Correlation matrix

The matrix collects the correlation coefficient of every pair of columns in one table: the diagonal is 1 (each column with itself) and the matrix is symmetric about it. Values lie between −1 and +1; the sign shows the direction (rising together, or one rising while the other falls) and the absolute value the strength of the relationship. With many variables it is a quick way to see at a glance which ones move together.

In the heat table the cell background darkens with |r| and the value itself is written in the cell. Because intensity and a number are used instead of colour, the table stays readable in black-and-white print and for colour-blind readers.

Pearson measures the linear relationship of the values; it is sensitive to outliers and can understate a curved relationship. Spearman replaces the values with their ranks and computes Pearson on those: only the ordering matters, so it catches every monotonic relationship (rising or falling, even if not linear) and resists outliers. Equal values (ties) get the average rank.

If the two results differ a lot there is usually curvature or an outlier; look at the scatter plot of that pair.

For each pair only the rows where both are filled are used (pairwise deletion); the n of each cell may differ, and the tool shows it. With many missing values different pairs come from different subsets, so be careful comparing cells with one another. The alternative is to reduce all rows to one common set (listwise deletion), which is more consistent but loses data.

Pairs with |r| > 0.9 carry almost the same information (multicollinearity). If you feed such columns together into a regression or machine-learning model the coefficients become unstable; dropping one, averaging them or moving to principal components are common remedies.