# Mindanao State University
# General Santos City
# Introduction to R base commands
# Submitted by: Rowie Grace N. Peralta
# Student
# Math Department
# March 18, 2023
# Lab Exercise 1: How to create Lines in with different styles in R
# Step 1: Create Data
x <- 1:10 # Create example data
y <- c(3, 1, 5, 2, 3, 8, 4, 7, 6, 9) # using the c() function to create an array
# Step 2: Plot the line graph using the base plot() command
plot(x, y, type = "l")
# Step 3: Add Main Title & Change Axis Labels
plot(x, y, type = "l",
main = "Hello: This is my Line Plot",
xlab = "My X-Values",
ylab = "My Y-Values")
# Step 4: Add color to the line using the col command
plot(x, y, type = "l",
main = "This is my Line Plot",
xlab = "My X-Values",
ylab = "My Y-Values",
col = "red")
# Step 5: Modify Thickness of Line using lwd command
plot(x, y, type = "l",
main = "This is my Line Plot",
xlab = "My X-Values",
ylab = "My Y-Values",
lwd=7,
col = "green")
# Step 6: Add points to line graph by changing the type command
plot(x, y, type = "b",
main = "This is my Line Plot",
xlab = "My X-Values",
ylab = "My Y-Values",
lwd=3,
col = "blue")
# Lab Exercise 2: How to create Lines in with different styles in R
# Step1: Assign values for different lines. We enclose the entire
# line with parenthesis symbol to force R to display the results instantly
# set the same value for the x variable
(x <- 1:10)
## [1] 1 2 3 4 5 6 7 8 9 10
# set different values for y variables
(y1 <- c(3, 1, 5, 2, 3, 8, 4, 7, 6, 9))
## [1] 3 1 5 2 3 8 4 7 6 9
(y2 <- c(5, 1, 4, 6, 2, 3, 7, 8, 2, 8))
## [1] 5 1 4 6 2 3 7 8 2 8
(y3 <- c(3, 3, 3, 3, 4, 4, 5, 5, 7, 7))
## [1] 3 3 3 3 4 4 5 5 7 7
# Plot first the pair x and y1.
plot(x, y1, type = "b",
main = "This is my Line Plot",
xlab = "My X-Values",
ylab = "My Y-Values",
lwd=3,
col = "blue")
# then Add the two lines (for x,y2) and (x,y3)
lines(x, y2, type = "b", col = "red",lwd=3)
lines(x, y3, type = "b", col = "green",lwd=3)
# Add legend to the plot
legend("topleft",
legend = c("Line y1", "Line y2", "Line y3"),
col = c("black", "red", "green"),
lty = 1)
# Step 2: Create Different Point Symbol for Each
# Line using the pch command
plot(x, y1, type = "b",pch = 16,
main = "This is my Line Plot",
xlab = "My X-Values",
ylab = "My Y-Values",
lwd=3,
col = "blue")
lines(x, y2, type = "b", col = "red",lwd=3, pch = 15)
lines(x, y3, type = "b", col = "green",lwd=3, pch = 8)
# Add legend
legend("topleft",
legend = c("Line y1", "Line y2", "Line y3"),
col = c("black", "red", "green"),
lty = 1)
# Lab Exercise 3: Create Line graph without x values
Pupils <- c(3.55 ,3.54 ,3.53 ,3.61 ,3.65 ,3.63 ,3.61
,3.61 ,3.59 ,3.63 ,3.59 ,3.63 ,3.62 ,3.62
,3.59 ,3.63 ,3.62 ,3.65 ,3.65)
# get number of elements of Pupils
length(Pupils)
## [1] 19
# Display the elements of Pupils
Pupils
## [1] 3.55 3.54 3.53 3.61 3.65 3.63 3.61 3.61 3.59 3.63 3.59 3.63 3.62 3.62 3.59
## [16] 3.63 3.62 3.65 3.65
# You can obtain the plot without x values
plot(Pupils, type = 'o')
# Lab Exercise 4: How to Create vertical, horizontal lines
# We will use buit-in cars dataset in R
# display the cars dataset
cars
## speed dist
## 1 4 2
## 2 4 10
## 3 7 4
## 4 7 22
## 5 8 16
## 6 9 10
## 7 10 18
## 8 10 26
## 9 10 34
## 10 11 17
## 11 11 28
## 12 12 14
## 13 12 20
## 14 12 24
## 15 12 28
## 16 13 26
## 17 13 34
## 18 13 34
## 19 13 46
## 20 14 26
## 21 14 36
## 22 14 60
## 23 14 80
## 24 15 20
## 25 15 26
## 26 15 54
## 27 16 32
## 28 16 40
## 29 17 32
## 30 17 40
## 31 17 50
## 32 18 42
## 33 18 56
## 34 18 76
## 35 18 84
## 36 19 36
## 37 19 46
## 38 19 68
## 39 20 32
## 40 20 48
## 41 20 52
## 42 20 56
## 43 20 64
## 44 22 66
## 45 23 54
## 46 24 70
## 47 24 92
## 48 24 93
## 49 24 120
## 50 25 85
# get the number of rows and columns using dim() command
dim(cars)
## [1] 50 2
# display the variable names of the cars dataset
names(cars)
## [1] "speed" "dist"
# display only the first column of the dataset
cars$speed # using the column name
## [1] 4 4 7 7 8 9 10 10 10 11 11 12 12 12 12 13 13 13 13 14 14 14 14 15 15
## [26] 15 16 16 17 17 17 18 18 18 18 19 19 19 20 20 20 20 20 22 23 24 24 24 24 25
cars[,1] # using the column number
## [1] 4 4 7 7 8 9 10 10 10 11 11 12 12 12 12 13 13 13 13 14 14 14 14 15 15
## [26] 15 16 16 17 17 17 18 18 18 18 19 19 19 20 20 20 20 20 22 23 24 24 24 24 25
# Remarks: the following commands will give you the same result
plot(cars,) # using the comma after the name
plot(cars[,1],cars[,2]) # using the column index 1 and 2
attach(cars); plot(speed,dist) # using the attach command to load the variables
plot(cars$speed,cars$dist) # using the dollar notation
# combine all 4 plots using the par() command
par(mfrow = c(2,2)) # set a 2x2 plot output
plot(cars,) # using the comma after the name
plot(cars[,1],cars[,2]) # using the column index 1 and 2
attach(cars); plot(speed,dist) # using the attach command to load the variables
## The following objects are masked from cars (pos = 3):
##
## dist, speed
plot(cars$speed,cars$dist) # using the dollar notation
par(mfrow = c(1,1)) # reset to default plot setting
# Problem: Create vertical lines using the v command
plot(cars)
abline(v = 15, col = "darkgreen",lwd=3) # vertical line
abline(v = 10, col = "blue",lwd=3) # vertical line
# Problem: Create horizontal lines using the h command
abline(h = 80, col = "darkgreen",lwd=3) # vertical line
abline(h = 20, col = "blue",lwd=3) # vertical line
# Create more lines simultaneously, using a vector of values
plot(cars)
abline(v = c(9, 22,25), col = c("darkgreen", "blue","red"),
lwd = c(1, 3,2), # line thickness
lty = c(2,2,2)) # dashed lines
plot(cars)
abline(v = c(9, 22,25), col = c("darkgreen", "blue","red"),
lwd = c(1, 3,2)) # line thickness and solid lines
# create horizontal lines
plot(cars)
abline(h = 60, col = "red",lty = 1, lwd = 3)
abline(h = 100, col = "red",lty = 2, lwd = 3)
abline(h = 20, col = "red",lty = 3, lwd = 3)
# Lab Exercise 5: How to Plot data by group
# We will use buit-in iris dataset in R
# this dataset is a collection of 4 species of flowers with different
# sepal length and width and also with different petal length and width
dim(iris) # iris dataset has 150 rows and 5 columns
## [1] 150 5
names(iris)
## [1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width" "Species"
# two different commands to get the frequency table
table(iris$Species) # refer to the dataset by variable name
##
## setosa versicolor virginica
## 50 50 50
table(iris[,5]) # refer to the dataset by column number
##
## setosa versicolor virginica
## 50 50 50
# get summary of all columns
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
## setosa :50
## versicolor:50
## virginica :50
##
##
##
#create scatterplot of sepal width vs. sepal length
plot(iris$Sepal.Width, iris$Sepal.Length,
col='steelblue',
main='Scatterplot',
xlab='Sepal Width',
ylab='Sepal Length',
pch=19)
plot(iris$Sepal.Width, iris$Sepal.Length,
col='steelblue',
main='Scatterplot',
xlab='Sepal Width',
ylab='Sepal Length',
pch=1)
# another way to retrieve columns of data
PL <- iris$Petal.Length
PW <- iris$Petal.Width
plot(PL, PW)
# add color by species
plot(PL, PW, col = iris$Species, main= "My Plot")
# draw a line along with the distribution of points
# using the abline and lm commands
abline(lm(PW ~ PL))
# add text annotation
text(5, 0.5, "Regression Line")
legend("topleft", # specify the location of the legend
levels(iris$Species), # specify the levels of species
pch = 1:3, # specify three symbols used for the three species
col = 1:3 # specify three colors for the three species
)
# Lab Exercise 6: Generate advance scatter plot
pairs(iris, col = rainbow(3)[iris$Species]) # set colors by species
# How to filter data for each flower
(Versicolor <- subset(iris, Species == "versicolor"))
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 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
(Setosa <- subset(iris, 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
(Virginica <- subset(iris, Species == "virginica"))
## Sepal.Length Sepal.Width Petal.Length Petal.Width Species
## 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
# Draw boxplot for each type of flower
boxplot(Versicolor[,1:4], main="Versicolor, Rainbow Palette",ylim = c(0,8),las=2, col=rainbow(4))
boxplot(Setosa[,1:4], main="Setosa, Heat color Palette",ylim = c(0,8),las=2, col=heat.colors(4))
boxplot(Virginica[,1:4], main="Virginica, Topo colors Palette",ylim = c(0,8),las=2, col=topo.colors(4))
# Lab Exercise 7: How to load external datasets
# From a local directory
# the folder that contains the file should be specified completely
# using the forward slash symbol instead of the backward splash
folder <- "C:/Users/rowie grace/OneDrive/Desktop/New folder"
filename<- "Cancer.csv"
(file <- paste0(folder,"/",filename))
## [1] "C:/Users/rowie grace/OneDrive/Desktop/New folder/Cancer.csv"
cancer <- read.csv (file)
dim(cancer)
## [1] 173 17
names(cancer)
## [1] "country" "incomeperperson" "alcconsumption"
## [4] "armedforcesrate" "breastcancer" "co2emissions"
## [7] "femaleemployrate" "hivrate" "internetuserate"
## [10] "lifeexpectancy" "oilperperson" "polityscore"
## [13] "relectricperperson" "suicideper100th" "employrate"
## [16] "urbanrate" "continent"
# compute mean value for every continent
(means <- round(tapply(cancer$breastcancer, cancer$continent, mean), digits=2))
## AF AS EE LATAM NORAM OC WE
## 24.02 24.51 49.44 36.70 71.73 45.80 74.80
# draw boxplot per continent
boxplot(cancer$breastcancer ~ cancer$continent, main= "Breast cancer by continent (brown dot = mean value)", xlab="continents", ylab="new cases per 100,00 residents", col=rainbow(7))
# insert the mean value using brown dot
points(means, col="brown", pch=18)
# Lab Exercise 8: How to load external datasets and change data layout
folder <- "C:/Users/rowie grace/OneDrive/Desktop/New folder"
filename <- "hsb2.csv"
(file <- paste0(folder,"/",filename))
## [1] "C:/Users/rowie grace/OneDrive/Desktop/New folder/hsb2.csv"
hsb2_wide <- read.csv(file)
# display only the top 6 rows
head(hsb2_wide)
## X id female race ses schtyp prog read write math science socst
## 1 1 70 0 4 1 1 1 57 52 41 47 57
## 2 2 121 1 4 2 1 3 68 59 53 63 61
## 3 3 86 0 4 3 1 1 44 33 54 58 31
## 4 4 141 0 4 3 1 3 63 44 47 53 56
## 5 5 172 0 4 2 1 2 47 52 57 53 61
## 6 6 113 0 4 2 1 2 44 52 51 63 61
# display only the last 6 rows
tail(hsb2_wide)
## X id female race ses schtyp prog read write math science socst
## 195 195 179 1 4 2 2 2 47 65 60 50 56
## 196 196 31 1 2 2 2 1 55 59 52 42 56
## 197 197 145 1 4 2 1 3 42 46 38 36 46
## 198 198 187 1 4 2 2 1 57 41 57 55 52
## 199 199 118 1 4 2 1 1 55 62 58 58 61
## 200 200 137 1 4 3 1 2 63 65 65 53 61
# delete redundant first column (run only once)
(hsb2_wide <- hsb2_wide[-1])
## id female race ses schtyp prog read write math science socst
## 1 70 0 4 1 1 1 57 52 41 47 57
## 2 121 1 4 2 1 3 68 59 53 63 61
## 3 86 0 4 3 1 1 44 33 54 58 31
## 4 141 0 4 3 1 3 63 44 47 53 56
## 5 172 0 4 2 1 2 47 52 57 53 61
## 6 113 0 4 2 1 2 44 52 51 63 61
## 7 50 0 3 2 1 1 50 59 42 53 61
## 8 11 0 1 2 1 2 34 46 45 39 36
## 9 84 0 4 2 1 1 63 57 54 58 51
## 10 48 0 3 2 1 2 57 55 52 50 51
## 11 75 0 4 2 1 3 60 46 51 53 61
## 12 60 0 4 2 1 2 57 65 51 63 61
## 13 95 0 4 3 1 2 73 60 71 61 71
## 14 104 0 4 3 1 2 54 63 57 55 46
## 15 38 0 3 1 1 2 45 57 50 31 56
## 16 115 0 4 1 1 1 42 49 43 50 56
## 17 76 0 4 3 1 2 47 52 51 50 56
## 18 195 0 4 2 2 1 57 57 60 58 56
## 19 114 0 4 3 1 2 68 65 62 55 61
## 20 85 0 4 2 1 1 55 39 57 53 46
## 21 167 0 4 2 1 1 63 49 35 66 41
## 22 143 0 4 2 1 3 63 63 75 72 66
## 23 41 0 3 2 1 2 50 40 45 55 56
## 24 20 0 1 3 1 2 60 52 57 61 61
## 25 12 0 1 2 1 3 37 44 45 39 46
## 26 53 0 3 2 1 3 34 37 46 39 31
## 27 154 0 4 3 1 2 65 65 66 61 66
## 28 178 0 4 2 2 3 47 57 57 58 46
## 29 196 0 4 3 2 2 44 38 49 39 46
## 30 29 0 2 1 1 1 52 44 49 55 41
## 31 126 0 4 2 1 1 42 31 57 47 51
## 32 103 0 4 3 1 2 76 52 64 64 61
## 33 192 0 4 3 2 2 65 67 63 66 71
## 34 150 0 4 2 1 3 42 41 57 72 31
## 35 199 0 4 3 2 2 52 59 50 61 61
## 36 144 0 4 3 1 1 60 65 58 61 66
## 37 200 0 4 2 2 2 68 54 75 66 66
## 38 80 0 4 3 1 2 65 62 68 66 66
## 39 16 0 1 1 1 3 47 31 44 36 36
## 40 153 0 4 2 1 3 39 31 40 39 51
## 41 176 0 4 2 2 2 47 47 41 42 51
## 42 177 0 4 2 2 2 55 59 62 58 51
## 43 168 0 4 2 1 2 52 54 57 55 51
## 44 40 0 3 1 1 1 42 41 43 50 41
## 45 62 0 4 3 1 1 65 65 48 63 66
## 46 169 0 4 1 1 1 55 59 63 69 46
## 47 49 0 3 3 1 3 50 40 39 49 47
## 48 136 0 4 2 1 2 65 59 70 63 51
## 49 189 0 4 2 2 2 47 59 63 53 46
## 50 7 0 1 2 1 2 57 54 59 47 51
## 51 27 0 2 2 1 2 53 61 61 57 56
## 52 128 0 4 3 1 2 39 33 38 47 41
## 53 21 0 1 2 1 1 44 44 61 50 46
## 54 183 0 4 2 2 2 63 59 49 55 71
## 55 132 0 4 2 1 2 73 62 73 69 66
## 56 15 0 1 3 1 3 39 39 44 26 42
## 57 67 0 4 1 1 3 37 37 42 33 32
## 58 22 0 1 2 1 3 42 39 39 56 46
## 59 185 0 4 2 2 2 63 57 55 58 41
## 60 9 0 1 2 1 3 48 49 52 44 51
## 61 181 0 4 2 2 2 50 46 45 58 61
## 62 170 0 4 3 1 2 47 62 61 69 66
## 63 134 0 4 1 1 1 44 44 39 34 46
## 64 108 0 4 2 1 1 34 33 41 36 36
## 65 197 0 4 3 2 2 50 42 50 36 61
## 66 140 0 4 2 1 3 44 41 40 50 26
## 67 171 0 4 2 1 2 60 54 60 55 66
## 68 107 0 4 1 1 3 47 39 47 42 26
## 69 81 0 4 1 1 2 63 43 59 65 44
## 70 18 0 1 2 1 3 50 33 49 44 36
## 71 155 0 4 2 1 1 44 44 46 39 51
## 72 97 0 4 3 1 2 60 54 58 58 61
## 73 68 0 4 2 1 2 73 67 71 63 66
## 74 157 0 4 2 1 1 68 59 58 74 66
## 75 56 0 4 2 1 3 55 45 46 58 51
## 76 5 0 1 1 1 2 47 40 43 45 31
## 77 159 0 4 3 1 2 55 61 54 49 61
## 78 123 0 4 3 1 1 68 59 56 63 66
## 79 164 0 4 2 1 3 31 36 46 39 46
## 80 14 0 1 3 1 2 47 41 54 42 56
## 81 127 0 4 3 1 2 63 59 57 55 56
## 82 165 0 4 1 1 3 36 49 54 61 36
## 83 174 0 4 2 2 2 68 59 71 66 56
## 84 3 0 1 1 1 2 63 65 48 63 56
## 85 58 0 4 2 1 3 55 41 40 44 41
## 86 146 0 4 3 1 2 55 62 64 63 66
## 87 102 0 4 3 1 2 52 41 51 53 56
## 88 117 0 4 3 1 3 34 49 39 42 56
## 89 133 0 4 2 1 3 50 31 40 34 31
## 90 94 0 4 3 1 2 55 49 61 61 56
## 91 24 0 2 2 1 2 52 62 66 47 46
## 92 149 0 4 1 1 1 63 49 49 66 46
## 93 82 1 4 3 1 2 68 62 65 69 61
## 94 8 1 1 1 1 2 39 44 52 44 48
## 95 129 1 4 1 1 1 44 44 46 47 51
## 96 173 1 4 1 1 1 50 62 61 63 51
## 97 57 1 4 2 1 2 71 65 72 66 56
## 98 100 1 4 3 1 2 63 65 71 69 71
## 99 1 1 1 1 1 3 34 44 40 39 41
## 100 194 1 4 3 2 2 63 63 69 61 61
## 101 88 1 4 3 1 2 68 60 64 69 66
## 102 99 1 4 3 1 1 47 59 56 66 61
## 103 47 1 3 1 1 2 47 46 49 33 41
## 104 120 1 4 3 1 2 63 52 54 50 51
## 105 166 1 4 2 1 2 52 59 53 61 51
## 106 65 1 4 2 1 2 55 54 66 42 56
## 107 101 1 4 3 1 2 60 62 67 50 56
## 108 89 1 4 1 1 3 35 35 40 51 33
## 109 54 1 3 1 2 1 47 54 46 50 56
## 110 180 1 4 3 2 2 71 65 69 58 71
## 111 162 1 4 2 1 3 57 52 40 61 56
## 112 4 1 1 1 1 2 44 50 41 39 51
## 113 131 1 4 3 1 2 65 59 57 46 66
## 114 125 1 4 1 1 2 68 65 58 59 56
## 115 34 1 1 3 2 2 73 61 57 55 66
## 116 106 1 4 2 1 3 36 44 37 42 41
## 117 130 1 4 3 1 1 43 54 55 55 46
## 118 93 1 4 3 1 2 73 67 62 58 66
## 119 163 1 4 1 1 2 52 57 64 58 56
## 120 37 1 3 1 1 3 41 47 40 39 51
## 121 35 1 1 1 2 1 60 54 50 50 51
## 122 87 1 4 2 1 1 50 52 46 50 56
## 123 73 1 4 2 1 2 50 52 53 39 56
## 124 151 1 4 2 1 3 47 46 52 48 46
## 125 44 1 3 1 1 3 47 62 45 34 46
## 126 152 1 4 3 1 2 55 57 56 58 61
## 127 105 1 4 2 1 2 50 41 45 44 56
## 128 28 1 2 2 1 1 39 53 54 50 41
## 129 91 1 4 3 1 3 50 49 56 47 46
## 130 45 1 3 1 1 3 34 35 41 29 26
## 131 116 1 4 2 1 2 57 59 54 50 56
## 132 33 1 2 1 1 2 57 65 72 54 56
## 133 66 1 4 2 1 3 68 62 56 50 51
## 134 72 1 4 2 1 3 42 54 47 47 46
## 135 77 1 4 1 1 2 61 59 49 44 66
## 136 61 1 4 3 1 2 76 63 60 67 66
## 137 190 1 4 2 2 2 47 59 54 58 46
## 138 42 1 3 2 1 3 46 52 55 44 56
## 139 2 1 1 2 1 3 39 41 33 42 41
## 140 55 1 3 2 2 2 52 49 49 44 61
## 141 19 1 1 1 1 1 28 46 43 44 51
## 142 90 1 4 3 1 2 42 54 50 50 52
## 143 142 1 4 2 1 3 47 42 52 39 51
## 144 17 1 1 2 1 2 47 57 48 44 41
## 145 122 1 4 2 1 2 52 59 58 53 66
## 146 191 1 4 3 2 2 47 52 43 48 61
## 147 83 1 4 2 1 3 50 62 41 55 31
## 148 182 1 4 2 2 2 44 52 43 44 51
## 149 6 1 1 1 1 2 47 41 46 40 41
## 150 46 1 3 1 1 2 45 55 44 34 41
## 151 43 1 3 1 1 2 47 37 43 42 46
## 152 96 1 4 3 1 2 65 54 61 58 56
## 153 138 1 4 2 1 3 43 57 40 50 51
## 154 10 1 1 2 1 1 47 54 49 53 61
## 155 71 1 4 2 1 1 57 62 56 58 66
## 156 139 1 4 2 1 2 68 59 61 55 71
## 157 110 1 4 2 1 3 52 55 50 54 61
## 158 148 1 4 2 1 3 42 57 51 47 61
## 159 109 1 4 2 1 1 42 39 42 42 41
## 160 39 1 3 3 1 2 66 67 67 61 66
## 161 147 1 4 1 1 2 47 62 53 53 61
## 162 74 1 4 2 1 2 57 50 50 51 58
## 163 198 1 4 3 2 2 47 61 51 63 31
## 164 161 1 4 1 1 2 57 62 72 61 61
## 165 112 1 4 2 1 2 52 59 48 55 61
## 166 69 1 4 1 1 3 44 44 40 40 31
## 167 156 1 4 2 1 2 50 59 53 61 61
## 168 111 1 4 1 1 1 39 54 39 47 36
## 169 186 1 4 2 2 2 57 62 63 55 41
## 170 98 1 4 1 1 3 57 60 51 53 37
## 171 119 1 4 1 1 1 42 57 45 50 43
## 172 13 1 1 2 1 3 47 46 39 47 61
## 173 51 1 3 3 1 1 42 36 42 31 39
## 174 26 1 2 3 1 2 60 59 62 61 51
## 175 36 1 3 1 1 1 44 49 44 35 51
## 176 135 1 4 1 1 2 63 60 65 54 66
## 177 59 1 4 2 1 2 65 67 63 55 71
## 178 78 1 4 2 1 2 39 54 54 53 41
## 179 64 1 4 3 1 3 50 52 45 58 36
## 180 63 1 4 1 1 1 52 65 60 56 51
## 181 79 1 4 2 1 2 60 62 49 50 51
## 182 193 1 4 2 2 2 44 49 48 39 51
## 183 92 1 4 3 1 1 52 67 57 63 61
## 184 160 1 4 2 1 2 55 65 55 50 61
## 185 32 1 2 3 1 3 50 67 66 66 56
## 186 23 1 2 1 1 2 65 65 64 58 71
## 187 158 1 4 2 1 1 52 54 55 53 51
## 188 25 1 2 2 1 1 47 44 42 42 36
## 189 188 1 4 3 2 2 63 62 56 55 61
## 190 52 1 3 1 1 2 50 46 53 53 66
## 191 124 1 4 1 1 3 42 54 41 42 41
## 192 175 1 4 3 2 1 36 57 42 50 41
## 193 184 1 4 2 2 3 50 52 53 55 56
## 194 30 1 2 3 1 2 41 59 42 34 51
## 195 179 1 4 2 2 2 47 65 60 50 56
## 196 31 1 2 2 2 1 55 59 52 42 56
## 197 145 1 4 2 1 3 42 46 38 36 46
## 198 187 1 4 2 2 1 57 41 57 55 52
## 199 118 1 4 2 1 1 55 62 58 58 61
## 200 137 1 4 3 1 2 63 65 65 53 61
# Remarks
# hsb2 dataset consists of 200 selected random samples from senior
# high school students in the US.
# We want to compare the student performance across different subjects
# change data layout by grouping different subjects
# into one column using melt() command. Install first reshape2 package
# install.packages("reshape2")
library(reshape2)
(hsb2_long <- melt(hsb2_wide, measure.vars = c("read","write","math","science","socst")))
## id female race ses schtyp prog variable value
## 1 70 0 4 1 1 1 read 57
## 2 121 1 4 2 1 3 read 68
## 3 86 0 4 3 1 1 read 44
## 4 141 0 4 3 1 3 read 63
## 5 172 0 4 2 1 2 read 47
## 6 113 0 4 2 1 2 read 44
## 7 50 0 3 2 1 1 read 50
## 8 11 0 1 2 1 2 read 34
## 9 84 0 4 2 1 1 read 63
## 10 48 0 3 2 1 2 read 57
## 11 75 0 4 2 1 3 read 60
## 12 60 0 4 2 1 2 read 57
## 13 95 0 4 3 1 2 read 73
## 14 104 0 4 3 1 2 read 54
## 15 38 0 3 1 1 2 read 45
## 16 115 0 4 1 1 1 read 42
## 17 76 0 4 3 1 2 read 47
## 18 195 0 4 2 2 1 read 57
## 19 114 0 4 3 1 2 read 68
## 20 85 0 4 2 1 1 read 55
## 21 167 0 4 2 1 1 read 63
## 22 143 0 4 2 1 3 read 63
## 23 41 0 3 2 1 2 read 50
## 24 20 0 1 3 1 2 read 60
## 25 12 0 1 2 1 3 read 37
## 26 53 0 3 2 1 3 read 34
## 27 154 0 4 3 1 2 read 65
## 28 178 0 4 2 2 3 read 47
## 29 196 0 4 3 2 2 read 44
## 30 29 0 2 1 1 1 read 52
## 31 126 0 4 2 1 1 read 42
## 32 103 0 4 3 1 2 read 76
## 33 192 0 4 3 2 2 read 65
## 34 150 0 4 2 1 3 read 42
## 35 199 0 4 3 2 2 read 52
## 36 144 0 4 3 1 1 read 60
## 37 200 0 4 2 2 2 read 68
## 38 80 0 4 3 1 2 read 65
## 39 16 0 1 1 1 3 read 47
## 40 153 0 4 2 1 3 read 39
## 41 176 0 4 2 2 2 read 47
## 42 177 0 4 2 2 2 read 55
## 43 168 0 4 2 1 2 read 52
## 44 40 0 3 1 1 1 read 42
## 45 62 0 4 3 1 1 read 65
## 46 169 0 4 1 1 1 read 55
## 47 49 0 3 3 1 3 read 50
## 48 136 0 4 2 1 2 read 65
## 49 189 0 4 2 2 2 read 47
## 50 7 0 1 2 1 2 read 57
## 51 27 0 2 2 1 2 read 53
## 52 128 0 4 3 1 2 read 39
## 53 21 0 1 2 1 1 read 44
## 54 183 0 4 2 2 2 read 63
## 55 132 0 4 2 1 2 read 73
## 56 15 0 1 3 1 3 read 39
## 57 67 0 4 1 1 3 read 37
## 58 22 0 1 2 1 3 read 42
## 59 185 0 4 2 2 2 read 63
## 60 9 0 1 2 1 3 read 48
## 61 181 0 4 2 2 2 read 50
## 62 170 0 4 3 1 2 read 47
## 63 134 0 4 1 1 1 read 44
## 64 108 0 4 2 1 1 read 34
## 65 197 0 4 3 2 2 read 50
## 66 140 0 4 2 1 3 read 44
## 67 171 0 4 2 1 2 read 60
## 68 107 0 4 1 1 3 read 47
## 69 81 0 4 1 1 2 read 63
## 70 18 0 1 2 1 3 read 50
## 71 155 0 4 2 1 1 read 44
## 72 97 0 4 3 1 2 read 60
## 73 68 0 4 2 1 2 read 73
## 74 157 0 4 2 1 1 read 68
## 75 56 0 4 2 1 3 read 55
## 76 5 0 1 1 1 2 read 47
## 77 159 0 4 3 1 2 read 55
## 78 123 0 4 3 1 1 read 68
## 79 164 0 4 2 1 3 read 31
## 80 14 0 1 3 1 2 read 47
## 81 127 0 4 3 1 2 read 63
## 82 165 0 4 1 1 3 read 36
## 83 174 0 4 2 2 2 read 68
## 84 3 0 1 1 1 2 read 63
## 85 58 0 4 2 1 3 read 55
## 86 146 0 4 3 1 2 read 55
## 87 102 0 4 3 1 2 read 52
## 88 117 0 4 3 1 3 read 34
## 89 133 0 4 2 1 3 read 50
## 90 94 0 4 3 1 2 read 55
## 91 24 0 2 2 1 2 read 52
## 92 149 0 4 1 1 1 read 63
## 93 82 1 4 3 1 2 read 68
## 94 8 1 1 1 1 2 read 39
## 95 129 1 4 1 1 1 read 44
## 96 173 1 4 1 1 1 read 50
## 97 57 1 4 2 1 2 read 71
## 98 100 1 4 3 1 2 read 63
## 99 1 1 1 1 1 3 read 34
## 100 194 1 4 3 2 2 read 63
## 101 88 1 4 3 1 2 read 68
## 102 99 1 4 3 1 1 read 47
## 103 47 1 3 1 1 2 read 47
## 104 120 1 4 3 1 2 read 63
## 105 166 1 4 2 1 2 read 52
## 106 65 1 4 2 1 2 read 55
## 107 101 1 4 3 1 2 read 60
## 108 89 1 4 1 1 3 read 35
## 109 54 1 3 1 2 1 read 47
## 110 180 1 4 3 2 2 read 71
## 111 162 1 4 2 1 3 read 57
## 112 4 1 1 1 1 2 read 44
## 113 131 1 4 3 1 2 read 65
## 114 125 1 4 1 1 2 read 68
## 115 34 1 1 3 2 2 read 73
## 116 106 1 4 2 1 3 read 36
## 117 130 1 4 3 1 1 read 43
## 118 93 1 4 3 1 2 read 73
## 119 163 1 4 1 1 2 read 52
## 120 37 1 3 1 1 3 read 41
## 121 35 1 1 1 2 1 read 60
## 122 87 1 4 2 1 1 read 50
## 123 73 1 4 2 1 2 read 50
## 124 151 1 4 2 1 3 read 47
## 125 44 1 3 1 1 3 read 47
## 126 152 1 4 3 1 2 read 55
## 127 105 1 4 2 1 2 read 50
## 128 28 1 2 2 1 1 read 39
## 129 91 1 4 3 1 3 read 50
## 130 45 1 3 1 1 3 read 34
## 131 116 1 4 2 1 2 read 57
## 132 33 1 2 1 1 2 read 57
## 133 66 1 4 2 1 3 read 68
## 134 72 1 4 2 1 3 read 42
## 135 77 1 4 1 1 2 read 61
## 136 61 1 4 3 1 2 read 76
## 137 190 1 4 2 2 2 read 47
## 138 42 1 3 2 1 3 read 46
## 139 2 1 1 2 1 3 read 39
## 140 55 1 3 2 2 2 read 52
## 141 19 1 1 1 1 1 read 28
## 142 90 1 4 3 1 2 read 42
## 143 142 1 4 2 1 3 read 47
## 144 17 1 1 2 1 2 read 47
## 145 122 1 4 2 1 2 read 52
## 146 191 1 4 3 2 2 read 47
## 147 83 1 4 2 1 3 read 50
## 148 182 1 4 2 2 2 read 44
## 149 6 1 1 1 1 2 read 47
## 150 46 1 3 1 1 2 read 45
## 151 43 1 3 1 1 2 read 47
## 152 96 1 4 3 1 2 read 65
## 153 138 1 4 2 1 3 read 43
## 154 10 1 1 2 1 1 read 47
## 155 71 1 4 2 1 1 read 57
## 156 139 1 4 2 1 2 read 68
## 157 110 1 4 2 1 3 read 52
## 158 148 1 4 2 1 3 read 42
## 159 109 1 4 2 1 1 read 42
## 160 39 1 3 3 1 2 read 66
## 161 147 1 4 1 1 2 read 47
## 162 74 1 4 2 1 2 read 57
## 163 198 1 4 3 2 2 read 47
## 164 161 1 4 1 1 2 read 57
## 165 112 1 4 2 1 2 read 52
## 166 69 1 4 1 1 3 read 44
## 167 156 1 4 2 1 2 read 50
## 168 111 1 4 1 1 1 read 39
## 169 186 1 4 2 2 2 read 57
## 170 98 1 4 1 1 3 read 57
## 171 119 1 4 1 1 1 read 42
## 172 13 1 1 2 1 3 read 47
## 173 51 1 3 3 1 1 read 42
## 174 26 1 2 3 1 2 read 60
## 175 36 1 3 1 1 1 read 44
## 176 135 1 4 1 1 2 read 63
## 177 59 1 4 2 1 2 read 65
## 178 78 1 4 2 1 2 read 39
## 179 64 1 4 3 1 3 read 50
## 180 63 1 4 1 1 1 read 52
## 181 79 1 4 2 1 2 read 60
## 182 193 1 4 2 2 2 read 44
## 183 92 1 4 3 1 1 read 52
## 184 160 1 4 2 1 2 read 55
## 185 32 1 2 3 1 3 read 50
## 186 23 1 2 1 1 2 read 65
## 187 158 1 4 2 1 1 read 52
## 188 25 1 2 2 1 1 read 47
## 189 188 1 4 3 2 2 read 63
## 190 52 1 3 1 1 2 read 50
## 191 124 1 4 1 1 3 read 42
## 192 175 1 4 3 2 1 read 36
## 193 184 1 4 2 2 3 read 50
## 194 30 1 2 3 1 2 read 41
## 195 179 1 4 2 2 2 read 47
## 196 31 1 2 2 2 1 read 55
## 197 145 1 4 2 1 3 read 42
## 198 187 1 4 2 2 1 read 57
## 199 118 1 4 2 1 1 read 55
## 200 137 1 4 3 1 2 read 63
## 201 70 0 4 1 1 1 write 52
## 202 121 1 4 2 1 3 write 59
## 203 86 0 4 3 1 1 write 33
## 204 141 0 4 3 1 3 write 44
## 205 172 0 4 2 1 2 write 52
## 206 113 0 4 2 1 2 write 52
## 207 50 0 3 2 1 1 write 59
## 208 11 0 1 2 1 2 write 46
## 209 84 0 4 2 1 1 write 57
## 210 48 0 3 2 1 2 write 55
## 211 75 0 4 2 1 3 write 46
## 212 60 0 4 2 1 2 write 65
## 213 95 0 4 3 1 2 write 60
## 214 104 0 4 3 1 2 write 63
## 215 38 0 3 1 1 2 write 57
## 216 115 0 4 1 1 1 write 49
## 217 76 0 4 3 1 2 write 52
## 218 195 0 4 2 2 1 write 57
## 219 114 0 4 3 1 2 write 65
## 220 85 0 4 2 1 1 write 39
## 221 167 0 4 2 1 1 write 49
## 222 143 0 4 2 1 3 write 63
## 223 41 0 3 2 1 2 write 40
## 224 20 0 1 3 1 2 write 52
## 225 12 0 1 2 1 3 write 44
## 226 53 0 3 2 1 3 write 37
## 227 154 0 4 3 1 2 write 65
## 228 178 0 4 2 2 3 write 57
## 229 196 0 4 3 2 2 write 38
## 230 29 0 2 1 1 1 write 44
## 231 126 0 4 2 1 1 write 31
## 232 103 0 4 3 1 2 write 52
## 233 192 0 4 3 2 2 write 67
## 234 150 0 4 2 1 3 write 41
## 235 199 0 4 3 2 2 write 59
## 236 144 0 4 3 1 1 write 65
## 237 200 0 4 2 2 2 write 54
## 238 80 0 4 3 1 2 write 62
## 239 16 0 1 1 1 3 write 31
## 240 153 0 4 2 1 3 write 31
## 241 176 0 4 2 2 2 write 47
## 242 177 0 4 2 2 2 write 59
## 243 168 0 4 2 1 2 write 54
## 244 40 0 3 1 1 1 write 41
## 245 62 0 4 3 1 1 write 65
## 246 169 0 4 1 1 1 write 59
## 247 49 0 3 3 1 3 write 40
## 248 136 0 4 2 1 2 write 59
## 249 189 0 4 2 2 2 write 59
## 250 7 0 1 2 1 2 write 54
## 251 27 0 2 2 1 2 write 61
## 252 128 0 4 3 1 2 write 33
## 253 21 0 1 2 1 1 write 44
## 254 183 0 4 2 2 2 write 59
## 255 132 0 4 2 1 2 write 62
## 256 15 0 1 3 1 3 write 39
## 257 67 0 4 1 1 3 write 37
## 258 22 0 1 2 1 3 write 39
## 259 185 0 4 2 2 2 write 57
## 260 9 0 1 2 1 3 write 49
## 261 181 0 4 2 2 2 write 46
## 262 170 0 4 3 1 2 write 62
## 263 134 0 4 1 1 1 write 44
## 264 108 0 4 2 1 1 write 33
## 265 197 0 4 3 2 2 write 42
## 266 140 0 4 2 1 3 write 41
## 267 171 0 4 2 1 2 write 54
## 268 107 0 4 1 1 3 write 39
## 269 81 0 4 1 1 2 write 43
## 270 18 0 1 2 1 3 write 33
## 271 155 0 4 2 1 1 write 44
## 272 97 0 4 3 1 2 write 54
## 273 68 0 4 2 1 2 write 67
## 274 157 0 4 2 1 1 write 59
## 275 56 0 4 2 1 3 write 45
## 276 5 0 1 1 1 2 write 40
## 277 159 0 4 3 1 2 write 61
## 278 123 0 4 3 1 1 write 59
## 279 164 0 4 2 1 3 write 36
## 280 14 0 1 3 1 2 write 41
## 281 127 0 4 3 1 2 write 59
## 282 165 0 4 1 1 3 write 49
## 283 174 0 4 2 2 2 write 59
## 284 3 0 1 1 1 2 write 65
## 285 58 0 4 2 1 3 write 41
## 286 146 0 4 3 1 2 write 62
## 287 102 0 4 3 1 2 write 41
## 288 117 0 4 3 1 3 write 49
## 289 133 0 4 2 1 3 write 31
## 290 94 0 4 3 1 2 write 49
## 291 24 0 2 2 1 2 write 62
## 292 149 0 4 1 1 1 write 49
## 293 82 1 4 3 1 2 write 62
## 294 8 1 1 1 1 2 write 44
## 295 129 1 4 1 1 1 write 44
## 296 173 1 4 1 1 1 write 62
## 297 57 1 4 2 1 2 write 65
## 298 100 1 4 3 1 2 write 65
## 299 1 1 1 1 1 3 write 44
## 300 194 1 4 3 2 2 write 63
## 301 88 1 4 3 1 2 write 60
## 302 99 1 4 3 1 1 write 59
## 303 47 1 3 1 1 2 write 46
## 304 120 1 4 3 1 2 write 52
## 305 166 1 4 2 1 2 write 59
## 306 65 1 4 2 1 2 write 54
## 307 101 1 4 3 1 2 write 62
## 308 89 1 4 1 1 3 write 35
## 309 54 1 3 1 2 1 write 54
## 310 180 1 4 3 2 2 write 65
## 311 162 1 4 2 1 3 write 52
## 312 4 1 1 1 1 2 write 50
## 313 131 1 4 3 1 2 write 59
## 314 125 1 4 1 1 2 write 65
## 315 34 1 1 3 2 2 write 61
## 316 106 1 4 2 1 3 write 44
## 317 130 1 4 3 1 1 write 54
## 318 93 1 4 3 1 2 write 67
## 319 163 1 4 1 1 2 write 57
## 320 37 1 3 1 1 3 write 47
## 321 35 1 1 1 2 1 write 54
## 322 87 1 4 2 1 1 write 52
## 323 73 1 4 2 1 2 write 52
## 324 151 1 4 2 1 3 write 46
## 325 44 1 3 1 1 3 write 62
## 326 152 1 4 3 1 2 write 57
## 327 105 1 4 2 1 2 write 41
## 328 28 1 2 2 1 1 write 53
## 329 91 1 4 3 1 3 write 49
## 330 45 1 3 1 1 3 write 35
## 331 116 1 4 2 1 2 write 59
## 332 33 1 2 1 1 2 write 65
## 333 66 1 4 2 1 3 write 62
## 334 72 1 4 2 1 3 write 54
## 335 77 1 4 1 1 2 write 59
## 336 61 1 4 3 1 2 write 63
## 337 190 1 4 2 2 2 write 59
## 338 42 1 3 2 1 3 write 52
## 339 2 1 1 2 1 3 write 41
## 340 55 1 3 2 2 2 write 49
## 341 19 1 1 1 1 1 write 46
## 342 90 1 4 3 1 2 write 54
## 343 142 1 4 2 1 3 write 42
## 344 17 1 1 2 1 2 write 57
## 345 122 1 4 2 1 2 write 59
## 346 191 1 4 3 2 2 write 52
## 347 83 1 4 2 1 3 write 62
## 348 182 1 4 2 2 2 write 52
## 349 6 1 1 1 1 2 write 41
## 350 46 1 3 1 1 2 write 55
## 351 43 1 3 1 1 2 write 37
## 352 96 1 4 3 1 2 write 54
## 353 138 1 4 2 1 3 write 57
## 354 10 1 1 2 1 1 write 54
## 355 71 1 4 2 1 1 write 62
## 356 139 1 4 2 1 2 write 59
## 357 110 1 4 2 1 3 write 55
## 358 148 1 4 2 1 3 write 57
## 359 109 1 4 2 1 1 write 39
## 360 39 1 3 3 1 2 write 67
## 361 147 1 4 1 1 2 write 62
## 362 74 1 4 2 1 2 write 50
## 363 198 1 4 3 2 2 write 61
## 364 161 1 4 1 1 2 write 62
## 365 112 1 4 2 1 2 write 59
## 366 69 1 4 1 1 3 write 44
## 367 156 1 4 2 1 2 write 59
## 368 111 1 4 1 1 1 write 54
## 369 186 1 4 2 2 2 write 62
## 370 98 1 4 1 1 3 write 60
## 371 119 1 4 1 1 1 write 57
## 372 13 1 1 2 1 3 write 46
## 373 51 1 3 3 1 1 write 36
## 374 26 1 2 3 1 2 write 59
## 375 36 1 3 1 1 1 write 49
## 376 135 1 4 1 1 2 write 60
## 377 59 1 4 2 1 2 write 67
## 378 78 1 4 2 1 2 write 54
## 379 64 1 4 3 1 3 write 52
## 380 63 1 4 1 1 1 write 65
## 381 79 1 4 2 1 2 write 62
## 382 193 1 4 2 2 2 write 49
## 383 92 1 4 3 1 1 write 67
## 384 160 1 4 2 1 2 write 65
## 385 32 1 2 3 1 3 write 67
## 386 23 1 2 1 1 2 write 65
## 387 158 1 4 2 1 1 write 54
## 388 25 1 2 2 1 1 write 44
## 389 188 1 4 3 2 2 write 62
## 390 52 1 3 1 1 2 write 46
## 391 124 1 4 1 1 3 write 54
## 392 175 1 4 3 2 1 write 57
## 393 184 1 4 2 2 3 write 52
## 394 30 1 2 3 1 2 write 59
## 395 179 1 4 2 2 2 write 65
## 396 31 1 2 2 2 1 write 59
## 397 145 1 4 2 1 3 write 46
## 398 187 1 4 2 2 1 write 41
## 399 118 1 4 2 1 1 write 62
## 400 137 1 4 3 1 2 write 65
## 401 70 0 4 1 1 1 math 41
## 402 121 1 4 2 1 3 math 53
## 403 86 0 4 3 1 1 math 54
## 404 141 0 4 3 1 3 math 47
## 405 172 0 4 2 1 2 math 57
## 406 113 0 4 2 1 2 math 51
## 407 50 0 3 2 1 1 math 42
## 408 11 0 1 2 1 2 math 45
## 409 84 0 4 2 1 1 math 54
## 410 48 0 3 2 1 2 math 52
## 411 75 0 4 2 1 3 math 51
## 412 60 0 4 2 1 2 math 51
## 413 95 0 4 3 1 2 math 71
## 414 104 0 4 3 1 2 math 57
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## 423 41 0 3 2 1 2 math 45
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## 426 53 0 3 2 1 3 math 46
## 427 154 0 4 3 1 2 math 66
## 428 178 0 4 2 2 3 math 57
## 429 196 0 4 3 2 2 math 49
## 430 29 0 2 1 1 1 math 49
## 431 126 0 4 2 1 1 math 57
## 432 103 0 4 3 1 2 math 64
## 433 192 0 4 3 2 2 math 63
## 434 150 0 4 2 1 3 math 57
## 435 199 0 4 3 2 2 math 50
## 436 144 0 4 3 1 1 math 58
## 437 200 0 4 2 2 2 math 75
## 438 80 0 4 3 1 2 math 68
## 439 16 0 1 1 1 3 math 44
## 440 153 0 4 2 1 3 math 40
## 441 176 0 4 2 2 2 math 41
## 442 177 0 4 2 2 2 math 62
## 443 168 0 4 2 1 2 math 57
## 444 40 0 3 1 1 1 math 43
## 445 62 0 4 3 1 1 math 48
## 446 169 0 4 1 1 1 math 63
## 447 49 0 3 3 1 3 math 39
## 448 136 0 4 2 1 2 math 70
## 449 189 0 4 2 2 2 math 63
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## 488 117 0 4 3 1 3 math 39
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## 497 57 1 4 2 1 2 math 72
## 498 100 1 4 3 1 2 math 71
## 499 1 1 1 1 1 3 math 40
## 500 194 1 4 3 2 2 math 69
## 501 88 1 4 3 1 2 math 64
## 502 99 1 4 3 1 1 math 56
## 503 47 1 3 1 1 2 math 49
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## 506 65 1 4 2 1 2 math 66
## 507 101 1 4 3 1 2 math 67
## 508 89 1 4 1 1 3 math 40
## 509 54 1 3 1 2 1 math 46
## 510 180 1 4 3 2 2 math 69
## 511 162 1 4 2 1 3 math 40
## 512 4 1 1 1 1 2 math 41
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#Remark: Pay extra attention to the last 2 columns
head(hsb2_long)
## id female race ses schtyp prog variable value
## 1 70 0 4 1 1 1 read 57
## 2 121 1 4 2 1 3 read 68
## 3 86 0 4 3 1 1 read 44
## 4 141 0 4 3 1 3 read 63
## 5 172 0 4 2 1 2 read 47
## 6 113 0 4 2 1 2 read 44
tail(hsb2_long)
## id female race ses schtyp prog variable value
## 995 179 1 4 2 2 2 socst 56
## 996 31 1 2 2 2 1 socst 56
## 997 145 1 4 2 1 3 socst 46
## 998 187 1 4 2 2 1 socst 52
## 999 118 1 4 2 1 1 socst 61
## 1000 137 1 4 3 1 2 socst 61
# get thefrequency
table(hsb2_long$variable)
##
## read write math science socst
## 200 200 200 200 200
# This means that the tables hsb2_long and hsb2_wide are the same
# tables displayed in two ways
# display data structure of the hsb2_long dataset
str(hsb2_long)
## 'data.frame': 1000 obs. of 8 variables:
## $ id : int 70 121 86 141 172 113 50 11 84 48 ...
## $ female : int 0 1 0 0 0 0 0 0 0 0 ...
## $ race : int 4 4 4 4 4 4 3 1 4 3 ...
## $ ses : int 1 2 3 3 2 2 2 2 2 2 ...
## $ schtyp : int 1 1 1 1 1 1 1 1 1 1 ...
## $ prog : int 1 3 1 3 2 2 1 2 1 2 ...
## $ variable: Factor w/ 5 levels "read","write",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ value : int 57 68 44 63 47 44 50 34 63 57 ...
# the variables female, race, ses, schtyp, prog are stored as numbers
# for encoding purposes. However these variables are actually qualitative variables
# so we convert each from integer type to categorical type
# defining some variables to become factor variable
# we use another variable to preserve the file hsb2_long
data <- hsb2_long
data$ses = factor(data$ses, labels=c("low", "middle", "high"))
data$schtyp = factor(data$schtyp, labels=c("public", "private"))
data$prog = factor(data$prog, labels=c("general", "academic", "vocational"))
data$race = factor(data$race, labels=c("hispanic", "asian", "african-amer","white"))
data$female = factor(data$female, labels=c("female", "male"))
# check data structure again. The former integer variables are now categorical variable
str(data)
## 'data.frame': 1000 obs. of 8 variables:
## $ id : int 70 121 86 141 172 113 50 11 84 48 ...
## $ female : Factor w/ 2 levels "female","male": 1 2 1 1 1 1 1 1 1 1 ...
## $ race : Factor w/ 4 levels "hispanic","asian",..: 4 4 4 4 4 4 3 1 4 3 ...
## $ ses : Factor w/ 3 levels "low","middle",..: 1 2 3 3 2 2 2 2 2 2 ...
## $ schtyp : Factor w/ 2 levels "public","private": 1 1 1 1 1 1 1 1 1 1 ...
## $ prog : Factor w/ 3 levels "general","academic",..: 1 3 1 3 2 2 1 2 1 2 ...
## $ variable: Factor w/ 5 levels "read","write",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ value : int 57 68 44 63 47 44 50 34 63 57 ...
# we compare student performance by using boxplots
library(gplots)
##
## Attaching package: 'gplots'
## The following object is masked from 'package:stats':
##
## lowess
# compute the average value by group using tapply() command
means <- round(tapply(data$value, data$variable, mean), digits=2)
# create boxplot by group
boxplot(data$value ~ data$variable, main= "Student Performance by Subject (brown dot = mean score)",
xlab="Subject matter", ylab="Percentage Scores", col=rainbow(5))
# insert the average values
points(means, col="brown", pch=18)
# can also compute the median values
medians = round(tapply(data$value, data$variable, median), digits=2)
medians
## read write math science socst
## 50 54 52 53 52
points(medians, col="red", pch=18)
# Lab Exercise 9: How to plot categorical variables
library(ggplot2)
# we load variable names to memory to avoid the dollar notation
attach(hsb2_long)
# create the plot object p
p <- ggplot(hsb2_long, aes(ses, fill = prog)) + facet_wrap(~race)
p + geom_bar()
## Warning: The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
## The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
## The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
## The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
p + geom_bar(position = "dodge")
## Warning: The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
## The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
## The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
## The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
library(ggplot2)
attach(hsb2_long)
## The following objects are masked from hsb2_long (pos = 3):
##
## female, id, prog, race, schtyp, ses, value, variable
p <- ggplot(hsb2_long, aes(ses, fill = prog)) + facet_wrap(~schtyp)
p + geom_bar()
## Warning: The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
## The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
p + geom_bar(position = "dodge")
## Warning: The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
## The following aesthetics were dropped during statistical transformation: fill
## ℹ This can happen when ggplot fails to infer the correct grouping structure in
## the data.
## ℹ Did you forget to specify a `group` aesthetic or to convert a numerical
## variable into a factor?
# Lab Exercise 10: Scatter Plots with marginal Distributions
# Advance Scatter plots using libraries
# install.packages("ggExtra")
# install.packages("tidyverse")
library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.0 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ lubridate 1.9.2 ✔ tibble 3.2.0
## ✔ purrr 1.0.1 ✔ tidyr 1.3.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errors
library(ggExtra)
# set theme appearance of grid background
theme_set(theme_bw(1))
# create X and Y vector
(xAxis <- rnorm(1000)) # normal distribution with mean 0 and sd=1
## [1] 0.0004198344 1.8714405209 1.2095426091 -0.4083386311 -0.9574034944
## [6] 0.9537401581 -0.5604881697 -1.0776455056 0.7813176587 -0.5199671404
## [11] 0.0049742323 -2.2219240772 -1.2461902850 0.0355926893 0.6806511717
## [16] -1.3769070890 0.4618470910 -0.6032610913 -1.2610414885 -1.0786390745
## [21] -0.8700491411 -0.0856777421 -0.7391987917 0.0013214297 2.0348088445
## [26] 0.6785081201 -0.5361816421 0.0948717805 -2.2033818748 1.7553224548
## [31] -0.7650695747 -1.6975967045 0.1843548507 -0.0283691656 -0.8382039928
## [36] -1.1797354328 -0.9567791014 -0.4048423569 1.3116014825 0.8468406635
## [41] 0.3667363844 0.2126520457 -2.2618126469 1.3622483086 0.6124121070
## [46] -0.7341631785 -1.6438376313 -0.4673781088 -0.1674771835 -1.2030988941
## [51] -1.5318877029 -1.7175080641 1.2716263448 0.3916848039 0.3448028237
## [56] -0.0746542642 -1.3682180271 0.9080185992 -1.2752441092 -1.0343318611
## [61] 1.9153285599 0.3182986888 0.1048984499 0.2311638035 -1.0666657291
## [66] 1.2808440411 -1.6694542422 0.6723671797 0.2990716092 0.1901096844
## [71] 0.9903832407 2.0683116012 0.4778890062 1.2337530474 0.5335494126
## [76] -0.1224968622 -0.1785683345 -1.4454404389 0.1604747688 -0.0326987984
## [81] 0.0479016726 0.7539445734 0.2614098848 -1.2492541016 0.3210227484
## [86] 0.5073086056 -0.7190391956 -0.1278956275 -0.5073552962 -0.3717621780
## [91] -0.3742898298 0.2713610375 0.1707915817 0.7081708483 1.1439259440
## [96] -0.7009792816 0.3546245890 0.1167770140 1.5433136446 1.0257084323
## [101] -0.6416804678 0.2847301052 -0.4572140489 1.0835336375 0.6750935711
## [106] 1.8310271226 2.0439329584 0.7399521608 0.9825750709 1.0191788645
## [111] 2.2395740432 -0.5125200577 1.5621667263 0.1748763440 -0.5773508926
## [116] -0.4109427232 0.3831901719 1.0447882940 0.1011009525 0.7381211005
## [121] 0.6839294023 0.2907651826 1.7391490212 0.5880298145 -0.9255475222
## [126] -0.0133840762 0.3601792738 1.4593828588 -0.1428283069 -1.5699159652
## [131] 1.2801900303 -0.8402569184 1.0113311196 1.0827300463 -2.3219818323
## [136] -0.6715494157 0.9768959432 -0.9177387469 1.5674946696 -0.2621862106
## [141] 1.4980911136 1.2672355027 0.8006568501 -0.2589707373 -1.0983693816
## [146] 0.6849702703 -0.0695905820 -0.7594641395 -0.6277427831 -1.0452737107
## [151] -0.4406532417 0.1816362855 -0.0412604941 -0.9790645941 1.9843808783
## [156] 0.1516738149 -1.5112596654 -1.1778141049 -1.7336852036 -0.7116043042
## [161] 1.9423002088 0.4989420145 -0.6023851208 0.8335132929 1.4711818525
## [166] -0.4809504165 1.0892643607 -0.3709977666 -1.9284121957 0.5397422189
## [171] 1.1013986973 -0.2466306091 1.8552991294 1.1586081393 -1.2483978036
## [176] 2.7549906400 0.2159386132 1.4386948164 0.1020479518 -0.0685893338
## [181] 1.3020277869 -0.1836459400 -1.0305094677 0.4947844174 0.2457199848
## [186] 0.5277074483 0.0747163140 1.4708682560 -0.5082703474 -0.4332101157
## [191] -2.1908031361 1.0111347045 -0.1897199635 -1.7222836417 -0.6471191322
## [196] -0.2733113688 -1.0636423475 0.8058750807 -0.1308091734 -0.3829783104
## [201] 1.5551272332 1.3920622298 -1.3976391661 2.1726118390 -0.2297980744
## [206] -0.3778147795 -1.1683430204 0.4835841655 -1.7397040772 0.0103125130
## [211] 0.0772759179 0.3850863328 1.3963255282 0.8249335754 -0.4673069902
## [216] 1.2578183056 1.6528956140 -0.6267425658 -0.8582893094 -0.7830988611
## [221] -1.0944691957 -0.4730449244 -0.8855845043 -1.2748638100 -2.5927629926
## [226] 0.7168422479 0.0101499277 0.2088022985 -0.8056082983 1.8752323712
## [231] -0.7882154380 0.3479105756 0.8513321413 -0.8449642500 0.1974061185
## [236] 0.8874621173 0.6099261667 -0.2268923098 0.8544038870 -1.1996679974
## [241] 0.1795806501 0.3452609735 1.1406128403 0.5774645196 -0.7262764513
## [246] -1.2850933473 1.4391213557 -2.8865602976 0.0140716423 0.0643564055
## [251] -1.4031912013 0.0567452489 -1.1141536973 0.4674112048 -1.4401112228
## [256] -0.8810085456 0.7397564101 1.4572331056 -2.1257740091 1.0520253910
## [261] -0.6412631083 0.3547824445 -0.9466331414 -1.2299124459 0.3250668091
## [266] -0.1305583804 1.2636196181 -0.7176652094 -0.5499703828 1.8865988568
## [271] -0.5883059413 -1.0500753050 1.0805007520 0.2849181482 1.3707439614
## [276] 0.0624737727 0.7135540000 1.1247423797 -1.4133026309 0.5472569005
## [281] 0.4096222015 1.9182849628 0.5342464390 -0.6403583648 -0.1484664494
## [286] -0.1316943576 0.6219943181 -1.2226504025 0.2203777369 -1.2961703161
## [291] -1.4611641192 0.2109504685 -0.8410401116 -0.7336959343 -0.2927512036
## [296] -0.4105503740 -2.0751788977 1.5914948144 -0.5743466138 1.1406000570
## [301] -0.4098849116 -1.1266022304 -0.4027821338 0.1451956462 0.3126247909
## [306] 0.1720779789 -0.2279093041 -1.0921904441 0.5914766342 -0.1866014543
## [311] 0.9131833665 -0.2307614599 -1.0929665525 1.6963970295 -1.2733625690
## [316] 0.4807293240 0.7160582320 0.4685713342 -1.3988788288 -0.3995688579
## [321] 0.9002041880 0.3607482440 1.6163558936 -0.1358596066 2.7614676673
## [326] -0.8618696657 -0.5133200779 0.5568398977 -0.7125589402 -0.4087582403
## [331] 0.1559466370 -0.6178721579 -0.1788183546 -1.1104302298 -0.1343683453
## [336] -1.2021578045 -0.3444610256 0.8948967126 0.7586509797 -0.2223628228
## [341] 1.2880277903 0.9150987872 0.3147727095 -0.1801305558 -0.2836944236
## [346] -1.3783321012 1.1767641652 1.3112482958 0.4984813901 -0.3843054931
## [351] 0.7653201827 -0.3850383442 -0.4149821970 -0.3602005785 0.7547646690
## [356] -0.3610311833 0.4238562918 -0.5250025964 -1.6612414801 0.4033700919
## [361] -0.7326407269 -0.2041489897 0.7023994111 -0.1553682135 0.3016261629
## [366] -0.5913550395 -0.7425063641 1.1396669974 0.5156951801 -3.0647449879
## [371] -2.3724277407 -0.6469749588 -1.8274374552 0.9675697616 0.4025281815
## [376] 0.4991258279 0.9345056403 0.9929973959 -0.3540202478 0.6675787068
## [381] -0.3396617617 1.0940974322 -0.2436964475 1.6570201911 -0.8055719401
## [386] -0.7277859546 -0.8137629812 -2.1119902918 -0.9123250367 -0.1691127479
## [391] -0.5126200912 0.2379084826 0.9109879034 0.4412802227 -0.7229704330
## [396] 0.7381111250 0.9182625541 1.2025457778 -0.7748916015 0.2555526095
## [401] -0.5122189748 -0.6790783462 1.3655588735 -0.1882742436 -1.1081458627
## [406] 0.1591638543 1.5858977821 1.0375284323 0.0415569693 -0.8117634359
## [411] -0.0127259778 0.4613576517 -0.6357099667 0.2924854471 2.3814461774
## [416] -0.9383412614 0.4633329643 0.6301677405 0.4018219710 -0.9495939558
## [421] 0.3127358408 -0.2936360094 0.5850289846 0.4575019279 -0.1728769264
## [426] -0.3389683260 0.8007330895 -1.4035558127 -0.0005091201 1.2729161369
## [431] 0.9439659768 0.2476947313 1.0336860476 -0.1554156060 0.1199205068
## [436] 0.4797368603 -1.4773245676 -1.7486452381 -0.9677550403 0.2795325774
## [441] -1.1980949729 -0.5246064095 0.3847837925 0.4022191419 -0.0063201910
## [446] 0.6975736625 0.8342618773 -0.3622399121 -1.0141362439 0.6212688499
## [451] 1.5365680997 -1.2392537282 1.1675466005 0.4323751207 0.3706459132
## [456] -0.3246034134 0.0518391744 1.4802888969 0.0116846533 2.2892344390
## [461] 0.0747102530 0.3248860842 -0.4177494874 1.7761124751 -2.1603982400
## [466] -0.0683323084 0.6546797955 1.2921300846 -0.4598494136 1.1283909616
## [471] 1.5469517127 -0.4558180065 -0.2090089024 0.2187794701 -0.9669558344
## [476] -2.2557537348 -1.3048302849 -0.8916519534 -0.5410634853 0.1474146799
## [481] 0.5140836682 -0.2213435844 1.5622233254 -0.3681375424 -0.1439182341
## [486] 0.7269279528 -0.4723144108 -2.0324888145 1.5173003900 0.5561095973
## [491] -0.3335931333 -0.6742061001 1.3479418313 0.6385963761 -0.9555243413
## [496] 0.3126108174 0.5734694911 -0.0493140049 1.9679983306 -0.2312646539
## [501] 0.6781797124 1.5860653591 0.4216908212 -0.6802335146 -0.1710785225
## [506] -1.3070957359 0.0520560588 0.9849891401 -0.3446266647 -0.0658139059
## [511] -2.1946402949 0.7276198220 -0.1669555914 0.3198599044 0.5860225482
## [516] 2.2155500073 0.1743625820 0.7883667412 0.5596670465 -0.0172593449
## [521] -0.4509850073 -0.2834431120 -0.6023627444 0.9783414722 -1.8000907515
## [526] 1.0873669886 -0.2759648902 0.5182770432 0.9641632273 0.4387801039
## [531] 0.8666757643 -0.7321623064 0.6795851571 0.1807886336 1.0312761179
## [536] -0.3519978966 -0.9510222849 -0.0389439539 -2.0635382569 -0.7203228649
## [541] -0.4213196867 1.1806069084 -1.8206112296 -0.4299644949 2.2721758754
## [546] 1.0593125470 0.9294088746 1.7666463241 -0.8338286861 0.1023923826
## [551] 0.2126399952 -0.0288509441 0.3188025321 -0.2838728420 2.3107459596
## [556] 1.5379139840 -0.4583605467 -0.4630083123 0.0323433167 0.9834229567
## [561] 0.2713903176 0.5609184518 -0.4754163717 0.2887287293 -1.5234145040
## [566] -0.5155742370 1.8642874251 2.1158202764 -0.5339175817 -0.9364591040
## [571] 0.3780121941 0.2105820915 -1.2280088913 -0.2294026445 -1.6438649712
## [576] -2.6938397523 -0.0827872716 1.1160385387 -0.1884163260 0.3225323507
## [581] 0.7460450146 -0.4612769136 0.5728352281 0.7397976877 0.7685751144
## [586] 1.7966428451 0.2154180391 -0.5714392433 -0.1360977608 0.4264573062
## [591] 1.0026850812 0.1414800747 -0.6609057483 -0.1694992692 -0.7216501578
## [596] -0.2040395150 1.4748722334 -1.6278107583 1.2084467598 -1.4136358231
## [601] -0.9099420075 0.4645684851 1.0846923724 -0.2042384634 -1.3664021694
## [606] -0.4307824649 0.0774712672 1.6031527299 -1.2803518481 0.7105432297
## [611] 0.3699412253 -0.5858070621 1.3897340260 1.5726483162 2.0134103671
## [616] -0.6137777227 -0.4196035829 1.5081627047 0.6157220086 -0.5231377634
## [621] 1.1946676130 -0.9398602457 -0.0647799169 0.5835773658 -0.7887996896
## [626] 0.2373694186 0.3619746828 -0.6740665351 -0.0521780553 -0.6698064127
## [631] -1.9580105515 0.0518472125 1.0592510887 0.9090230030 0.8714563492
## [636] 1.6415805873 -1.2429452384 0.2339835194 0.6110387664 -1.4681323150
## [641] 0.2775478932 1.2885333074 -0.6082274855 0.8617726543 -2.1724230454
## [646] 1.8063021822 -0.7790895282 -1.8671371048 -0.8473449578 1.4121916399
## [651] -0.2461329689 0.9577056598 0.2312648893 -0.5728972154 -1.4916080684
## [656] 1.1471257473 1.0287522945 -1.0512365396 1.0145064062 -0.9648674061
## [661] -0.5390265864 0.3506398359 1.3423792240 -0.1319853416 -0.6532623335
## [666] 0.7053249821 0.2927920036 1.0001135156 0.9297354370 -0.0121882720
## [671] 0.2422522139 0.8941574256 -0.2328495216 -1.8927873179 -0.0513493975
## [676] 1.6434013821 0.1982472404 0.4583935441 -0.0641961866 -1.8759354095
## [681] -0.1174057487 -0.0456320517 -1.5931559066 -1.1158684486 1.3434671396
## [686] 0.3220825464 -0.8626208246 -1.1130560725 0.1763180086 1.3629710576
## [691] -0.4118511589 -0.6127420958 0.1167441898 -0.2473303025 0.2929430239
## [696] 0.7178230040 0.3340058306 -0.7708340155 -1.0229286618 0.0038072869
## [701] 0.2259856403 1.3324613339 -0.5576173192 1.0489656095 -0.6680477493
## [706] -0.4394236342 -0.9637830911 -0.9580488794 -0.6768402833 -0.5547737710
## [711] -0.3481459847 1.3054338306 1.4293073112 -0.0031419937 0.7094529568
## [716] -1.0788349619 0.5793534165 -0.7641731100 0.3780227329 -0.8687066615
## [721] 0.9009081161 0.0650680271 -0.1720514240 -0.1675581309 -0.0662530858
## [726] 1.5474745175 -1.7879183069 -0.4140558648 1.0730465133 0.7681536230
## [731] 0.0583831595 -1.1334908115 0.2139182488 3.2587560674 -0.4227819956
## [736] 0.2385327458 1.0740027091 0.2791037757 0.1631032443 -2.0297270084
## [741] 0.4509505864 -0.4082895815 1.0591103730 1.3511939032 0.5145950737
## [746] 2.1350251612 0.0182640404 0.2111685545 -1.0761696252 -1.8934177281
## [751] 0.4964493663 -1.2525524481 -0.4108846487 0.6660499131 0.8237194272
## [756] -0.7081480975 1.1526974929 1.6760848075 -0.1548946377 0.7841783701
## [761] -0.1876872676 -1.0637984571 0.2146135786 0.3418298186 1.2354557979
## [766] -0.1474740622 1.8325045298 -1.3942412059 0.1866021730 -0.8950526110
## [771] 0.3020321713 0.3470253362 0.2066492325 0.1489129120 0.8901574989
## [776] 1.4521132449 -0.3925406863 -0.4823041632 -1.2400826343 0.0641249226
## [781] 0.7734726719 0.0841405449 -0.5815127790 -0.2807562411 -0.6407040776
## [786] -0.3212333975 0.3504291841 -0.4311220667 -0.8130779291 -0.6365792116
## [791] -0.2593823033 -0.2265302021 0.2803362298 -0.4308067291 -0.8713399911
## [796] 0.2003610652 -0.0213491579 -0.8662179280 -0.3054740180 0.6828710742
## [801] -0.7878122145 -0.4229914815 1.1959994088 -0.8570981760 -0.7412085251
## [806] 1.1886196071 0.2817335709 0.1323842583 -0.0994512099 0.2089951904
## [811] -1.1008184126 -0.3758517131 0.4631187139 2.4039029183 0.2819737514
## [816] -0.9500092951 0.5052488639 -0.3172411843 0.4383374867 0.5438706511
## [821] 0.3506962962 -1.6509866462 -0.5428055652 -0.9041124615 -0.9005727788
## [826] 0.6027822930 0.1033326364 -0.7832165395 1.5372002101 0.9350313395
## [831] 0.2508610510 0.7256587469 -0.0783975944 1.2818646259 -0.2169585343
## [836] -0.9487925722 1.6055713398 -0.6856739599 -0.7527286076 0.3117982782
## [841] 0.8647749305 0.2283757203 -0.8022222660 -0.6479770812 -0.0836435170
## [846] -0.1837081633 1.6641484724 0.2927516955 0.0164304387 0.3751961682
## [851] 0.2884022317 -0.4932395510 0.9248359672 0.8273335087 1.2140285957
## [856] 0.0888142423 -0.6055820750 -0.1349069529 0.4654092145 -0.7936290077
## [861] 0.0955312423 0.8769615090 -0.2782817680 -0.3757275388 1.3704534263
## [866] 0.7170616964 -0.8656894477 -0.2691378332 0.4107542488 -1.7596694290
## [871] -0.1862895936 -0.6567584825 0.9400149852 -1.0860996626 2.0530621618
## [876] -0.9597583528 -1.9349184753 -0.4158585909 0.9043998173 0.2687210088
## [881] 0.9644146926 -0.8774303419 -0.4748529170 0.1352621930 1.0917207866
## [886] 0.9398072380 -1.5633306614 0.3019338423 -0.0878201324 -0.7265020333
## [891] 1.4321556771 0.6957493314 0.6253943895 -1.5506307971 -0.6551182054
## [896] -0.5522078256 -0.6115784371 -1.0882712179 -0.0219122114 0.0279531463
## [901] 0.4794138099 -1.3190951816 -0.7614225438 -2.2023804308 -1.4502462159
## [906] 1.0609951571 -0.2966863916 0.3481243351 -0.1317468803 -1.4146954975
## [911] -0.8034350105 -2.0406311415 -0.1978213547 0.8900589281 1.3074617521
## [916] 0.1195306467 -0.1939807824 0.1383205545 -0.8980966539 1.4749545293
## [921] 0.3155924388 1.1198072290 -0.7852491932 -0.1981316907 -0.6947875307
## [926] 0.4144983386 0.3905679838 -1.1018119200 -0.0678617901 0.1021736302
## [931] 2.5354147038 1.2612606429 -0.9256783106 -0.0522901637 1.5396069505
## [936] -0.3909446288 -0.3901886399 0.7581062913 -1.4585425081 -0.7005924754
## [941] -0.8846615898 -0.2340428287 1.5683128217 -1.7900883506 -0.7395749566
## [946] -0.3734254962 0.1082963910 -0.2658373574 0.8646510843 1.2369760280
## [951] 2.0848192102 -0.9215101660 -1.5882323470 -1.2307663427 -0.9622924255
## [956] -0.3823858456 -0.2569934762 0.5663616920 1.7504323260 0.1482185780
## [961] 1.5967307294 1.3490868027 -0.4958999102 0.3005796491 -1.7949737618
## [966] -0.8807269636 0.0746539561 -1.8963866732 -0.1050018748 0.4778541306
## [971] 0.8703680255 1.3746191244 2.1207570860 -0.3405457308 0.0407384289
## [976] -1.0846280664 0.9640796598 1.3328573556 2.3613110930 1.1873542478
## [981] 0.3058669974 -0.2858112873 -0.5494841695 1.0000081468 0.9119604734
## [986] 0.8426901270 0.7673553279 0.5834778928 0.9263207650 -0.5658619180
## [991] -1.3573161497 -0.7501636742 -1.4599411446 -1.7674430872 0.1640371179
## [996] -1.4821890868 -1.3880747843 -0.5324091396 1.9765455013 1.6949078753
yAxis <- rnorm(1000) + xAxis + 10
yAxis
## [1] 8.971520 12.944879 11.689388 8.830740 8.239262 11.628597 8.622316
## [8] 10.999943 10.740294 10.609661 9.430498 7.172653 8.715246 10.227272
## [15] 10.639882 8.698124 12.531792 9.236242 9.346171 8.880106 9.103996
## [22] 10.649032 10.456888 9.485788 13.970491 10.713874 8.831469 9.929228
## [29] 6.461372 12.135368 6.950795 7.940369 12.596671 9.079005 7.673183
## [36] 8.697279 9.382490 9.323819 11.824739 10.775502 9.998641 11.010150
## [43] 8.051223 11.308975 10.033811 9.726484 7.547542 9.884053 9.260751
## [50] 9.587223 7.384634 9.004797 10.851043 11.224434 9.374969 9.771523
## [57] 8.615322 11.430331 8.949553 9.771196 11.037804 8.694312 9.473543
## [64] 8.540004 10.145308 9.501418 7.706898 10.592456 8.917085 10.597722
## [71] 11.860814 12.304442 10.358330 12.637060 8.977440 10.957944 10.900145
## [78] 8.196954 9.083468 9.716475 10.549277 10.588213 8.959309 9.998103
## [85] 7.606657 11.360074 10.947273 10.330730 9.516119 7.412309 10.631683
## [92] 9.570996 10.657788 11.250382 12.239262 8.028144 8.339986 11.786684
## [99] 10.336729 11.764789 10.063227 12.316270 8.917863 12.943783 12.876161
## [106] 12.516237 11.738261 10.472302 9.623603 9.940340 10.933927 9.906724
## [113] 10.864845 8.590833 8.800130 9.981526 10.598518 11.262051 10.056286
## [120] 9.181050 9.977548 11.698133 12.277689 12.247059 9.485028 9.366710
## [127] 10.409482 9.778361 8.867477 9.273090 10.592764 9.327868 12.038835
## [134] 11.627493 8.575352 9.827522 10.508904 8.231456 12.376227 12.267319
## [141] 11.811802 10.718909 9.270863 11.830369 7.787602 10.171103 9.985306
## [148] 10.092966 8.095907 9.072368 8.535960 8.968919 9.084468 9.346215
## [155] 11.890981 7.975277 7.564712 7.877926 8.225105 9.877240 11.690189
## [162] 10.593969 9.084904 12.304333 11.947491 7.933449 10.605818 9.014496
## [169] 9.188930 10.541537 10.679449 9.481487 12.690492 10.500648 9.182489
## [176] 12.406513 10.640520 9.586323 11.750864 9.576266 10.838107 10.907033
## [183] 8.840232 10.796317 9.437081 12.104139 13.126992 10.355637 8.742137
## [190] 8.676553 7.713316 12.539195 9.982941 7.271448 8.112184 7.782217
## [197] 9.688368 11.689077 9.962097 10.124405 12.092435 10.530980 8.253539
## [204] 9.871532 9.729820 8.674931 9.197184 8.951753 7.753186 9.386305
## [211] 10.478861 10.093474 10.206221 12.322141 10.778539 11.558359 10.943440
## [218] 8.529556 8.506693 10.859452 11.173248 10.286818 9.872508 9.066705
## [225] 7.607741 10.619178 9.009742 12.992062 8.109432 11.039847 10.722154
## [232] 10.552358 10.259701 9.090794 10.786924 9.311704 9.788881 10.417003
## [239] 10.310304 8.728303 10.532399 8.956073 12.351022 11.590401 8.198827
## [246] 7.581239 12.144809 7.610323 9.840561 10.023563 8.909985 9.560237
## [253] 8.450123 10.734265 8.789327 9.645720 8.746021 9.151656 8.246030
## [260] 12.140144 8.943757 11.752547 9.965679 10.377799 9.219032 8.535274
## [267] 11.889394 10.231439 7.555667 10.631097 9.599728 9.741143 11.990391
## [274] 10.661153 13.276314 9.377308 12.194877 9.630687 8.367345 10.169840
## [281] 9.923998 11.572678 9.439511 8.599549 10.995661 9.255429 9.767621
## [288] 10.073061 9.457945 8.522352 8.178645 9.095650 8.698542 8.827624
## [295] 9.327579 8.512004 8.150479 8.992394 7.750094 11.155277 9.687207
## [302] 8.237678 8.198823 9.339652 9.980313 9.038661 9.562846 9.617562
## [309] 9.200822 10.198424 9.906478 9.952528 9.657221 11.798035 8.259057
## [316] 11.338835 8.549238 8.688190 8.573198 9.214205 10.176454 11.503199
## [323] 11.191748 10.395474 13.280864 9.773232 8.879966 11.020212 9.150325
## [330] 9.157330 9.757431 7.935741 10.261013 9.905682 8.875212 7.421986
## [337] 8.916658 12.316108 8.796110 12.322595 11.661018 10.266085 9.419829
## [344] 12.177058 8.988244 9.698123 9.906610 11.391704 11.087007 10.282968
## [351] 10.766332 10.407061 11.035800 10.640658 12.010686 9.945185 10.662140
## [358] 8.767124 9.388909 10.822845 8.321963 9.933938 11.116171 9.096058
## [365] 10.039742 9.798819 11.074653 10.379175 11.438135 7.691088 8.848773
## [372] 7.454977 6.643681 11.454759 12.796011 12.134032 11.598521 12.942752
## [379] 10.854245 11.198969 8.644107 10.342188 10.545334 12.284578 9.629605
## [386] 9.411138 8.220674 7.287793 7.308776 10.330792 8.796553 10.472989
## [393] 11.022629 10.229734 9.654569 10.549621 11.340171 11.504041 9.270998
## [400] 11.155667 9.957565 10.114075 11.043890 10.930640 10.405598 10.903079
## [407] 10.300144 11.636688 9.237287 10.940460 8.335630 10.961286 10.275719
## [414] 9.894794 11.396277 9.412165 9.885864 9.009337 8.134184 10.401647
## [421] 9.985370 11.184014 11.828695 10.908279 8.940592 9.306357 11.133354
## [428] 6.981739 10.258074 12.047846 11.850577 9.565231 11.392716 7.928283
## [435] 9.998327 10.529698 7.552721 8.371372 8.989602 11.630594 10.352946
## [442] 8.292105 9.403170 9.652459 6.715607 10.224225 9.832772 9.050432
## [449] 7.876011 8.261299 11.597098 10.136198 12.058701 10.685803 10.194043
## [456] 11.053749 11.498350 12.483417 10.767223 12.032960 10.331048 9.303433
## [463] 9.832009 11.531821 8.299532 10.073590 13.250876 10.081219 9.013299
## [470] 11.875104 11.542175 9.814995 9.675646 10.015130 9.701856 9.512761
## [477] 9.665422 10.530389 9.299715 10.778414 8.684345 11.333201 12.226292
## [484] 9.728428 8.792919 11.604993 10.712930 6.720266 12.350620 9.851583
## [491] 7.957281 9.958560 9.967863 11.442099 9.777568 10.649071 11.353135
## [498] 9.797450 10.921675 9.853902 9.949689 12.440802 11.965891 9.280708
## [505] 10.128495 6.407267 9.017956 10.620404 8.180133 9.998477 8.471894
## [512] 11.262735 9.663225 9.980608 9.030880 11.784912 10.819701 10.678221
## [519] 10.306257 9.970727 10.942412 8.273209 8.261877 11.260841 8.425498
## [526] 9.724513 10.666519 10.735196 10.827490 9.346711 8.377435 9.273033
## [533] 10.113410 11.064261 11.662485 11.239670 8.274855 11.699486 6.242329
## [540] 9.840142 8.582294 11.203683 8.858061 8.362042 11.508342 11.921275
## [547] 11.509623 13.301280 10.213560 9.772424 8.840488 10.104101 9.776939
## [554] 10.379103 13.735031 11.464745 10.086182 10.056097 8.893217 10.840624
## [561] 7.961356 9.475339 8.811149 9.678106 9.957262 10.176190 11.268053
## [568] 11.527162 9.075826 8.419758 11.662903 10.647351 8.917185 8.895662
## [575] 7.776384 7.526703 10.280793 12.550011 9.026609 11.168862 12.387382
## [582] 10.087888 9.717597 10.067692 10.793034 11.514880 8.075300 10.372122
## [589] 9.880107 10.427891 10.129498 12.308361 10.080354 8.521102 9.348006
## [596] 11.079716 11.919672 7.559817 11.735707 7.359057 9.796891 9.325331
## [603] 10.017150 11.929515 10.229313 9.201461 9.861904 10.871255 9.172389
## [610] 10.083391 9.752016 7.821614 11.562647 9.562831 13.568153 11.042070
## [617] 8.526959 11.291550 9.250965 10.816281 12.336242 8.749860 9.867920
## [624] 11.779533 7.284003 13.356499 10.592799 8.615373 11.623062 10.408307
## [631] 8.713416 9.419472 9.614942 10.149691 13.024616 12.691311 10.013926
## [638] 11.176305 10.177138 9.142109 9.367648 11.520884 11.997113 11.164524
## [645] 5.725474 12.576352 7.546819 7.202311 8.394952 12.469570 8.751228
## [652] 10.776621 9.856603 7.995126 9.082275 13.524509 10.536013 8.131210
## [659] 12.200008 9.559698 9.911287 10.896028 10.001893 10.681755 9.130275
## [666] 10.676302 11.687081 11.789314 9.986011 9.428344 10.808584 11.169196
## [673] 9.498355 8.400916 10.009079 13.263166 12.305809 10.338888 11.266098
## [680] 7.751266 10.015180 9.668740 8.162574 7.957433 10.957117 11.691190
## [687] 8.981288 8.910672 8.424860 12.473458 10.125449 8.563888 8.256069
## [694] 9.854449 10.276196 11.034367 10.319217 10.082414 8.090102 11.622549
## [701] 9.580649 12.366604 9.090678 10.442898 10.225455 9.576480 9.666135
## [708] 9.915796 7.832307 9.230189 10.206288 10.114856 11.289408 9.920757
## [715] 9.084362 9.112935 10.255572 11.149174 11.345757 10.047845 8.860069
## [722] 9.864006 9.680268 9.260313 8.900237 10.884695 7.095742 8.203355
## [729] 11.150683 11.203196 10.610653 6.919296 11.196110 14.573949 9.988786
## [736] 10.636882 13.338494 11.018243 10.125534 7.898790 13.299305 9.957848
## [743] 12.672443 9.666399 9.043591 11.016860 8.172604 9.316849 9.216569
## [750] 8.611017 11.036036 8.468621 9.829747 10.776319 11.005475 9.375743
## [757] 11.041810 12.092828 9.804848 11.238577 10.095603 10.473545 9.658206
## [764] 10.557232 8.508433 9.131327 12.302361 8.179401 7.978997 8.328701
## [771] 11.794633 9.240898 9.157841 10.045598 11.487950 13.370274 9.552346
## [778] 9.433889 9.772778 9.723281 11.181800 9.835535 9.198637 9.416468
## [785] 10.705177 10.565777 11.565185 10.097948 9.535706 11.261993 9.036362
## [792] 9.439329 10.839830 8.651921 10.409619 11.486514 10.791323 10.057152
## [799] 10.200492 9.861076 9.753839 8.954090 11.210197 8.496803 9.789867
## [806] 10.801709 10.251650 9.021768 10.358129 9.419954 7.509067 8.492845
## [813] 10.080519 12.828131 9.901021 8.205614 8.919104 9.424066 10.479648
## [820] 10.294535 9.362781 10.648555 8.649019 7.693390 8.307188 10.521848
## [827] 9.602870 10.361620 11.230623 10.822718 8.845196 12.642444 8.558209
## [834] 12.019776 10.748056 8.475957 11.554209 9.719968 9.521884 10.013788
## [841] 11.484670 10.950377 10.164262 8.150568 9.169981 8.741547 12.223221
## [848] 9.757156 9.698310 9.253828 10.533010 9.122355 12.212719 9.930821
## [855] 10.171005 11.008834 9.072781 9.794032 9.678384 9.815210 10.474637
## [862] 10.473965 10.436752 9.478881 12.022638 8.735539 8.892020 10.686698
## [869] 9.197562 8.919908 10.975591 10.114663 11.317097 9.911710 11.562648
## [876] 10.596904 7.600141 10.265486 10.575657 10.156133 11.097468 8.994758
## [883] 9.141556 11.563313 11.212761 12.280001 8.459046 9.563715 10.890966
## [890] 9.101553 10.739876 11.201526 10.994277 7.248978 9.503957 9.661594
## [897] 10.073127 9.526020 9.934603 9.070350 9.871101 7.604991 11.063156
## [904] 7.915433 8.075550 11.311830 9.909482 9.802298 10.112079 9.149689
## [911] 9.281329 7.355490 11.496314 11.099173 11.473001 7.606567 9.536209
## [918] 10.373756 10.861605 12.407872 10.296498 10.099247 7.004073 10.920915
## [925] 9.747754 10.499922 10.910213 8.060921 9.880006 9.238631 10.986904
## [932] 12.548033 9.528712 9.888953 11.719835 8.181194 9.990176 11.964539
## [939] 8.713518 8.255028 8.616592 9.982776 12.054601 6.649813 9.589526
## [946] 9.546561 10.669255 10.169117 9.382793 12.553855 13.768783 10.256025
## [953] 10.154402 9.134171 10.346181 9.751754 10.067358 11.458656 9.890157
## [960] 10.783526 11.443099 10.936170 8.198493 10.742284 10.042304 9.087219
## [967] 10.827633 7.590683 8.820824 10.310636 11.280903 10.766833 12.828171
## [974] 8.686488 10.684050 10.074458 10.710911 10.100621 11.616903 10.375815
## [981] 10.238670 9.994847 10.489097 11.049403 12.359568 10.641246 9.543924
## [988] 12.051730 9.669012 9.661073 10.778300 10.688655 7.780788 9.468269
## [995] 11.491371 8.992074 9.365683 10.516274 11.504224 10.634667
# create groups for different values of X
(group <- rep(1,1000)) # a vector consisting of 1000 elements
## [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [260] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [482] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [556] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [630] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [667] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [704] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [778] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
## [1000] 1
group[xAxis > -1.5] <- 2
group[xAxis > -.5] <- 3
group[xAxis > .5] <- 4
group[xAxis > 1.5] <- 5
group
## [1] 3 5 4 3 2 4 2 2 4 2 3 1 2 3 4 2 3 2 2 2 2 3 2 3 5 4 2 3 1 5 2 1 3 3 2 2 2
## [38] 3 4 4 3 3 1 4 4 2 1 3 3 2 1 1 4 3 3 3 2 4 2 2 5 3 3 3 2 4 1 4 3 3 4 5 3 4
## [75] 4 3 3 2 3 3 3 4 3 2 3 4 2 3 2 3 3 3 3 4 4 2 3 3 5 4 2 3 3 4 4 5 5 4 4 4 5
## [112] 2 5 3 2 3 3 4 3 4 4 3 5 4 2 3 3 4 3 1 4 2 4 4 1 2 4 2 5 3 4 4 4 3 2 4 3 2
## [149] 2 2 3 3 3 2 5 3 1 2 1 2 5 3 2 4 4 3 4 3 1 4 4 3 5 4 2 5 3 4 3 3 4 3 2 3 3
## [186] 4 3 4 2 3 1 4 3 1 2 3 2 4 3 3 5 4 2 5 3 3 2 3 1 3 3 3 4 4 3 4 5 2 2 2 2 3
## [223] 2 2 1 4 3 3 2 5 2 3 4 2 3 4 4 3 4 2 3 3 4 4 2 2 4 1 3 3 2 3 2 3 2 2 4 4 1
## [260] 4 2 3 2 2 3 3 4 2 2 5 2 2 4 3 4 3 4 4 2 4 3 5 4 2 3 3 4 2 3 2 2 3 2 2 3 3
## [297] 1 5 2 4 3 2 3 3 3 3 3 2 4 3 4 3 2 5 2 3 4 3 2 3 4 3 5 3 5 2 2 4 2 3 3 2 3
## [334] 2 3 2 3 4 4 3 4 4 3 3 3 2 4 4 3 3 4 3 3 3 4 3 3 2 1 3 2 3 4 3 3 2 2 4 4 1
## [371] 1 2 1 4 3 3 4 4 3 4 3 4 3 5 2 2 2 1 2 3 2 3 4 3 2 4 4 4 2 3 2 2 4 3 2 3 5
## [408] 4 3 2 3 3 2 3 5 2 3 4 3 2 3 3 4 3 3 3 4 2 3 4 4 3 4 3 3 3 2 1 2 3 2 2 3 3
## [445] 3 4 4 3 2 4 5 2 4 3 3 3 3 4 3 5 3 3 3 5 1 3 4 4 3 4 5 3 3 3 2 1 2 2 2 3 4
## [482] 3 5 3 3 4 3 1 5 4 3 2 4 4 2 3 4 3 5 3 4 5 3 2 3 2 3 4 3 3 1 4 3 3 4 5 3 4
## [519] 4 3 3 3 2 4 1 4 3 4 4 3 4 2 4 3 4 3 2 3 1 2 3 4 1 3 5 4 4 5 2 3 3 3 3 3 5
## [556] 5 3 3 3 4 3 4 3 3 1 2 5 5 2 2 3 3 2 3 1 1 3 4 3 3 4 3 4 4 4 5 3 2 3 3 4 3
## [593] 2 3 2 3 4 1 4 2 2 3 4 3 2 3 3 5 2 4 3 2 4 5 5 2 3 5 4 2 4 2 3 4 2 3 3 2 3
## [630] 2 1 3 4 4 4 5 2 3 4 2 3 4 2 4 1 5 2 1 2 4 3 4 3 2 2 4 4 2 4 2 2 3 4 3 2 4
## [667] 3 4 4 3 3 4 3 1 3 5 3 3 3 1 3 3 1 2 4 3 2 2 3 4 3 2 3 3 3 4 3 2 2 3 3 4 2
## [704] 4 2 3 2 2 2 2 3 4 4 3 4 2 4 2 3 2 4 3 3 3 3 5 1 3 4 4 3 2 3 5 3 3 4 3 3 1
## [741] 3 3 4 4 4 5 3 3 2 1 3 2 3 4 4 2 4 5 3 4 3 2 3 3 4 3 5 2 3 2 3 3 3 3 4 4 3
## [778] 3 2 3 4 3 2 3 2 3 3 3 2 2 3 3 3 3 2 3 3 2 3 4 2 3 4 2 2 4 3 3 3 3 2 3 3 5
## [815] 3 2 4 3 3 4 3 1 2 2 2 4 3 2 5 4 3 4 3 4 3 2 5 2 2 3 4 3 2 2 3 3 5 3 3 3 3
## [852] 3 4 4 4 3 2 3 3 2 3 4 3 3 4 4 2 3 3 1 3 2 4 2 5 2 1 3 4 3 4 2 3 3 4 4 1 3
## [889] 3 2 4 4 4 1 2 2 2 2 3 3 3 2 2 1 2 4 3 3 3 2 2 1 3 4 4 3 3 3 2 4 3 4 2 3 2
## [926] 3 3 2 3 3 5 4 2 3 5 3 3 4 2 2 2 3 5 1 2 3 3 3 4 4 5 2 1 2 2 3 3 4 5 3 5 4
## [963] 3 3 1 2 3 1 3 3 4 4 5 3 3 2 4 4 5 4 3 3 2 4 4 4 4 4 4 2 2 2 2 1 3 2 2 2 5
## [1000] 5
# create sample dataframe by joining variables
sample_data <- data.frame(xAxis,yAxis,group)
sample_data
## xAxis yAxis group
## 1 0.0004198344 8.971520 3
## 2 1.8714405209 12.944879 5
## 3 1.2095426091 11.689388 4
## 4 -0.4083386311 8.830740 3
## 5 -0.9574034944 8.239262 2
## 6 0.9537401581 11.628597 4
## 7 -0.5604881697 8.622316 2
## 8 -1.0776455056 10.999943 2
## 9 0.7813176587 10.740294 4
## 10 -0.5199671404 10.609661 2
## 11 0.0049742323 9.430498 3
## 12 -2.2219240772 7.172653 1
## 13 -1.2461902850 8.715246 2
## 14 0.0355926893 10.227272 3
## 15 0.6806511717 10.639882 4
## 16 -1.3769070890 8.698124 2
## 17 0.4618470910 12.531792 3
## 18 -0.6032610913 9.236242 2
## 19 -1.2610414885 9.346171 2
## 20 -1.0786390745 8.880106 2
## 21 -0.8700491411 9.103996 2
## 22 -0.0856777421 10.649032 3
## 23 -0.7391987917 10.456888 2
## 24 0.0013214297 9.485788 3
## 25 2.0348088445 13.970491 5
## 26 0.6785081201 10.713874 4
## 27 -0.5361816421 8.831469 2
## 28 0.0948717805 9.929228 3
## 29 -2.2033818748 6.461372 1
## 30 1.7553224548 12.135368 5
## 31 -0.7650695747 6.950795 2
## 32 -1.6975967045 7.940369 1
## 33 0.1843548507 12.596671 3
## 34 -0.0283691656 9.079005 3
## 35 -0.8382039928 7.673183 2
## 36 -1.1797354328 8.697279 2
## 37 -0.9567791014 9.382490 2
## 38 -0.4048423569 9.323819 3
## 39 1.3116014825 11.824739 4
## 40 0.8468406635 10.775502 4
## 41 0.3667363844 9.998641 3
## 42 0.2126520457 11.010150 3
## 43 -2.2618126469 8.051223 1
## 44 1.3622483086 11.308975 4
## 45 0.6124121070 10.033811 4
## 46 -0.7341631785 9.726484 2
## 47 -1.6438376313 7.547542 1
## 48 -0.4673781088 9.884053 3
## 49 -0.1674771835 9.260751 3
## 50 -1.2030988941 9.587223 2
## 51 -1.5318877029 7.384634 1
## 52 -1.7175080641 9.004797 1
## 53 1.2716263448 10.851043 4
## 54 0.3916848039 11.224434 3
## 55 0.3448028237 9.374969 3
## 56 -0.0746542642 9.771523 3
## 57 -1.3682180271 8.615322 2
## 58 0.9080185992 11.430331 4
## 59 -1.2752441092 8.949553 2
## 60 -1.0343318611 9.771196 2
## 61 1.9153285599 11.037804 5
## 62 0.3182986888 8.694312 3
## 63 0.1048984499 9.473543 3
## 64 0.2311638035 8.540004 3
## 65 -1.0666657291 10.145308 2
## 66 1.2808440411 9.501418 4
## 67 -1.6694542422 7.706898 1
## 68 0.6723671797 10.592456 4
## 69 0.2990716092 8.917085 3
## 70 0.1901096844 10.597722 3
## 71 0.9903832407 11.860814 4
## 72 2.0683116012 12.304442 5
## 73 0.4778890062 10.358330 3
## 74 1.2337530474 12.637060 4
## 75 0.5335494126 8.977440 4
## 76 -0.1224968622 10.957944 3
## 77 -0.1785683345 10.900145 3
## 78 -1.4454404389 8.196954 2
## 79 0.1604747688 9.083468 3
## 80 -0.0326987984 9.716475 3
## 81 0.0479016726 10.549277 3
## 82 0.7539445734 10.588213 4
## 83 0.2614098848 8.959309 3
## 84 -1.2492541016 9.998103 2
## 85 0.3210227484 7.606657 3
## 86 0.5073086056 11.360074 4
## 87 -0.7190391956 10.947273 2
## 88 -0.1278956275 10.330730 3
## 89 -0.5073552962 9.516119 2
## 90 -0.3717621780 7.412309 3
## 91 -0.3742898298 10.631683 3
## 92 0.2713610375 9.570996 3
## 93 0.1707915817 10.657788 3
## 94 0.7081708483 11.250382 4
## 95 1.1439259440 12.239262 4
## 96 -0.7009792816 8.028144 2
## 97 0.3546245890 8.339986 3
## 98 0.1167770140 11.786684 3
## 99 1.5433136446 10.336729 5
## 100 1.0257084323 11.764789 4
## 101 -0.6416804678 10.063227 2
## 102 0.2847301052 12.316270 3
## 103 -0.4572140489 8.917863 3
## 104 1.0835336375 12.943783 4
## 105 0.6750935711 12.876161 4
## 106 1.8310271226 12.516237 5
## 107 2.0439329584 11.738261 5
## 108 0.7399521608 10.472302 4
## 109 0.9825750709 9.623603 4
## 110 1.0191788645 9.940340 4
## 111 2.2395740432 10.933927 5
## 112 -0.5125200577 9.906724 2
## 113 1.5621667263 10.864845 5
## 114 0.1748763440 8.590833 3
## 115 -0.5773508926 8.800130 2
## 116 -0.4109427232 9.981526 3
## 117 0.3831901719 10.598518 3
## 118 1.0447882940 11.262051 4
## 119 0.1011009525 10.056286 3
## 120 0.7381211005 9.181050 4
## 121 0.6839294023 9.977548 4
## 122 0.2907651826 11.698133 3
## 123 1.7391490212 12.277689 5
## 124 0.5880298145 12.247059 4
## 125 -0.9255475222 9.485028 2
## 126 -0.0133840762 9.366710 3
## 127 0.3601792738 10.409482 3
## 128 1.4593828588 9.778361 4
## 129 -0.1428283069 8.867477 3
## 130 -1.5699159652 9.273090 1
## 131 1.2801900303 10.592764 4
## 132 -0.8402569184 9.327868 2
## 133 1.0113311196 12.038835 4
## 134 1.0827300463 11.627493 4
## 135 -2.3219818323 8.575352 1
## 136 -0.6715494157 9.827522 2
## 137 0.9768959432 10.508904 4
## 138 -0.9177387469 8.231456 2
## 139 1.5674946696 12.376227 5
## 140 -0.2621862106 12.267319 3
## 141 1.4980911136 11.811802 4
## 142 1.2672355027 10.718909 4
## 143 0.8006568501 9.270863 4
## 144 -0.2589707373 11.830369 3
## 145 -1.0983693816 7.787602 2
## 146 0.6849702703 10.171103 4
## 147 -0.0695905820 9.985306 3
## 148 -0.7594641395 10.092966 2
## 149 -0.6277427831 8.095907 2
## 150 -1.0452737107 9.072368 2
## 151 -0.4406532417 8.535960 3
## 152 0.1816362855 8.968919 3
## 153 -0.0412604941 9.084468 3
## 154 -0.9790645941 9.346215 2
## 155 1.9843808783 11.890981 5
## 156 0.1516738149 7.975277 3
## 157 -1.5112596654 7.564712 1
## 158 -1.1778141049 7.877926 2
## 159 -1.7336852036 8.225105 1
## 160 -0.7116043042 9.877240 2
## 161 1.9423002088 11.690189 5
## 162 0.4989420145 10.593969 3
## 163 -0.6023851208 9.084904 2
## 164 0.8335132929 12.304333 4
## 165 1.4711818525 11.947491 4
## 166 -0.4809504165 7.933449 3
## 167 1.0892643607 10.605818 4
## 168 -0.3709977666 9.014496 3
## 169 -1.9284121957 9.188930 1
## 170 0.5397422189 10.541537 4
## 171 1.1013986973 10.679449 4
## 172 -0.2466306091 9.481487 3
## 173 1.8552991294 12.690492 5
## 174 1.1586081393 10.500648 4
## 175 -1.2483978036 9.182489 2
## 176 2.7549906400 12.406513 5
## 177 0.2159386132 10.640520 3
## 178 1.4386948164 9.586323 4
## 179 0.1020479518 11.750864 3
## 180 -0.0685893338 9.576266 3
## 181 1.3020277869 10.838107 4
## 182 -0.1836459400 10.907033 3
## 183 -1.0305094677 8.840232 2
## 184 0.4947844174 10.796317 3
## 185 0.2457199848 9.437081 3
## 186 0.5277074483 12.104139 4
## 187 0.0747163140 13.126992 3
## 188 1.4708682560 10.355637 4
## 189 -0.5082703474 8.742137 2
## 190 -0.4332101157 8.676553 3
## 191 -2.1908031361 7.713316 1
## 192 1.0111347045 12.539195 4
## 193 -0.1897199635 9.982941 3
## 194 -1.7222836417 7.271448 1
## 195 -0.6471191322 8.112184 2
## 196 -0.2733113688 7.782217 3
## 197 -1.0636423475 9.688368 2
## 198 0.8058750807 11.689077 4
## 199 -0.1308091734 9.962097 3
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## 201 1.5551272332 12.092435 5
## 202 1.3920622298 10.530980 4
## 203 -1.3976391661 8.253539 2
## 204 2.1726118390 9.871532 5
## 205 -0.2297980744 9.729820 3
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## 226 0.7168422479 10.619178 4
## 227 0.0101499277 9.009742 3
## 228 0.2088022985 12.992062 3
## 229 -0.8056082983 8.109432 2
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## 234 -0.8449642500 9.090794 2
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## 240 -1.1996679974 8.728303 2
## 241 0.1795806501 10.532399 3
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## 243 1.1406128403 12.351022 4
## 244 0.5774645196 11.590401 4
## 245 -0.7262764513 8.198827 2
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## 248 -2.8865602976 7.610323 1
## 249 0.0140716423 9.840561 3
## 250 0.0643564055 10.023563 3
## 251 -1.4031912013 8.909985 2
## 252 0.0567452489 9.560237 3
## 253 -1.1141536973 8.450123 2
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## 255 -1.4401112228 8.789327 2
## 256 -0.8810085456 9.645720 2
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## 258 1.4572331056 9.151656 4
## 259 -2.1257740091 8.246030 1
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## 262 0.3547824445 11.752547 3
## 263 -0.9466331414 9.965679 2
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## 272 -1.0500753050 9.741143 2
## 273 1.0805007520 11.990391 4
## 274 0.2849181482 10.661153 3
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## 279 -1.4133026309 8.367345 2
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## 946 -0.3734254962 9.546561 3
## 947 0.1082963910 10.669255 3
## 948 -0.2658373574 10.169117 3
## 949 0.8646510843 9.382793 4
## 950 1.2369760280 12.553855 4
## 951 2.0848192102 13.768783 5
## 952 -0.9215101660 10.256025 2
## 953 -1.5882323470 10.154402 1
## 954 -1.2307663427 9.134171 2
## 955 -0.9622924255 10.346181 2
## 956 -0.3823858456 9.751754 3
## 957 -0.2569934762 10.067358 3
## 958 0.5663616920 11.458656 4
## 959 1.7504323260 9.890157 5
## 960 0.1482185780 10.783526 3
## 961 1.5967307294 11.443099 5
## 962 1.3490868027 10.936170 4
## 963 -0.4958999102 8.198493 3
## 964 0.3005796491 10.742284 3
## 965 -1.7949737618 10.042304 1
## 966 -0.8807269636 9.087219 2
## 967 0.0746539561 10.827633 3
## 968 -1.8963866732 7.590683 1
## 969 -0.1050018748 8.820824 3
## 970 0.4778541306 10.310636 3
## 971 0.8703680255 11.280903 4
## 972 1.3746191244 10.766833 4
## 973 2.1207570860 12.828171 5
## 974 -0.3405457308 8.686488 3
## 975 0.0407384289 10.684050 3
## 976 -1.0846280664 10.074458 2
## 977 0.9640796598 10.710911 4
## 978 1.3328573556 10.100621 4
## 979 2.3613110930 11.616903 5
## 980 1.1873542478 10.375815 4
## 981 0.3058669974 10.238670 3
## 982 -0.2858112873 9.994847 3
## 983 -0.5494841695 10.489097 2
## 984 1.0000081468 11.049403 4
## 985 0.9119604734 12.359568 4
## 986 0.8426901270 10.641246 4
## 987 0.7673553279 9.543924 4
## 988 0.5834778928 12.051730 4
## 989 0.9263207650 9.669012 4
## 990 -0.5658619180 9.661073 2
## 991 -1.3573161497 10.778300 2
## 992 -0.7501636742 10.688655 2
## 993 -1.4599411446 7.780788 2
## 994 -1.7674430872 9.468269 1
## 995 0.1640371179 11.491371 3
## 996 -1.4821890868 8.992074 2
## 997 -1.3880747843 9.365683 2
## 998 -0.5324091396 10.516274 2
## 999 1.9765455013 11.504224 5
## 1000 1.6949078753 10.634667 5
# creates plot object using ggplot
plot <- ggplot(sample_data, aes(x = xAxis, y= yAxis, col = as.factor(group)))+
geom_point()+theme(legend.position = "none")
# Display plot
plot
# Insert marginal ditribution using marginal function
ggMarginal(plot,type= 'histogram',groupColour=TRUE,groupFill=TRUE)
