Scatter Diagrams

To better visualize the association between two data sets {x1, …, xn} and {y1, …, yn} we can employ a chart called a scatter diagram (also called a scatter plot). This is done in Excel by highlighting the data in the two data sets and selecting Insert > Charts|Scatter.

Figure 1 illustrates the relationship between a scatter diagram and the correlation coefficient (or covariance).

Figure 1 – Scatter diagrams

Figure 1 – Scatter diagrams

Notice that the x and y values in the example with r = .976 are very strongly positively correlated. This is not too surprising since r is almost at its maximum value of 1. In the example with r = -.912, the linear correlation is also quite strong, but negative (note that the slope of the line that seems to fit the data is negative).

In the example where r = .300 and r = .068, there is no apparent linear relationship between x and y. In fact in the latter case it seems that the points are randomly scattered, indicated by a correlation coefficient near zero, which is consistent with the fact that x and y are independent or nearly so.