Scatter Plots

1 What is a scatter plot?

A scatter plot compares both a numerical values on the x and y axes. They can be used to show trends over time, or to show the correlation between two variables.

Here is the plot framework:

2 Penguin Data

In the penguin data set, we can examine the relationship between bill depth and bill length.

Note: To generate a scatter plot, we call on the geom_point( ) function with ggplot.

ggplot(data=penguins, mapping=aes(x=bill_length_mm, y=bill_depth_mm))+
  geom_point()

3 Line of best fit

So we have these dots, but how do we know the relationship between x and y-variables?

In order to perform regression analysis, or how the x and y variables are related, we can use a linear model equation y=mx + b, where y is a function of the change in a given y-value times its respective x-value, plus the y-intercept, or where the y-value crosses the y=0 axis.

All this information can be found using this skeletal formula:

variable=lm(data = df, fomula = y-variable ~ x-variable)
summary(variable)

Here is the skeletal fomula applied to our scatter plot of the penguin bill depth vs. bill length. Below is the output: the summary statistics associated with this linear model.

billDepthAndLengthModel=lm(data=penguins, formula=bill_depth_mm~bill_length_mm)

summary(billDepthAndLengthModel)

While this output is intimidating, we only need two numbers for our purposes: the estimate intercept (b) and the slope (m), located right below that number.

Our line of regression can be represented in the equation y = -0.08502x + 20.88574

Here is the same scatter plot with the line of best fit:

ggplot(data=penguins, mapping=aes(x=bill_length_mm, y=bill_depth_mm))+
  geom_point()+
  geom_smooth(method="lm")

4 Chick Data

Using the ChickWeight data set, that shows the the change in weight (variable: “weight”) over time in days (variable: “Time”) for chick 4.

First, we must filter the ChickWeight data to include only data from chick 4 by creating a new variable, “chick4”.

Now let’s create a scatter plot of chick 4’s weight over time. Don’t worry about adding a title or axes labels. Make sure to add a line of best fit!

Code editor

Hint

R is case sensitive! The data set is named “ChickWeight” and the variables are “Time” and “weight”. Which variable belongs on the x-axis? Which variable belongs on the y-axis.

Answer

ggplot(data=chick4, mapping=aes(x=Time, y=weight))+
  geom_point()+
  geom_smooth(method=lm)

Let’s generate the line of best fit summary table for the chick4 data, using the model code from above.

Write the linear regression equation (y=mx+b) based on the summary model.

Code editor

Hint

Make sure you have the slope and y-intercept in their respective spots!

Answer

This equation shows the relationship between the x-variable (time) and the y-variable (weight) for chick 4 from the ChickWeight data set.