Scatter Diagram with Linear Regression

We will explore the process of embedding a linear regression line within a scatter plot using R. For illustration, we will use the well-known Iris dataset, which is readily available in R. The Iris dataset contains measurements of sepal length, sepal width, petal length, and petal width for three different species of iris flowers: Setosa, Versicolor, and Virginica. By visualizing the relationship between two numerical variables through a scatter plot, we can better understand the correlation between them. To enhance this visualization, we will overlay a linear regression line, which helps in identifying trends and patterns in the data. We will implement this using the base R and ggplot2 package in R, which provides a powerful and flexible approach for creating high-quality visualizations.

data(iris)
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  
##                 
##                 
##

We will consider the scatter diagram connecting sepal length and sepal width.

plot(iris$Sepal.Length,iris$Sepal.Width, xlab="Sepal Length", ylab="Sepal Width",main="Sepal Length against Sepal Width")

Now to embed the regression line into the scatter diagram, we first find the regression line connecting these points and plot suing abline() function avalable in base r.

model=lm(iris$Sepal.Width~iris$Sepal.Length)
plot(iris$Sepal.Length,iris$Sepal.Width, xlab="Sepal Length", ylab="Sepal Width",main="Sepal Length against Sepal Width",col='blue')
abline(model,col='red')

Note that while plotting using base r, make sure that there is agreement between dependent variable given in plot (given along x axis) and in linear model (given after ~ symbol).

Plotting using ggplot2

Now we shall consider the above plot using ggplot2.

library(ggplot2)
ggplot(iris,aes(x=Sepal.Length,y=Sepal.Width))+geom_point()+labs(title = 'Sepal Length against Sepal Width',x='Sepal Length',y='Sepal Width')

We can format the background of the plot using theme_minimal() along with ggplot. Advantages of using theme_minimal() are

  • Removes the Gray Background – Unlike the default theme_grey(), it removes the gray panel background and replaces it with a white background.
  • Uses Thin Grid Lines – The grid lines are subtle and less distracting.
  • No Border or Panel Grid Lines – It removes the border and background panel grid lines, making the plot look cleaner.
  • Simplifies Axis Lines and Labels – Axis lines are minimal, and text labels are clear.
ggplot(iris,aes(x=Sepal.Length,y=Sepal.Width))+geom_point()+labs(title='Sepal Length against Sepal Width',x='Sepal Length',y='Sepal Width')+theme_minimal()

Now we will embed the linear regression line into the plot using ggplot.

ggplot(iris,aes(x=Sepal.Length,y=Sepal.Width))+geom_point()+geom_smooth(method='lm')+labs(title='Sepal Length against Sepal Width',x='Sepal Length',y='Sepal Width')+theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

If we do not want to show the confidence interval shown in the shadow, using the parameter se=FALSE in geom_smooth.

ggplot(iris,aes(x=Sepal.Length,y=Sepal.Width))+geom_point()+geom_smooth(method='lm',se=FALSE)+labs(title='Sepal Length against Sepal Width',x='Sepal Length',y='Sepal Width')+theme_minimal()
## `geom_smooth()` using formula = 'y ~ x'

Embedding Regression Lines based on Species

Now we shall consider separate colours for each species in the scatter diagram.

ggplot(iris,aes(x=Sepal.Length,y=Sepal.Width,color=Species))+geom_point()+labs(title='Sepal Length against Sepal Width',x='Sepal Length',y='Sepal Width')+theme_minimal()

We shall format the position of the legend using theme() function. Note that theme() should be applied after theme_minimal(). Also in centalizing the title of the plot is also done using theme().

ggplot(iris,aes(x=Sepal.Length,y=Sepal.Width,color=Species))+geom_point()+labs(title='Sepal Length against Sepal Width',x='Sepal Length',y='Sepal Width')+theme_minimal()+theme(legend.position = "bottom", legend.direction = "horizontal",plot.title = element_text(hjust = 0.5))

Custom Colours for Species

In the previous section we had seen the case where each species is coloured with default colours. Now lets consider the case we are assigning custom colours to each species. Yellow to Setosa, Green to Virginica, cyan to Versicolor.

custom_colors=c("setosa"='yellow',"virginica"='green','versicolor'='cyan')
library(ggplot2)
ggplot(iris,aes(x=Sepal.Length,y=Sepal.Width,color=Species))+geom_point()+labs(title="Sepal Length against Sepal Width",x='Sepal Length',y='Sepal Width')+scale_color_manual(values=custom_colors)+theme_minimal()

Embedding Regression lines in Scatter Diagram

ggplot(iris,aes(x=Sepal.Length,y=Sepal.Width,color=Species))+geom_point()+geom_smooth(method='lm',se=FALSE)+labs(title='Sepal Length against Sepal Width',x='Sepal Length',y='Sepal Width')+theme_minimal()+theme(legend.position = "bottom", legend.direction = "horizontal",plot.title = element_text(hjust = 0.5))
## `geom_smooth()` using formula = 'y ~ x'

Now we shall assign cutom colours to each species.

custom_colors=c("setosa"='yellow',"virginica"='green','versicolor'='cyan')
library(ggplot2)
ggplot(iris,aes(x=Sepal.Length,y=Sepal.Width,color=Species))+geom_point()+labs(title="Sepal Length against Sepal Width",x='Sepal Length',y='Sepal Width')+scale_color_manual(values=custom_colors)+geom_smooth(method='lm',se=FALSE)+theme_minimal()+theme(plot.title = element_text(hjust = 0.5),legend.position = 'bottom',legend.direction = 'horizontal')
## `geom_smooth()` using formula = 'y ~ x'

#### Shape of the points varies with Species

ggplot(iris,aes(x=Sepal.Length,y=Sepal.Width,color=Species,shape=Species))+geom_point()

Custom shapes for the points varies

custom_shape=c('setosa'=18,'virginica'=22,'versicolor'=25)
ggplot(iris,aes(x=Sepal.Length,y=Sepal.Width,color=Species,shape=Species))+geom_point()+scale_color_manual(values=custom_colors)+scale_shape_manual(values=custom_shape)+theme_minimal()

Inserting Labels to each data point in the scatter plot

# Load necessary library
library(ggplot2)

data(iris)

# Create scatter plot
iris$id=as.numeric(row.names(iris))
ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width,color=Species, label = id)) +
  geom_point(size = 3) +  # Scatter points
  geom_text(vjust = -0.75, size = 2) +  # Labels for points
  labs(
    title = "Scatter Plot of Sepal Length and Sepal width",
    x = "Sepal Length in cm",
    y = "Sepal Width in cm"
  ) +
  theme_minimal()+theme(legend.position = 'bottom',legend.direction = 'horizontal',plot.title = element_text(hjust = 0.5))