Math 221 – Principles of Statistics

Examples of Scatterplots and Their Interpretation

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Here are some scatterplots, with interpretations. Look them over and get a feel for what all the vocabulary means.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This looks like a strong, positive, linear association. (But some students say they think there is a slight curve to the pattern.)

 

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This is a “matrix” or array of scatterplots. You may think there are six scatterplots here, but look very carefully, and you’ll see that the one in the row labeled “chck” (check) and in the column “sales” is the mirror image of the one in the row labeled “sales” and the column labeled “chck.” In fact, the three plots in the upper right portion of the matrix are the same as the three in the lower left part, but with their axes interchanged.

 

Now, the labels on the axes tell you which variables are plotted in each plot. For example, in the lower left-hand corner, we have a plot of “card” versus “sales.” It seems fairly linear, though there may be an influential point (the point farthest right.) To see an association in this plot isn’t too surprising, as an increase in credit card sales should be associated with an increase in sales.

 

Next to this plot, on the right of it, we have a plot of “card” versus “chck.” There seems to be no recognizable pattern in this plot, and there could be three or four unusual points.

 

In the next row up (the middle row), and in the left-most column, we have a plot of “chck” versus ‘sales.” Again, there seems to be a positive linear association between these two variables. It seems fairly strong, at that. The uppermost point (which is also the point farthest right) could be an unusual point.

 

Odd, isn’t it, how we “usually” seem to see “unusual” points!

 

These are the only three plots we need to interpret, since the other three are mirror images of these three.

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There’s a fairly strong, positive association here, but it’s definitely not linear! There are also some possible unusual points dangling down (in the $5000 - $8000 range).

 

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There is a positive association here, but it’s too weak to determine whether it’s linear. However, there are those who would be willing to give it the benefit of the doubt.

 

 

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There is a strong, negative association, but it’s not strictly linear. There seems to be some curvature to it.

 

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This scatterplot is for the same data as the previous one, but with the axes interchanged. Notice that the negativity of the association is still evident. So—as far as the strength and direction of the association are concerned—it doesn’t matter which variable goes on which axis.

 

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Some see no association in this scatterplot at all, your author included. Some say there’s a weak positive association, but if you remove the unusual point in the upper-right corner, that impression seems to disappear. Some say there’s a weak negative association, but that impression is seriously strengthened by the removal of the unusual point in the upper-right corner. If there really is a pattern in the data, its existence should not depend so heavily on a single point!

 

 

 

Scatterplots reference page: Click here.

 

SPSS instructions for constructing scatterplots: Click here.

 

Related topics:

 

Simple linear correlation

 

Simple linear regression

 

Exploratory data analysis

 

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David E. Brown

BYU-Idaho                                            mailto:brownd@byui.edu

232 Ricks Building                              208-496-1839 voice

Rexburg, ID 83460                              208-496-2005 fax

                Please do not call me at home.