R Tutorial: Characterizing bivariate relationships
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Scatter plots can reveal characteristics of the relationship between two variables. Any patterns and deviations from those patterns, we see in these plots could give us some insight into the nature of the underlying phenomenon. Specifically, we look for four things: form, direction, strength, and outliers.
Form is the overall shape made by the points. Since we are learning about linear regression, our primary concern is whether the form is linear or nonlinear.
Direction is either positive or negative. Here, the question is whether the two variables tend to move in the same direction, that is, when one goes up, the other tends to go up, or in the opposite direction. We'll see examples of both in just a minute.
The strength of the relationship is governed by how much scatter is present. Do the points seem to be clustered together in a way that suggests a close relationship? Or are they very loosely organized?
Finally, any points that don't fit the overall pattern, or simply lie far away, are important to investigate. These outliers may be erroneous measurements, or they can be exceptions that help clarify the general trend. Either way, outliers can be revealing and we'll learn more about them later in the course.
We're going to look at a bunch of scatter plots that we found "in the wild" and talk about what we see, so that you can start to build some experience in interpreting them.
You can continue this exercise on your own by doing a Google image search for "scatter plot".
As we work through these, please keep in mind that much of what we are doing at this stage involves making judgment calls. This is part of the nature of statistics and while it can be frustrating, especially as a beginner, it is inescapable. For better or for worse, s
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