Example 2: Bivariate (scatter) Plots

Is the correlation between two quantitative measures appropriate? That is, check distributions, identify outliers, assess the need for a transformation, etc.

• Display the scatterplot with or without supporting statistics—correlation, equation of regression line, means, sample size, etc.
• Display the least squares regression line across the point cloud
• Click on a plot point of an outlier to find its x-y coordinates
• Display a LOWESS smoother when not positive about the shape of the relation.
• Apply a power transformation to values on a plot scale without affecting values in the data file. For example, typing 0.5 as the power plots the data on a square root scale, typing 0, a log scale, and so on. Thus, a quick interactive way to see what transformation best meets a necessary linearity assumption.
• Click on image opposite to enlarge

Just a few clicks to see the effect of a transformation.

For 57 countries, the data are 1990 population in millions and population projected by the UN for 2020. The distribution of points in the bivariate point cloud on the top left opposite is far from ideal for computing a correlation—its shape is not like that of an American football with points falling symmetrically across the area. In the top right plot, the spreads of residuals (from program 2R) across the predicted population values should be equal—they’re not, for countries with small predicted values, the spread is smaller than that for countries with larger values. To identify the data for the largest positive residual on the right, click on the point to find its coordinates.

In the bottom left plot, we return to the first plot in the   Graph window and request the data on the y-axis be displayed on a square root scale and the x-axis values on a log scale. The smoother added to this plot shows the relation is not linear. For the bottom right plot, the y-axis scale is changed from square root units to a log scale, resulting in the desired linear relation.