Scatter Plots

Students create scatter plots, which are visualizations that show the relationship between two quantitative variables. They learn how to construct scatter plots by hand, and in Pyret.

Pie and Bar charts help us see the frequency of values in a categorical column. There are other displays, like histograms and box plots, that help us explore the distribution of values in a quantitative column.

What we really want is a display that will help us search for a relationship between two quantitative columns, and that’s exactly what scatter plots do.

Before we can draw a scatter plot, we have to make an important decision: which variable is explanatory and which is the response?

Which of the following makes the most sense?

It’s customary to use the horizontal axis for our explanatory variable and the vertical axis for the response variable. Each row in the dataset will be a point on the scatter plot with age for x and weeks for y.

We will produce our scatter plot by graphing each animal as a point, using age for x and weeks for y.

Scatter plots show us a collection of points, arranged along two axes. If there’s a relationship between these axes, we’ll see clumps and clouds of points in the graph.

Here’s an example of a point cloud in a scatter plot from a different data set. We could describe these points as clustering around a line that slopes from the bottom left to the top right.

When you created the scatter plot by hand, you started with a Table. Then you plotted a series of dots, using one column for your x’s, one column for your y’s, and the name column to provide a label for each dot.

Pyret has a scatter-plot function that works exactly the same way: it starts with a table, and then needs to know which columns to use for labels , x-coordinates (xs), and y-coordinates (ys). Here’s the Contract:

How do patterns or trends show up in a scatter plot?

Students apply what they’ve learned about scatter plots to the Data Cycle, using it to answer questions about relationships in the animals dataset.

Many apartment buildings do not allow large breeds of dogs, and have a limit on how heavy a tenant’s dog can be. Bigger dogs are not welcome in many apartments.

Perhaps the weight of an animal influences the adoption time!

Do you think there’s a relationship between pounds and weeks in this table? Why or why not?

Discuss as a class:

Students are asked to identify patterns in their scatter plots. This activity builds towards the idea of linear associations, but does not go into depth (as as a later lesson on correlations does).

Shown below is a scatter plot of the relationships between the animals' pounds and the number of weeks it takes to be adopted.

A straight-line pattern in the cloud of points suggests a linear relationship between two columns. If we can find a line around which the points cluster (as we’ll do in a future lesson), it would be useful for making predictions. For example, our line might predict how many weeks a new dog would wait to be adopted, if it weighs 68 pounds.

These points are called unusual observations. Unusual observations in a scatter plot are like outliers in a histogram, but more complicated because it’s the combination of x and y values that makes them stand apart from the rest of the cloud.

Data Scientists and Statisticians use their eyes all the time. Sometimes there’s a pattern hiding in the data, which can’t be seen just by focusing on numbers and measures. Until we really look at the shape of the data, we aren’t seeing the whole picture.

Each of these scatter plots and accompanying set of numbers corresponds to a dataset. The patterns in the scatter plots vary wildly, but the numbers that summarize the datasets barely change at all!

It is important to note that making a scatter plot will not always give us the information we’re looking for.

If we wanted to know how weeks to adoption may be affected by age, for example, it would be important to consider the fact that different species have very different lifespans!

With differences like this, it doesn’t make sense to put them all on the same scatter plot because we may be hiding a real relationship, or creating the illusion of a relationship that isn’t really there!

Students apply what they have learned about scatter plots to their chosen dataset. They will add two items to their Data Exploration Project Slide Template: (1) at least two scatter plots and (2) any interesting questions that emerge.

Let’s review what we have learned about making and interpreting scatter plots.

Let’s connect what we know about scatter plots to your chosen dataset.