240e-06
pca$eig
##        eigenvalue percentage of variance cumulative percentage of variance
## comp 1 2.91849782             72.9624454                          72.96245
## comp 2 0.91403047             22.8507618                          95.81321
## comp 3 0.14675688              3.6689219                          99.48213
## comp 4 0.02071484              0.5178709                         100.00000
plot(pca$eig[,3], type = "b")
eig = data.frame(comp = rownames(pca$eig),
                 setNames(pca$eig, c("eigenvalue", "percent", "cum.percent")))
ggplot(eig) +
    geom_bar(aes(comp, percent), stat = "identity") +
    stat_summary(aes(comp, cum.percent, group = 1), 
                 fun.y = sum, geom = "line")
plotellipses(pca)
plot(pca, choix = "ind", habillage = 5, invisible = "quali", label = "none")
ggplot(cbind(iris, pca$ind$coord), aes(Dim.1, Dim.2, col = Species)) +
    geom_point() +
    stat_ellipse()

Some work

Download the two following files :

Data description can be found here: each line represent a draw of a digit between 0 and 9, with 8 points (\((x,y)\) coordinates for each point) and the number drawn.

  1. Import the two files, and group them into one data.frame
    • data.frame dimensions: 10992 rows and 17 columns
    • column names: X1, Y1, X2, Y2, X3, Y3, X4, Y4, X5, Y5, X6, Y6, X7, Y7, X8, Y8, digit
  2. Describe (quickly) all attributes
    • one by one first
    • coordinates with respect to digit
  3. Represent the first "0" drawn as following
  4. Use the preceding code to create a function, with
    • Parameters:
      • a vector with the 16 values of each point (if it is a data.frame, transform it as simple vector)
      • a numeric value (with NULL value by default), denoting the number to drawn (possibly not pass)
      • a boolean vector (with FALSE value by default), indicating if the point number has to be added to the graph
      • a boolean vector (with FALSE value by default), indicating if the plot is to added to the previous one
      • a specific color (with "black" value by default)
    • Output:
      • line representing the drawn
      • number drawn as title (if known)
      • point number (if wanted)
  5. Use the function to represent, in one graph, each first drawn for each number
  6. Compute the mean drawn for each number and represent it, with each drawn in (very) light gray
  7. Perform a PCA on the data, and represent the first plan, with a specific color for each number
  8. Represent each number projections on a specific plot

We conclude here that we surely need to clusters data separatly for each digit, to detect if there really are different ways to write a digit (and how).

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