Scatter Plot: Visualizing Relationships Between Two Variables

Why it exists

Before running complex statistical models, you need a way to simply see your data. A scatter plot was created to provide an immediate, intuitive visual check for a potential relationship between two numerical variables, forming the foundation of exploratory data analysis.

The mental model

Think of a scatter plot as a target practice sheet where each shot is a data point. Each shot has a horizontal (X) and vertical (Y) position. Looking at the whole pattern of shots tells you if your aim is consistent or if your horizontal and vertical errors are related. A scatter plot does this for any two variables, revealing the 'shape' of their relationship.

How it works

Using a Cartesian grid, a scatter plot displays data as a collection of points. For each item in a dataset, it takes two numeric values. One value determines the point's position on the horizontal axis (X-axis), and the other determines its position on the vertical axis (Y-axis). When you plot all the items, the resulting cloud of points can reveal linear trends, clusters, or a complete lack of a relationship. You can also display a third variable by encoding it with the color, shape, or size of the points.

When to use it

Use a scatter plot as a first step when exploring a new dataset to understand how two variables interact. It's perfect for checking for correlations between two continuous variables, such as server response time versus CPU load, or advertising spend versus sales revenue. It is one of the most fundamental and widely used charts in quality control and data science.

When not to use it

Scatter plots are less effective when one or both variables are categorical (e.g., 'country' or 'product type'), as the points will just stack on top of each other in columns or rows. They also become unreadable with too many data points, a problem called 'overplotting,' where the individual points merge into a dense blob. In that case, other chart types or techniques like data sampling are better.

One canonical example

To see if there's a link between daily temperature and ice cream sales, you would collect data over several weeks. For each day, you record the high temperature (X-axis) and total sales revenue (Y-axis), then plot one point per day. You would likely see a pattern where points trend upwards from left to right, visually confirming that as temperature increases, so do sales.