Problems with correlation
The correlation coefficient, r, is a good summary of the strength of the relationship between two variables if their scatterplot is an elliptical cloud of points.
If the relationship is nonlinear, the correlation coefficient understates the strength of the relationship. On the other hand, an outlier can strongly influence r and may potentially make the relationship appear stronger than is justified by the remaining points. If there are clusters, the overall correlation coefficient may be very different from the correlation within each cluster.
The following exercise presents four scatterplots with different features and different correlations. Drag the four correlation coefficients that are shown under the scatterplots so that each correlation coefficient matches the scatterplot above it.
Repeat with a few different questions.