## Chapter 3. Two Variables: Establishing Relationships

WHEN WE ARE DEALING WITH A DATA SET THAT CONSISTS OF TWO VARIABLES (THAT IS, A BIVARIATE DATA SET), we are mostly interested in seeing whether some kind of relationship exists between the two variables and, if so, what kind of relationship this is.

Plotting one variable against another is pretty straightforward, therefore most of our effort will be spent on various tools and transformations that can be applied to characterize the nature of the relationship between the two inputs.

## Scatter Plots

Plotting one variable against another is simple—you just do it! In fact, this is precisely what most people mean when they speak about “plotting” something. Yet there are differences, as we shall see.

Figure 3-1 and Figure 3-2 show two examples. The data in Figure 3-1 might come from an experiment that measures the force between two surfaces separated by a short distance. The force is clearly a complicated function of the distance—on the other hand, the data points fall on a relatively smooth curve, and we can have confidence that it represents the data accurately. (To be sure, we should ask for the accuracy of the measurements shown in this graph: are there significant error bars attached to the data points? But it doesn’t matter; the data itself shows clearly that the amount of random noise in the data is small. This does not mean that there aren’t problems with the data but only that any problems will be systematic ones—for instance, with ...

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