# Mindanao State University
# General Santos City
# Introduction to R base commands
# Submitted by: John Michael H. Macawili
# Submitted to: Prof. Carlito O. Daarol
# Faculty
# Math Department
# March 28, 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\\johnm\\OneDrive\\Documents\\Lecture"
filename <- "cancer.csv"
(file <- paste0(folder,"/",filename))
## [1] "C:\\Users\\johnm\\OneDrive\\Documents\\Lecture/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\\johnm\\OneDrive\\Documents\\Lecture"
filename <- "hsb2.csv"
(file <- paste0(folder,"/",filename))
## [1] "C:\\Users\\johnm\\OneDrive\\Documents\\Lecture/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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## 417 76 0 4 3 1 2 math 51
## 418 195 0 4 2 2 1 math 60
## 419 114 0 4 3 1 2 math 62
## 420 85 0 4 2 1 1 math 57
## 421 167 0 4 2 1 1 math 35
## 422 143 0 4 2 1 3 math 75
## 423 41 0 3 2 1 2 math 45
## 424 20 0 1 3 1 2 math 57
## 425 12 0 1 2 1 3 math 45
## 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
## 450 7 0 1 2 1 2 math 59
## 451 27 0 2 2 1 2 math 61
## 452 128 0 4 3 1 2 math 38
## 453 21 0 1 2 1 1 math 61
## 454 183 0 4 2 2 2 math 49
## 455 132 0 4 2 1 2 math 73
## 456 15 0 1 3 1 3 math 44
## 457 67 0 4 1 1 3 math 42
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## 467 171 0 4 2 1 2 math 60
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## 470 18 0 1 2 1 3 math 49
## 471 155 0 4 2 1 1 math 46
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## 474 157 0 4 2 1 1 math 58
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## 486 146 0 4 3 1 2 math 64
## 487 102 0 4 3 1 2 math 51
## 488 117 0 4 3 1 3 math 39
## 489 133 0 4 2 1 3 math 40
## 490 94 0 4 3 1 2 math 61
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## 493 82 1 4 3 1 2 math 65
## 494 8 1 1 1 1 2 math 52
## 495 129 1 4 1 1 1 math 46
## 496 173 1 4 1 1 1 math 61
## 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
## 504 120 1 4 3 1 2 math 54
## 505 166 1 4 2 1 2 math 53
## 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
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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", "africanamer","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 1.1.1 ✔ readr 2.1.4
## ✔ forcats 1.0.0 ✔ stringr 1.5.0
## ✔ lubridate 1.9.2 ✔ tibble 3.2.1
## ✔ purrr 1.0.1 ✔ tidyr 1.3.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) 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] -0.532929453 -0.535658736 1.113188584 1.985900210 1.269813300
## [6] -0.744221693 0.924422156 -0.606340157 -0.739791319 1.152078655
## [11] 0.448616674 0.300946762 -0.532224587 -0.629677189 -0.501911701
## [16] -0.536270736 1.269512675 -2.333708216 -0.593750192 0.889048655
## [21] -0.131389880 0.279469767 -1.521413415 0.611669397 -1.656321076
## [26] -0.506490365 -0.302172602 2.374396751 -0.367986381 -1.199343290
## [31] 1.103640414 -0.225791069 0.770140249 0.862025496 -0.761131679
## [36] 0.636406127 1.541807345 -0.323449051 1.635897973 -0.068416983
## [41] -1.127776021 1.764631606 -1.853999668 -1.033986251 -1.475897790
## [46] -0.714116560 1.274540530 0.296324560 1.556244523 -0.610212256
## [51] 0.242123871 1.937782414 -0.527439827 1.455543269 0.893837845
## [56] 0.116245457 0.683257705 -0.474749278 0.972151649 0.592832640
## [61] -0.155191850 0.205467519 0.164642754 1.235106516 -1.741987266
## [66] -1.249990233 -1.439495614 0.533372009 -0.085123456 -0.496441905
## [71] -0.438686120 -2.318285223 0.122178401 -1.221855707 0.124432462
## [76] 0.250616455 -0.636966016 0.483952475 1.174260637 0.930411132
## [81] 1.267662141 -0.350266867 -1.293820459 -1.556264341 -1.202197156
## [86] 0.680700705 -0.509954553 -0.450424660 -1.197078715 -0.152728685
## [91] 0.597760228 0.977353050 0.480028425 0.116080477 -0.240282895
## [96] 0.693202981 2.266117897 0.883925031 0.839591700 0.522252356
## [101] -0.350345835 -0.965816231 0.440588804 0.630633064 0.864382482
## [106] -0.610527268 0.513318210 -1.271658723 -0.793703124 -0.119721219
## [111] 0.329229689 -0.862987928 1.475263182 1.588615702 0.880354714
## [116] -0.126988230 0.627453641 -0.001965687 -0.887081437 -0.869064430
## [121] 0.236648849 0.480688012 1.098327686 -1.415755524 -0.291611940
## [126] 0.864009766 -0.588845554 -0.676810211 0.557515308 -0.792769726
## [131] -1.388208971 0.352786127 -1.327027803 0.408706950 -0.548492646
## [136] 1.891748287 0.430085621 -1.013527459 0.703877497 0.970719522
## [141] -0.772555652 -1.282947235 0.449758492 -0.890554115 0.062648516
## [146] 1.308924337 -0.295157434 2.358430994 1.032623574 -0.018375696
## [151] 1.628217245 1.813662138 -0.441792585 0.544502869 1.626246545
## [156] -1.384230576 0.796139018 0.556863979 -0.508825973 0.639429785
## [161] -0.390790759 -0.567169326 0.639769619 0.881322560 0.066068577
## [166] -0.359528976 -0.417331046 0.934265334 -0.343623433 1.813850027
## [171] -0.265327900 0.140870929 -0.908733535 1.181289958 -1.026600443
## [176] -0.071694047 -0.093342480 -1.753929314 0.549370157 -0.766360623
## [181] -0.371010126 0.116043073 -0.108274496 -0.981910596 1.422443483
## [186] -0.173727965 -0.395071673 1.244272162 -1.420333428 0.048735919
## [191] -1.091533129 -0.938984946 -0.480284999 0.878758683 -0.916555142
## [196] 0.452584500 -0.905726429 -0.181167517 0.627465215 -0.923299827
## [201] 0.394909004 -0.777459881 0.801790913 1.317322116 -0.325719437
## [206] -1.048025006 -0.916477625 -1.124872499 1.046339194 1.009687832
## [211] 0.833969346 0.575904434 -0.855581681 -1.187904881 -2.548263727
## [216] 1.393666862 -1.008740304 0.124064909 0.886219130 1.425045956
## [221] -1.439377216 -0.859581619 -0.438475951 1.081392372 -0.883514492
## [226] -0.035781127 1.773948704 0.253497064 -0.926652913 -0.567795147
## [231] -0.250335227 -0.089197283 0.891964468 -0.341345067 -1.169143212
## [236] 0.390897896 -0.690580930 -1.779920296 -0.378479259 -0.308087502
## [241] -0.333490268 -0.620721238 -0.977801972 0.910603140 0.583465104
## [246] -2.039381114 -1.281953599 0.672382489 -0.844087387 -1.116666475
## [251] -1.801048334 -1.583069194 1.893623335 0.215991510 1.600668783
## [256] 1.698265543 -0.436348942 -0.102311440 -0.245484789 -0.912729730
## [261] -0.857869452 -1.134968019 -0.639593757 -1.001124743 -0.818140720
## [266] 0.861424419 -0.560973274 0.322186675 -1.483682822 2.500485952
## [271] 0.543769368 -0.955954863 0.275067780 -0.712569581 -0.141189475
## [276] 0.134658791 -0.497177586 1.540476933 0.457290804 0.459973844
## [281] 0.263191287 -0.895523170 0.556888922 -1.137561523 -0.648874951
## [286] -0.612555741 -0.666688294 -0.684129167 1.646432659 0.699288101
## [291] 0.651352783 1.697201694 -0.561976649 0.622544258 0.288542867
## [296] -0.997466165 0.223108388 -0.208216623 1.457515097 -0.452684344
## [301] -0.184277227 -0.349131551 -0.922721823 -1.644151703 0.601001849
## [306] -0.868774121 1.508690780 -0.432245035 -0.941364794 1.061962714
## [311] 0.058053728 -0.076957720 -1.117858591 -1.569625389 -0.758904672
## [316] 0.239694757 -0.512698528 -1.098615259 -1.532304518 0.257586679
## [321] 0.461637667 -0.980919860 2.745811395 -2.080444167 -0.249247018
## [326] 0.628200319 -0.741049551 -1.215411994 -0.471808668 -0.361454476
## [331] -1.230167020 -0.526313403 -0.847491907 0.958429778 -1.321554143
## [336] 1.434701743 -0.314000207 1.583637517 -0.382739116 2.112176279
## [341] -1.038521290 -1.139800162 -1.058016437 -1.048815774 0.679188845
## [346] -0.081949694 -0.509076803 0.462263236 1.325543621 1.722655084
## [351] -0.429171152 0.177546270 0.273260846 -1.427874556 0.302895665
## [356] 0.042127473 -0.299221856 0.767960689 -0.470023212 -0.669587135
## [361] 1.283220238 1.080264165 1.138287359 -0.447652237 1.522473498
## [366] 0.895894194 0.577939641 -0.939412606 -0.141327472 0.101811365
## [371] 1.226777757 1.417620059 1.893025774 0.668950715 1.010865086
## [376] 0.190848980 1.231876995 1.231937016 1.094560147 0.932291931
## [381] 0.352541515 -0.795458796 -1.701613184 -1.473849895 -1.486411588
## [386] -0.406104027 -0.366809910 -0.392072782 -1.691900214 -0.663182768
## [391] -0.373546926 0.916261746 -1.112179283 -0.520091773 -0.947074037
## [396] 0.679826991 -1.276939839 0.335885903 -0.391730595 -1.673061854
## [401] -0.842033908 -0.386719324 -1.588346046 0.919766746 0.258981478
## [406] -0.246943353 -0.457215741 0.274804835 -1.373804478 0.131580777
## [411] -1.453680550 -0.154933988 -1.286285341 -3.194465777 -0.356530483
## [416] 0.385124543 2.048433778 -1.307319291 -1.956966884 -0.108787498
## [421] -0.509339221 -1.283857813 -1.097875025 0.037056782 0.464718265
## [426] -0.373974281 0.282684857 1.012947084 -1.371703763 0.986855589
## [431] 0.167565272 -0.350255265 -0.870741048 -0.093694049 -1.292202391
## [436] 1.673021944 0.419420656 0.306719179 1.429634663 -0.738157969
## [441] -0.291127194 -1.423886957 -0.357465135 -0.778511417 -0.169412601
## [446] -1.315819151 -1.885425124 1.114551926 -0.551942930 1.658662551
## [451] 0.998009240 -0.995110834 -0.359578396 0.638894477 0.463591778
## [456] 0.495086558 0.226083308 0.541688524 -1.702926765 -0.317079594
## [461] -0.164829955 0.745343007 -0.271040525 0.693534371 1.031703218
## [466] 1.982976005 -1.138177652 1.785997237 0.630305925 2.024935473
## [471] -1.218629015 1.695779582 0.579295750 1.513770802 0.494273450
## [476] -0.238876908 0.350680783 0.861629796 0.090901334 0.916281063
## [481] -1.637351979 0.787740605 -1.213961219 -1.344890057 -0.019867506
## [486] -0.825003626 1.247103476 -0.116383615 0.838727900 0.809968621
## [491] -0.290500799 -1.581336980 0.079323888 0.642284952 1.450272025
## [496] 0.005246886 0.356380436 0.761444554 -0.246936334 -0.207118174
## [501] 0.574623354 -1.264459606 0.778362549 -0.784837904 0.336496511
## [506] 0.121305951 -1.600714068 1.202384476 0.004742196 0.517841762
## [511] -0.515499926 0.412704685 -0.172193655 -1.091952900 -0.531111511
## [516] -1.691835964 -1.077136481 0.483225345 -0.751841596 0.391017920
## [521] 0.790532724 -0.162028933 1.392885821 -0.112009991 -1.284782763
## [526] 0.081247840 -0.526913210 1.313474660 -0.080198669 1.035642187
## [531] -1.289687521 0.272965488 0.068322476 2.009730407 -0.293452163
## [536] -0.686843044 -2.002244294 -1.514599863 0.337748744 1.182087540
## [541] 0.055832287 -1.593193571 -0.984197810 0.144764288 1.588248455
## [546] 1.461379907 -0.849575086 0.132117473 -1.672142453 1.571860957
## [551] -0.415525038 -0.598123627 -1.454107958 0.694402678 0.029018334
## [556] 0.743950474 0.459256771 -1.162419815 -0.471208005 1.303407545
## [561] -1.200727117 0.929196984 -1.287861659 -2.292528119 0.243961029
## [566] -1.589678401 -1.592211094 -1.982793027 0.710689002 -0.651862081
## [571] 0.150348699 0.099585498 -1.011749881 -0.022452261 0.487127826
## [576] 0.681425951 -0.216508340 -0.760497908 -0.739336548 0.771820084
## [581] 0.921513755 -0.025922584 -1.079553804 0.995515805 -0.175981035
## [586] -1.394089352 0.076527620 -0.624443738 -0.446220931 2.535493952
## [591] 0.489648215 -1.120558776 -1.873169764 -0.747990058 -0.779271410
## [596] -0.984028182 0.302988493 -0.747999942 0.915921105 1.271294525
## [601] -0.483148034 0.359281397 0.823418747 -1.079422593 -1.101078608
## [606] 1.124572080 -0.758262069 0.747642808 -0.252015008 0.098224715
## [611] -0.961462703 -1.701969541 0.035230575 -0.940018731 1.139118101
## [616] 0.135737199 1.077670414 -0.447655008 0.615682408 -1.885675943
## [621] -0.770906537 -0.520115111 0.250213000 1.908022398 0.896435020
## [626] 1.229976590 -1.065285887 0.662895960 -0.413542597 1.620758828
## [631] 0.076813000 -1.874717949 0.708202135 -1.016937303 -1.052728037
## [636] 0.302076375 -3.441651595 -1.565897119 -0.486336279 0.498553856
## [641] 0.340749786 0.182364173 0.034439998 -0.323538535 -2.747624895
## [646] -0.019155427 -1.319096857 0.257618057 1.960921973 0.581906854
## [651] -1.660211560 0.146434485 -0.351799610 0.742457302 0.612389473
## [656] 0.918775839 0.200287049 -0.200632618 0.014465050 -1.408550415
## [661] -1.463057746 -1.364458675 -0.350687986 0.159190656 -1.010319626
## [666] 0.154559542 0.300237556 1.874472986 1.181205358 0.652510823
## [671] 0.721213558 -0.566162129 -0.668197581 0.670173034 0.333815219
## [676] -1.550810214 -0.144054599 0.580507030 2.155624331 0.450518666
## [681] -0.949167106 1.746268746 -2.190754323 0.269147990 1.971226075
## [686] -0.817942403 0.045099880 -0.419498265 0.197823649 -0.747235400
## [691] 0.111922470 -1.631534880 -0.625022214 -1.168000398 -0.217296860
## [696] 0.104929228 -0.537567892 -1.352266082 -0.340365711 0.680083222
## [701] 1.276882272 -0.118889240 -0.599976621 -0.821353167 1.182852478
## [706] 1.801877584 -0.272971117 0.481705018 -0.506002162 0.415649586
## [711] -0.135526360 -1.712346317 0.681722138 -0.940059254 -1.589824745
## [716] -1.321557391 -0.762782453 0.197328202 -0.376036066 0.987390293
## [721] -0.234046334 -0.839934647 0.174244433 -1.209321582 1.214922299
## [726] -1.024551596 -1.210603475 -1.231888314 -0.645798436 0.399989138
## [731] -1.415913727 -0.472129419 0.430406526 -1.030175449 -1.012076947
## [736] -1.300889710 0.538175319 -0.926049976 -0.596715192 -0.877778889
## [741] 1.105248335 -0.056054761 -0.675540331 0.645318148 1.250463416
## [746] -0.116407470 0.422349108 0.424454008 -0.033700343 -0.353509363
## [751] -1.577160000 1.424770628 1.703205287 -0.643419378 -0.448053685
## [756] 0.113032048 -2.575082392 -0.033660220 -0.753756246 0.959141267
## [761] -0.537727956 0.151426519 -1.426574307 -1.314243711 0.488043105
## [766] 1.015161663 -1.939180030 0.107102797 0.649035343 -0.125288733
## [771] 1.568818489 1.298235038 0.328619977 -0.235697387 1.499665756
## [776] 0.996358995 -1.678479168 0.758330376 -1.321403913 0.208539178
## [781] -0.833203372 0.159655564 -0.724268619 0.805381548 0.016502602
## [786] 0.732506442 -0.363707373 1.271438265 -0.399559442 -1.387583626
## [791] -0.796135899 0.869708137 0.288143501 0.267264587 2.588814631
## [796] 0.995553209 -0.092786386 0.992048046 0.335793337 -0.490979414
## [801] -0.057777180 0.126592297 0.660193669 0.371440364 -0.311948101
## [806] -0.088310003 0.884235038 0.917064687 0.857385286 -2.327431255
## [811] 1.618941940 0.854267468 -0.331775153 -0.503955385 0.348046010
## [816] 0.970477360 -0.609184288 0.554750396 -0.426031286 -1.051086337
## [821] -0.493128529 -0.656251513 -0.832305639 0.589811798 -0.725013258
## [826] 0.894054600 -1.342726795 1.222694478 -0.756360176 -0.009364825
## [831] 0.248675118 1.027757778 1.248654255 0.575967210 -0.683610589
## [836] -0.684957559 -0.214325400 0.501990778 1.861313815 0.013801688
## [841] -0.256857393 0.716467285 0.261298004 1.173978060 0.024320627
## [846] -1.433850491 -0.078964240 1.119918609 0.962801029 -0.244377475
## [851] 0.212040417 -0.181541180 -0.691755272 -0.075068053 -1.687628981
## [856] -1.122397905 -1.243371878 -1.363105991 0.578685509 2.485386983
## [861] -1.303190325 -1.319996491 -1.268401853 -0.458925738 0.261510845
## [866] 0.171033516 -0.490732710 -1.241954283 1.592703564 -0.401129708
## [871] -0.243339552 0.460660152 0.739413853 -1.168947822 -0.228385760
## [876] 0.822103573 0.485597922 0.376031812 1.396524994 -0.933095858
## [881] -0.574732383 -1.385762089 -0.475490053 0.898827764 0.065214638
## [886] 1.421825910 1.142881447 -2.410282609 0.206918611 1.790457304
## [891] -0.324430609 -2.221052498 -0.127011164 0.456176828 -0.585084249
## [896] -0.881776837 -2.992812699 -0.436410398 0.546292775 0.160075982
## [901] -1.172272009 -0.730011909 1.216826873 1.722299968 0.457388252
## [906] -0.101200139 2.413037986 -0.815021651 -1.262599207 -0.115159393
## [911] -0.637911048 -0.597695782 -0.239120549 2.019507140 -0.802163845
## [916] -1.399599411 0.462799167 -0.387517805 0.060038577 -0.005557831
## [921] -0.796477993 0.825973714 1.992320474 0.896781807 0.769102389
## [926] 1.072830917 -1.306019988 1.251160134 -0.035404573 -0.463992770
## [931] -0.897028784 -0.885995426 -0.059898362 1.143270352 0.971440746
## [936] 1.348310163 -0.319881143 0.467798833 1.399809184 -0.639620667
## [941] 0.759968573 -0.304221696 -0.334995429 1.823493157 -0.279086049
## [946] 1.518691263 0.873308729 -1.466355395 0.077484992 0.482995650
## [951] -0.294003047 -1.756202393 -1.940660355 -1.377050663 -0.825390492
## [956] 0.632876542 -0.396158862 -0.387493905 -0.553148858 0.137112808
## [961] -0.503395336 -0.284301049 -0.796665650 -0.675871866 -0.340377852
## [966] -0.931783004 -1.108894119 0.620390550 -1.072650109 0.331292847
## [971] 2.362495850 -0.193442025 1.870761494 -0.558649122 0.422929200
## [976] 0.395329969 0.274155099 -1.462395953 0.419812537 0.202779287
## [981] -1.284849840 0.398166666 -1.996447343 -0.299881041 -0.763955478
## [986] -0.138663768 -2.740702499 0.541443570 1.754648731 0.201792046
## [991] -0.251002690 -1.420122625 0.360209047 -0.109891192 -0.599175938
## [996] 0.220022390 -0.876228645 0.052365405 0.071300159 -0.828530930
yAxis <- rnorm(1000) + xAxis + 10
yAxis
## [1] 10.259973 10.176995 14.366278 12.968278 12.526519 9.191013 9.793576
## [8] 10.978469 10.869235 9.136667 10.564207 11.409435 9.715982 9.820115
## [15] 10.339692 9.535011 11.237189 8.884966 10.070066 12.533501 9.787441
## [22] 10.020407 7.351603 11.032626 10.040938 10.572130 10.545772 10.735699
## [29] 10.485083 9.206358 10.303576 7.956571 10.876067 12.094359 10.402790
## [36] 11.699227 11.342056 8.308245 10.794654 9.355944 9.289369 12.787024
## [43] 7.759974 9.359151 8.327628 10.310888 11.983724 11.605021 11.377006
## [50] 7.476001 10.031427 12.121327 10.032589 11.198050 11.527174 10.100061
## [57] 11.249779 9.488884 11.101364 10.844061 11.118948 9.969037 10.038713
## [64] 10.415505 10.379474 8.474490 8.323028 11.983417 9.187417 10.571117
## [71] 10.682316 6.964034 9.412246 8.565245 10.257295 9.526058 9.026563
## [78] 10.881274 12.478042 12.145096 12.512737 9.361049 8.739613 8.457908
## [85] 8.450026 10.927375 11.008037 10.380402 9.729943 9.833895 10.972398
## [92] 11.027876 11.534266 10.826764 9.036614 12.342966 12.406449 11.471783
## [99] 9.535180 10.724211 9.282052 7.667430 9.718061 10.387633 10.410118
## [106] 7.590534 11.548693 7.994136 9.027457 8.999013 9.614768 8.882189
## [113] 12.107606 10.819599 11.380496 9.287947 11.102265 10.061163 10.594415
## [120] 9.529572 8.395148 11.103206 11.206128 6.150580 10.054513 10.295934
## [127] 9.927467 8.124185 9.430967 10.564357 7.963945 10.131157 9.032796
## [134] 10.476287 8.390327 11.458388 8.544396 9.410906 13.076018 10.102999
## [141] 10.736126 9.564659 9.411127 8.943538 9.914252 11.811508 10.141421
## [148] 12.081495 11.811472 8.476001 11.472979 12.177817 9.947745 10.781943
## [155] 12.160189 10.190145 10.523185 9.909178 10.178202 8.848395 9.955985
## [162] 8.796961 11.351663 10.815329 9.726301 9.017073 8.914137 10.247084
## [169] 8.335103 11.986584 7.693581 10.572694 9.989687 10.779203 7.624775
## [176] 8.214769 10.134080 6.905006 12.010719 9.648917 10.236303 10.529126
## [183] 9.575466 7.835445 10.982588 8.217730 9.192530 10.803097 8.471307
## [190] 11.887922 9.261910 9.006111 10.304272 11.638070 8.889462 10.876450
## [197] 8.809029 10.477386 9.885287 9.084418 11.046151 7.636414 8.398871
## [204] 13.152662 8.169612 7.383368 9.842856 7.191360 10.900867 10.721447
## [211] 10.259667 9.307973 10.017494 10.043632 8.216635 12.233014 8.597851
## [218] 12.446811 11.543087 11.725278 8.847317 8.355927 10.853001 11.846938
## [225] 9.927590 9.664916 12.096277 11.323006 8.958746 9.903497 10.221782
## [232] 8.958807 13.161015 9.585312 9.075397 10.112811 8.078827 7.936680
## [239] 8.553260 9.936539 9.455026 10.099122 9.700092 11.120941 11.875021
## [246] 7.222361 8.879372 11.428839 8.583735 8.604517 9.635595 8.229691
## [253] 12.240265 9.081865 11.110247 11.546305 9.888611 11.457041 8.076383
## [260] 9.063269 9.898544 8.854140 10.232617 8.982143 9.627712 10.684743
## [267] 9.129118 9.695650 8.492652 12.312660 10.182070 11.680777 10.793401
## [274] 10.563484 9.246814 9.798488 9.892758 11.376855 9.427030 11.106099
## [281] 8.704084 9.495078 9.647432 9.005952 9.945198 9.759201 9.181727
## [288] 9.062366 11.671066 6.907741 10.135067 9.048093 9.766064 11.162858
## [295] 10.463913 9.879614 10.307379 8.744901 12.464461 8.979283 10.416549
## [302] 10.433902 9.114769 8.444051 10.812853 8.958676 11.906133 11.187722
## [309] 9.762203 12.837584 10.039946 9.340671 7.381442 7.888425 9.379014
## [316] 9.334827 9.617508 9.703310 8.927647 9.582123 9.617632 11.031433
## [323] 14.773462 6.991496 10.926345 12.212933 9.933201 8.687947 10.649460
## [330] 9.852097 7.743352 9.082850 8.208386 12.368587 8.673161 13.662921
## [337] 9.010489 10.979335 8.360187 13.723736 8.972453 9.572543 9.459373
## [344] 7.839963 7.996765 10.361934 8.140752 8.903663 11.077678 10.897648
## [351] 9.284841 10.839174 8.530484 7.453548 8.975206 11.427711 8.826480
## [358] 12.261427 8.692300 9.984540 9.890454 10.343188 11.517111 10.670853
## [365] 11.615790 12.973023 10.579690 10.293103 9.110161 7.673777 12.212689
## [372] 11.822843 11.429903 9.403727 10.604755 10.527859 11.068057 11.575829
## [379] 10.689700 9.859929 10.007501 9.447405 9.543758 8.545192 7.737052
## [386] 10.194488 9.662382 9.289176 7.805250 8.338369 11.946355 12.616085
## [393] 7.842930 9.009306 8.508796 13.226975 7.114247 10.357523 9.303237
## [400] 9.289602 9.797581 9.397810 8.969280 9.279508 10.128070 8.918657
## [407] 7.910051 11.444316 6.470707 9.816761 7.722159 7.826464 9.854849
## [414] 7.329828 8.328529 10.766122 13.215145 7.519671 8.025016 11.280838
## [421] 9.107573 8.943336 8.678117 11.370293 12.548824 8.895554 10.659330
## [428] 11.214418 8.088737 10.777312 9.572057 9.162223 9.253819 8.570935
## [435] 9.084907 10.581767 10.535307 10.811116 13.260785 9.905136 9.850030
## [442] 9.094412 10.565372 8.932356 11.589428 7.334785 9.348718 12.508673
## [449] 9.508497 10.665672 10.567408 8.165165 10.187522 10.067228 10.256690
## [456] 10.889831 9.321893 10.739795 8.359916 10.485493 10.485210 12.081705
## [463] 10.934956 10.812625 9.862685 13.059643 7.342716 10.951433 10.554295
## [470] 13.376690 8.308798 10.824476 10.785569 13.186649 13.183607 9.558345
## [477] 11.188483 10.075667 9.916587 11.005809 8.100125 9.573964 10.550784
## [484] 7.463829 8.654387 8.399864 12.008618 9.242094 12.572091 12.216977
## [491] 10.689319 7.181427 9.643575 9.300810 11.578549 8.975279 10.474704
## [498] 11.543042 9.705904 10.164410 10.220034 9.295141 10.013140 8.415214
## [505] 10.729716 10.122955 8.756440 11.401986 8.294382 10.856183 9.756689
## [512] 11.149312 8.208821 9.594811 8.306238 8.793053 10.162161 11.902180
## [519] 9.735896 11.494806 10.942127 9.807073 10.914568 10.556195 8.583424
## [526] 10.643166 9.576670 13.205006 10.623131 11.843794 7.867563 10.073644
## [533] 11.200639 11.835022 10.151327 8.312576 9.819114 8.075417 10.610378
## [540] 13.126669 9.665168 6.953011 11.204145 11.103663 12.977946 11.366816
## [547] 9.527198 8.440462 8.391897 10.358593 9.433355 9.568494 10.253482
## [554] 10.335943 10.501335 10.779452 10.652759 9.042104 9.838565 11.020363
## [561] 9.471055 11.198334 9.621767 7.651150 10.994250 10.405041 7.822404
## [568] 10.562361 10.842075 9.202850 9.485825 8.924969 7.280351 10.181804
## [575] 11.225027 11.757140 10.325402 10.119776 10.069658 10.176368 10.642163
## [582] 9.317498 9.885670 9.778344 11.356913 8.793228 10.109361 9.404451
## [589] 11.278108 14.397653 11.752396 8.932427 9.077683 9.037913 7.329005
## [596] 9.405356 11.344973 9.543025 10.494339 9.971402 8.403778 9.829255
## [603] 9.125613 9.295481 9.699587 12.401029 10.799243 11.104704 10.311485
## [610] 9.718560 8.235431 8.943395 9.009048 8.102730 8.680533 11.028141
## [617] 12.691217 10.278445 10.738858 7.935156 9.933364 8.686626 10.439807
## [624] 12.142255 12.214759 11.714063 9.261323 12.191452 9.707725 12.453789
## [631] 9.690397 7.100060 11.153508 9.720768 8.650216 9.919967 6.981298
## [638] 8.120174 7.793000 10.895802 9.794289 10.933195 9.214253 10.207368
## [645] 7.480638 11.372005 9.953704 9.821073 10.700798 10.712164 8.762443
## [652] 8.880746 9.255899 11.520471 10.773010 10.674605 10.853250 9.847520
## [659] 9.318906 8.780997 7.557052 8.624293 7.650087 9.414662 10.032675
## [666] 10.000969 10.138716 12.726127 12.720032 10.678607 9.805085 9.300604
## [673] 9.698479 9.901619 9.819898 7.034352 9.679627 10.773958 12.536023
## [680] 9.157983 8.585508 11.101451 6.929429 8.462207 10.213166 8.314226
## [687] 9.820535 9.744995 9.635258 9.186584 11.120159 8.931861 9.295895
## [694] 9.761385 10.377718 9.439101 8.703591 7.386581 10.582240 9.016587
## [701] 10.026078 7.461143 8.759326 9.297430 10.997492 12.165746 10.019028
## [708] 10.504384 8.696882 8.262397 8.232342 8.656134 13.267964 8.844987
## [715] 9.011780 8.848049 8.022460 9.859278 10.374623 10.740053 9.338089
## [722] 8.113371 9.689985 7.642109 9.967175 9.515016 9.582228 9.698850
## [729] 8.414381 9.255388 7.484862 8.445592 11.389821 9.955819 8.689506
## [736] 7.960069 10.382850 7.443507 8.975226 9.088119 11.784032 10.949127
## [743] 9.871124 10.390047 11.658981 9.145261 11.037507 10.152366 7.998286
## [750] 8.202827 6.846299 13.077062 14.100520 9.343625 9.135618 10.112900
## [757] 7.381943 11.210143 10.281142 9.732905 10.467955 9.529712 8.068067
## [764] 7.947906 10.462331 10.786559 8.585764 9.883083 9.257889 8.905342
## [771] 12.482687 10.320948 10.362668 8.953278 11.754538 12.952166 9.353037
## [778] 10.333549 9.309045 10.238965 11.286836 12.996781 9.099176 8.622299
## [785] 9.972790 11.536075 11.546777 9.527939 9.778586 9.811687 9.592212
## [792] 10.301458 10.905285 10.444256 12.448764 11.653475 9.803670 10.523258
## [799] 10.166708 7.522631 11.851900 9.950003 8.664142 9.254888 9.859602
## [806] 8.449491 12.060609 10.741722 8.381531 7.065459 10.855308 11.394682
## [813] 9.948534 11.172368 9.640602 11.706468 10.458466 9.214609 9.774200
## [820] 9.034820 9.484454 9.978523 7.838315 10.356347 7.969154 11.569202
## [827] 8.151344 11.639095 8.767116 11.135299 10.187246 9.727251 9.231935
## [834] 12.298561 9.749488 9.388578 9.524660 10.169054 11.462876 10.744949
## [841] 9.434729 9.047710 8.534378 9.574376 9.315000 8.529366 9.052969
## [848] 12.288041 10.862446 10.484000 10.371675 7.913231 8.634826 9.567559
## [855] 10.548930 10.112241 9.310027 8.442009 11.386520 12.297076 9.441863
## [862] 7.572475 7.557896 8.304303 9.489146 9.703877 10.989116 10.067024
## [869] 11.296900 9.414943 8.846641 10.079747 8.663954 6.708925 9.805447
## [876] 10.226829 10.178875 11.650912 11.512082 10.667076 8.234483 8.064248
## [883] 9.917358 12.639615 10.696203 11.735753 9.441026 8.304217 10.485144
## [890] 12.180816 9.564086 9.114772 8.738988 9.881334 9.720192 8.681036
## [897] 7.887835 9.465173 9.036277 9.197995 8.352405 7.803566 10.421002
## [904] 12.244908 9.111850 9.136181 13.885924 10.637717 9.630570 10.813774
## [911] 7.927693 9.226154 7.577277 12.545403 8.677551 9.486126 13.090488
## [918] 9.157000 10.791053 11.632064 10.917158 9.552729 10.981735 10.618991
## [925] 10.768490 9.685472 8.571459 11.209948 8.629662 9.782572 9.327248
## [932] 8.595155 8.495976 11.577540 9.946124 11.660670 9.998317 10.677279
## [939] 12.416873 10.283617 10.172249 11.691093 7.982050 11.312803 8.457613
## [946] 9.633003 10.764354 6.871207 9.664236 11.109507 9.458736 8.255594
## [953] 8.470289 9.337262 8.727943 9.830720 9.187798 9.745151 9.881102
## [960] 10.444117 9.024661 9.235167 8.091692 10.039980 10.295156 11.269403
## [967] 9.500613 10.941080 9.290227 8.806781 12.887151 7.626076 10.855302
## [974] 9.706837 10.014914 12.151729 10.059845 8.147955 10.592926 11.349907
## [981] 8.052031 9.375395 6.643261 9.278516 9.927051 9.369211 7.499642
## [988] 10.190852 13.290368 10.148525 11.272519 6.910431 10.366423 10.160178
## [995] 11.507238 10.804314 7.649795 9.930565 10.718187 9.312169
# 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] 2 2 4 5 4 2 4 2 2 4 3 3 2 2 2 2 4 1 2 4 3 3 1 4 1 2 3 5 3 2 4 3 4 4 2 4 5
## [38] 3 5 3 2 5 1 2 2 2 4 3 5 2 3 5 2 4 4 3 4 3 4 4 3 3 3 4 1 2 2 4 3 3 3 1 3 2
## [75] 3 3 2 3 4 4 4 3 2 1 2 4 2 3 2 3 4 4 3 3 3 4 5 4 4 4 3 2 3 4 4 2 4 2 2 3 3
## [112] 2 4 5 4 3 4 3 2 2 3 3 4 2 3 4 2 2 4 2 2 3 2 3 2 5 3 2 4 4 2 2 3 2 3 4 3 5
## [149] 4 3 5 5 3 4 5 2 4 4 2 4 3 2 4 4 3 3 3 4 3 5 3 3 2 4 2 3 3 1 4 2 3 3 3 2 4
## [186] 3 3 4 2 3 2 2 3 4 2 3 2 3 4 2 3 2 4 4 3 2 2 2 4 4 4 4 2 2 1 4 2 3 4 4 2 2
## [223] 3 4 2 3 5 3 2 2 3 3 4 3 2 3 2 1 3 3 3 2 2 4 4 1 2 4 2 2 1 1 5 3 5 5 3 3 3
## [260] 2 2 2 2 2 2 4 2 3 2 5 4 2 3 2 3 3 3 5 3 3 3 2 4 2 2 2 2 2 5 4 4 5 2 4 3 2
## [297] 3 3 4 3 3 3 2 1 4 2 5 3 2 4 3 3 2 1 2 3 2 2 1 3 3 2 5 1 3 4 2 2 3 3 2 2 2
## [334] 4 2 4 3 5 3 5 2 2 2 2 4 3 2 3 4 5 3 3 3 2 3 3 3 4 3 2 4 4 4 3 5 4 4 2 3 3
## [371] 4 4 5 4 4 3 4 4 4 4 3 2 1 2 2 3 3 3 1 2 3 4 2 2 2 4 2 3 3 1 2 3 1 4 3 3 3
## [408] 3 2 3 2 3 2 1 3 3 5 2 1 3 2 2 2 3 3 3 3 4 2 4 3 3 2 3 2 5 3 3 4 2 3 2 3 2
## [445] 3 2 1 4 2 5 4 2 3 4 3 3 3 4 1 3 3 4 3 4 4 5 2 5 4 5 2 5 4 5 3 3 3 4 3 4 1
## [482] 4 2 2 3 2 4 3 4 4 3 1 3 4 4 3 3 4 3 3 4 2 4 2 3 3 1 4 3 4 2 3 3 2 2 1 2 3
## [519] 2 3 4 3 4 3 2 3 2 4 3 4 2 3 3 5 3 2 1 1 3 4 3 1 2 3 5 4 2 3 1 5 3 2 2 4 3
## [556] 4 3 2 3 4 2 4 2 1 3 1 1 1 4 2 3 3 2 3 3 4 3 2 2 4 4 3 2 4 3 2 3 2 3 5 3 2
## [593] 1 2 2 2 3 2 4 4 3 3 4 2 2 4 2 4 3 3 2 1 3 2 4 3 4 3 4 1 2 2 3 5 4 4 2 4 3
## [630] 5 3 1 4 2 2 3 1 1 3 3 3 3 3 3 1 3 2 3 5 4 1 3 3 4 4 4 3 3 3 2 2 2 3 3 2 3
## [667] 3 5 4 4 4 2 2 4 3 1 3 4 5 3 2 5 1 3 5 2 3 3 3 2 3 1 2 2 3 3 2 2 3 4 4 3 2
## [704] 2 4 5 3 3 2 3 3 1 4 2 1 2 2 3 3 4 3 2 3 2 4 2 2 2 2 3 2 3 3 2 2 2 4 2 2 2
## [741] 4 3 2 4 4 3 3 3 3 3 1 4 5 2 3 3 1 3 2 4 2 3 2 2 3 4 1 3 4 3 5 4 3 3 4 4 1
## [778] 4 2 3 2 3 2 4 3 4 3 4 3 2 2 4 3 3 5 4 3 4 3 3 3 3 4 3 3 3 4 4 4 1 5 4 3 2
## [815] 3 4 2 4 3 2 3 2 2 4 2 4 2 4 2 3 3 4 4 4 2 2 3 4 5 3 3 4 3 4 3 2 3 4 4 3 3
## [852] 3 2 3 1 2 2 2 4 5 2 2 2 3 3 3 3 2 5 3 3 3 4 2 3 4 3 3 4 2 2 2 3 4 3 4 4 1
## [889] 3 5 3 1 3 3 2 2 1 3 4 3 2 2 4 5 3 3 5 2 2 3 2 2 3 5 2 2 3 3 3 3 2 4 5 4 4
## [926] 4 2 4 3 3 2 2 3 4 4 4 3 3 4 2 4 3 3 5 3 5 4 2 3 3 3 1 1 2 2 4 3 3 2 3 2 3
## [963] 2 2 3 2 2 4 2 3 5 3 5 2 3 3 3 2 3 3 2 3 1 3 2 3 1 4 5 3 3 2 3 3 2 3 2 3 3
## [1000] 2
# create sample dataframe by joining variables
sample_data <- data.frame(xAxis,yAxis,group)
sample_data
## xAxis yAxis group
## 1 -0.532929453 10.259973 2
## 2 -0.535658736 10.176995 2
## 3 1.113188584 14.366278 4
## 4 1.985900210 12.968278 5
## 5 1.269813300 12.526519 4
## 6 -0.744221693 9.191013 2
## 7 0.924422156 9.793576 4
## 8 -0.606340157 10.978469 2
## 9 -0.739791319 10.869235 2
## 10 1.152078655 9.136667 4
## 11 0.448616674 10.564207 3
## 12 0.300946762 11.409435 3
## 13 -0.532224587 9.715982 2
## 14 -0.629677189 9.820115 2
## 15 -0.501911701 10.339692 2
## 16 -0.536270736 9.535011 2
## 17 1.269512675 11.237189 4
## 18 -2.333708216 8.884966 1
## 19 -0.593750192 10.070066 2
## 20 0.889048655 12.533501 4
## 21 -0.131389880 9.787441 3
## 22 0.279469767 10.020407 3
## 23 -1.521413415 7.351603 1
## 24 0.611669397 11.032626 4
## 25 -1.656321076 10.040938 1
## 26 -0.506490365 10.572130 2
## 27 -0.302172602 10.545772 3
## 28 2.374396751 10.735699 5
## 29 -0.367986381 10.485083 3
## 30 -1.199343290 9.206358 2
## 31 1.103640414 10.303576 4
## 32 -0.225791069 7.956571 3
## 33 0.770140249 10.876067 4
## 34 0.862025496 12.094359 4
## 35 -0.761131679 10.402790 2
## 36 0.636406127 11.699227 4
## 37 1.541807345 11.342056 5
## 38 -0.323449051 8.308245 3
## 39 1.635897973 10.794654 5
## 40 -0.068416983 9.355944 3
## 41 -1.127776021 9.289369 2
## 42 1.764631606 12.787024 5
## 43 -1.853999668 7.759974 1
## 44 -1.033986251 9.359151 2
## 45 -1.475897790 8.327628 2
## 46 -0.714116560 10.310888 2
## 47 1.274540530 11.983724 4
## 48 0.296324560 11.605021 3
## 49 1.556244523 11.377006 5
## 50 -0.610212256 7.476001 2
## 51 0.242123871 10.031427 3
## 52 1.937782414 12.121327 5
## 53 -0.527439827 10.032589 2
## 54 1.455543269 11.198050 4
## 55 0.893837845 11.527174 4
## 56 0.116245457 10.100061 3
## 57 0.683257705 11.249779 4
## 58 -0.474749278 9.488884 3
## 59 0.972151649 11.101364 4
## 60 0.592832640 10.844061 4
## 61 -0.155191850 11.118948 3
## 62 0.205467519 9.969037 3
## 63 0.164642754 10.038713 3
## 64 1.235106516 10.415505 4
## 65 -1.741987266 10.379474 1
## 66 -1.249990233 8.474490 2
## 67 -1.439495614 8.323028 2
## 68 0.533372009 11.983417 4
## 69 -0.085123456 9.187417 3
## 70 -0.496441905 10.571117 3
## 71 -0.438686120 10.682316 3
## 72 -2.318285223 6.964034 1
## 73 0.122178401 9.412246 3
## 74 -1.221855707 8.565245 2
## 75 0.124432462 10.257295 3
## 76 0.250616455 9.526058 3
## 77 -0.636966016 9.026563 2
## 78 0.483952475 10.881274 3
## 79 1.174260637 12.478042 4
## 80 0.930411132 12.145096 4
## 81 1.267662141 12.512737 4
## 82 -0.350266867 9.361049 3
## 83 -1.293820459 8.739613 2
## 84 -1.556264341 8.457908 1
## 85 -1.202197156 8.450026 2
## 86 0.680700705 10.927375 4
## 87 -0.509954553 11.008037 2
## 88 -0.450424660 10.380402 3
## 89 -1.197078715 9.729943 2
## 90 -0.152728685 9.833895 3
## 91 0.597760228 10.972398 4
## 92 0.977353050 11.027876 4
## 93 0.480028425 11.534266 3
## 94 0.116080477 10.826764 3
## 95 -0.240282895 9.036614 3
## 96 0.693202981 12.342966 4
## 97 2.266117897 12.406449 5
## 98 0.883925031 11.471783 4
## 99 0.839591700 9.535180 4
## 100 0.522252356 10.724211 4
## 101 -0.350345835 9.282052 3
## 102 -0.965816231 7.667430 2
## 103 0.440588804 9.718061 3
## 104 0.630633064 10.387633 4
## 105 0.864382482 10.410118 4
## 106 -0.610527268 7.590534 2
## 107 0.513318210 11.548693 4
## 108 -1.271658723 7.994136 2
## 109 -0.793703124 9.027457 2
## 110 -0.119721219 8.999013 3
## 111 0.329229689 9.614768 3
## 112 -0.862987928 8.882189 2
## 113 1.475263182 12.107606 4
## 114 1.588615702 10.819599 5
## 115 0.880354714 11.380496 4
## 116 -0.126988230 9.287947 3
## 117 0.627453641 11.102265 4
## 118 -0.001965687 10.061163 3
## 119 -0.887081437 10.594415 2
## 120 -0.869064430 9.529572 2
## 121 0.236648849 8.395148 3
## 122 0.480688012 11.103206 3
## 123 1.098327686 11.206128 4
## 124 -1.415755524 6.150580 2
## 125 -0.291611940 10.054513 3
## 126 0.864009766 10.295934 4
## 127 -0.588845554 9.927467 2
## 128 -0.676810211 8.124185 2
## 129 0.557515308 9.430967 4
## 130 -0.792769726 10.564357 2
## 131 -1.388208971 7.963945 2
## 132 0.352786127 10.131157 3
## 133 -1.327027803 9.032796 2
## 134 0.408706950 10.476287 3
## 135 -0.548492646 8.390327 2
## 136 1.891748287 11.458388 5
## 137 0.430085621 8.544396 3
## 138 -1.013527459 9.410906 2
## 139 0.703877497 13.076018 4
## 140 0.970719522 10.102999 4
## 141 -0.772555652 10.736126 2
## 142 -1.282947235 9.564659 2
## 143 0.449758492 9.411127 3
## 144 -0.890554115 8.943538 2
## 145 0.062648516 9.914252 3
## 146 1.308924337 11.811508 4
## 147 -0.295157434 10.141421 3
## 148 2.358430994 12.081495 5
## 149 1.032623574 11.811472 4
## 150 -0.018375696 8.476001 3
## 151 1.628217245 11.472979 5
## 152 1.813662138 12.177817 5
## 153 -0.441792585 9.947745 3
## 154 0.544502869 10.781943 4
## 155 1.626246545 12.160189 5
## 156 -1.384230576 10.190145 2
## 157 0.796139018 10.523185 4
## 158 0.556863979 9.909178 4
## 159 -0.508825973 10.178202 2
## 160 0.639429785 8.848395 4
## 161 -0.390790759 9.955985 3
## 162 -0.567169326 8.796961 2
## 163 0.639769619 11.351663 4
## 164 0.881322560 10.815329 4
## 165 0.066068577 9.726301 3
## 166 -0.359528976 9.017073 3
## 167 -0.417331046 8.914137 3
## 168 0.934265334 10.247084 4
## 169 -0.343623433 8.335103 3
## 170 1.813850027 11.986584 5
## 171 -0.265327900 7.693581 3
## 172 0.140870929 10.572694 3
## 173 -0.908733535 9.989687 2
## 174 1.181289958 10.779203 4
## 175 -1.026600443 7.624775 2
## 176 -0.071694047 8.214769 3
## 177 -0.093342480 10.134080 3
## 178 -1.753929314 6.905006 1
## 179 0.549370157 12.010719 4
## 180 -0.766360623 9.648917 2
## 181 -0.371010126 10.236303 3
## 182 0.116043073 10.529126 3
## 183 -0.108274496 9.575466 3
## 184 -0.981910596 7.835445 2
## 185 1.422443483 10.982588 4
## 186 -0.173727965 8.217730 3
## 187 -0.395071673 9.192530 3
## 188 1.244272162 10.803097 4
## 189 -1.420333428 8.471307 2
## 190 0.048735919 11.887922 3
## 191 -1.091533129 9.261910 2
## 192 -0.938984946 9.006111 2
## 193 -0.480284999 10.304272 3
## 194 0.878758683 11.638070 4
## 195 -0.916555142 8.889462 2
## 196 0.452584500 10.876450 3
## 197 -0.905726429 8.809029 2
## 198 -0.181167517 10.477386 3
## 199 0.627465215 9.885287 4
## 200 -0.923299827 9.084418 2
## 201 0.394909004 11.046151 3
## 202 -0.777459881 7.636414 2
## 203 0.801790913 8.398871 4
## 204 1.317322116 13.152662 4
## 205 -0.325719437 8.169612 3
## 206 -1.048025006 7.383368 2
## 207 -0.916477625 9.842856 2
## 208 -1.124872499 7.191360 2
## 209 1.046339194 10.900867 4
## 210 1.009687832 10.721447 4
## 211 0.833969346 10.259667 4
## 212 0.575904434 9.307973 4
## 213 -0.855581681 10.017494 2
## 214 -1.187904881 10.043632 2
## 215 -2.548263727 8.216635 1
## 216 1.393666862 12.233014 4
## 217 -1.008740304 8.597851 2
## 218 0.124064909 12.446811 3
## 219 0.886219130 11.543087 4
## 220 1.425045956 11.725278 4
## 221 -1.439377216 8.847317 2
## 222 -0.859581619 8.355927 2
## 223 -0.438475951 10.853001 3
## 224 1.081392372 11.846938 4
## 225 -0.883514492 9.927590 2
## 226 -0.035781127 9.664916 3
## 227 1.773948704 12.096277 5
## 228 0.253497064 11.323006 3
## 229 -0.926652913 8.958746 2
## 230 -0.567795147 9.903497 2
## 231 -0.250335227 10.221782 3
## 232 -0.089197283 8.958807 3
## 233 0.891964468 13.161015 4
## 234 -0.341345067 9.585312 3
## 235 -1.169143212 9.075397 2
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## 239 -0.378479259 8.553260 3
## 240 -0.308087502 9.936539 3
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## 242 -0.620721238 10.099122 2
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## 246 -2.039381114 7.222361 1
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## 249 -0.844087387 8.583735 2
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## 251 -1.801048334 9.635595 1
## 252 -1.583069194 8.229691 1
## 253 1.893623335 12.240265 5
## 254 0.215991510 9.081865 3
## 255 1.600668783 11.110247 5
## 256 1.698265543 11.546305 5
## 257 -0.436348942 9.888611 3
## 258 -0.102311440 11.457041 3
## 259 -0.245484789 8.076383 3
## 260 -0.912729730 9.063269 2
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## 262 -1.134968019 8.854140 2
## 263 -0.639593757 10.232617 2
## 264 -1.001124743 8.982143 2
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## 267 -0.560973274 9.129118 2
## 268 0.322186675 9.695650 3
## 269 -1.483682822 8.492652 2
## 270 2.500485952 12.312660 5
## 271 0.543769368 10.182070 4
## 272 -0.955954863 11.680777 2
## 273 0.275067780 10.793401 3
## 274 -0.712569581 10.563484 2
## 275 -0.141189475 9.246814 3
## 276 0.134658791 9.798488 3
## 277 -0.497177586 9.892758 3
## 278 1.540476933 11.376855 5
## 279 0.457290804 9.427030 3
## 280 0.459973844 11.106099 3
## 281 0.263191287 8.704084 3
## 282 -0.895523170 9.495078 2
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## 284 -1.137561523 9.005952 2
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## 286 -0.612555741 9.759201 2
## 287 -0.666688294 9.181727 2
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## 289 1.646432659 11.671066 5
## 290 0.699288101 6.907741 4
## 291 0.651352783 10.135067 4
## 292 1.697201694 9.048093 5
## 293 -0.561976649 9.766064 2
## 294 0.622544258 11.162858 4
## 295 0.288542867 10.463913 3
## 296 -0.997466165 9.879614 2
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## 317 -0.512698528 9.617508 2
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## 322 -0.980919860 11.031433 2
## 323 2.745811395 14.773462 5
## 324 -2.080444167 6.991496 1
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## 326 0.628200319 12.212933 4
## 327 -0.741049551 9.933201 2
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## 341 -1.038521290 8.972453 2
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## 979 0.419812537 10.592926 3
## 980 0.202779287 11.349907 3
## 981 -1.284849840 8.052031 2
## 982 0.398166666 9.375395 3
## 983 -1.996447343 6.643261 1
## 984 -0.299881041 9.278516 3
## 985 -0.763955478 9.927051 2
## 986 -0.138663768 9.369211 3
## 987 -2.740702499 7.499642 1
## 988 0.541443570 10.190852 4
## 989 1.754648731 13.290368 5
## 990 0.201792046 10.148525 3
## 991 -0.251002690 11.272519 3
## 992 -1.420122625 6.910431 2
## 993 0.360209047 10.366423 3
## 994 -0.109891192 10.160178 3
## 995 -0.599175938 11.507238 2
## 996 0.220022390 10.804314 3
## 997 -0.876228645 7.649795 2
## 998 0.052365405 9.930565 3
## 999 0.071300159 10.718187 3
## 1000 -0.828530930 9.312169 2
# 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)
