Scatterplots: Correlation, Outliers, and Model Types

A note on terminology: If a scatterplot is said to show a "high" or "strong" positive correlation, this does not mean that a straight line drawn amongst the dots (being a guess as to where the dots "ought" to be, were life not so messy) would have a high-number positive slope; instead, it means that the dots are closely clustered on or near the line drawn through the dots, so that the match of the dots to the line looks to be fairly strong. A "perfect" positive correlation means that the dots all lie on the line. The terminology works the same way for negative correlations.

• For each of the given scatterplots, determine whether the plotted points appear to have positive, negative, or no correlation.

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Outliers

You may also be asked about "outliers", which are the dots that don't seem to fit with the rest of the dots. (There are more technical definitions of "outliers", but they will have to wait until you take statistics classes.) Maybe you dropped the crucible in chem lab, or maybe you should never have left your idiot lab partner alone with the Bunsen burner in the middle of the experiment. Whatever the cause, having outliers means you have points that don't line up with everything else.

• Identity any points in the following scatterplot that appear to be outliers.

Outliers are the points that don't appear to fit, assuming that all the other points are valid. In order to get a good-fit line for whatever it is that you're measuring, you don't want to include the "bad" points; by ignoring the outliers, you can generally get a line that is a better fit to all the other data points in the scatterplot. This is why determination of, and elimination of, outliers can be very important.

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Model Types

Usually you'll be working with scatterplots where the dots line up in some sort of vaguely straight line. But you shouldn't expect everything to line up nice and neat, especially in "real life" (like, for instance, in a physics lab). And sometimes you'll need to pick a different sort of equation as a model, because the dots do appear to line up in a specific way, but that way happens not to be in a straight line.

The line that appears to be a good fit to the data points is often called a "model" or a "modelling equation", because you'll be using that line's equation as the description or rule for whatever it is that the data points relate (such as time after release versus the height of the object which has been released). Given a set of data points, you may be asked to decide which sort of model (that is, which type of equation) would provide the best fit to the scatterplot of data. To some extent, this will involve using your own judgement; fortunately, though, they usually give you only a few choices, and make the answers pretty obvious. (This will not be the case in real life!)

• Determine which sort of equation you think would best model the data in the following scatterplots, and explain why. (Choices are quadratic, exponential, and linear.)

In general, expect only to need to recognize linear (that is, straight-line) versus quadratic (that is, somewhat curvy-line) models. You will likely never need to recognize anything that you haven't already covered in class. For instance, if you haven't yet studied logarithms, then you won't be expected to recognize the need for a logarithmic model for a given scatterplot.

The next page explains how to define these models, called "regressions".