Visualization a Linear Model on a Scatterplot with ggvis

It is a statistical model used to describe the relationship between a dependent variable and one or more independent variables. The linear model is used in data analysis. We can say that a linear model assumes a linear relationship between the dependent variable and each independent variable. Linear models are represented in straight-line form.

Linear model on a Scatterplot means fitting a straight line to the data points on the plot and, that line represents the “Best Fit” to the data. It maximizes the distance between the bar and the data points. 

• If the slope of the straight line is positive, then the two variables are positively correlated, which means if one variable increases, another variable tends to increase.
• if the slope of the straight line is negative then the two variables have negatively correlated which means if one variable increases another variable tends to decrease.

Note: Linear model may not always be the best way to represent the relationship between two variables, it depends upon the nature of the data.

ggvis Package in R

The ggvis package in R Programming Language creates interactive and dynamic visualizations for exploring and presenting data. To create a liner model on a scatterplot with ggvis, we will use the “layer_smooth()” function. This function adds a regression line to the plot, and we can specify the type of smoothing function to use. Some standard smoothing methods in “layer_smooth()”. We can customize our scatterplot using different parameters in the “layer_smooth()” function. 

Parameters in layer_smooth()

Parameter	Uses Case	Default
tension	The smoothing method to use	loess
se	Whether to add error bars representing the standard error of the estimate	TRUE
span	The smoothing span controls the degree of smoothing. The value of smoothing must be from 0 to 1.	0.75
stroke	The color of the line	black
formula	A formula specifying the model to fit. This is only used if method = “lm”.	‘y ~ x’

R

# create data frame
x <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100)
y <- c(5, 15, 25, 35, 45, 55, 65, 75, 85, 95)
sampleData <- data.frame(x = x, y = y)

# create ggvis plots with smoothed line
sampleData %>% ggvis(x = ~x, y = ~y) %>%
               layer_points() %>%
               layer_smooths(tension = "lm",
                             span = 1, se = FALSE,
                             stroke := "red")

Output:

Linear model on a scatter plot

The previous case was that of a perfectly linear model. Now let’s look at an example of a non-linear example using the iris dataset and then plot the results obtained using this dataset.

R

#install and load ggvis package
install.packages("ggvis")
library(ggvis)

#install dataset iris
install.packages("iris")

#create ggvis plot with smoothed line
iris %>% ggvis(x = ~Sepal.Length, y = ~Petal.Length) %>%
         layer_points() %>%
         layer_smooths(tension = "loess",
                       span = 0.75,
                       stroke := "green")

Output:

Scatter plot along with the non-linear model using ggvis

Now let’s try to change some of the parameters and look at the changes in the model which is obtained after the changes.

R

# create a smoothed line
iris %>% ggvis(x = ~Sepal.Length,
               y = ~Petal.Length) %>%
         layer_points() %>%
         layer_smooths(tension = "lm",
                       span = 1.5,
                       stroke := "green")

Output:

Scatter Plot with the Linear model using ggvis