crossplots

Crossplots are a type of data visualization used to examine the relationship between two quantitative variables. Each observation is plotted as a point whose horizontal and vertical coordinates correspond to the two variables. As a form of scatter plot or bivariate plot, crossplots help reveal linear or nonlinear associations, clusters, gaps, and outliers.

Construction and interpretation: select the two variables of interest, check units and scales, and consider applying transforms (such as log scales) for skewed data. Display choices include color or symbol for categories, regression lines or smoothers to indicate trends, and annotation of correlation coefficients. With large datasets, density-based coloring or transparency reduces overplotting. A fitted line or curve can guide interpretation, but should not imply causation.

Applications: In statistics and data analysis, crossplots are used to explore relationships and check model assumptions. In earth science and reservoir characterization, crossplots compare petrophysical properties such as porosity versus permeability, clay content versus porosity, or resistivity versus porosity to classify lithology and estimate reservoir quality. Crossplots are also used in quality control to detect measurement biases and in finance to examine relationships between variables.

Limitations: A crossplot shows only two variables at a time and can obscure higher-dimensional structure. Correlation does not prove causation, and results can be distorted by outliers, measurement error, or inappropriate scaling. For non-linear relationships, simple linear fits may be misleading; nonparametric fits or transformations may be appropriate. Related terms include scatter plots and pair plots.