Level 5 · Which product numbers move together?

One call, every pair

Level 1 measured one pair. When a table has several numeric columns, DataFrame.corr() measures all of them at once and returns a square correlation matrix: one row and one column per variable, r in every cell.

per_product.corr().round(2)

Three things are always true of it. The diagonal is 1 (each column against itself). The matrix is symmetric: the cell for price and units equals the cell for units and price. And pandas uses the rows where both columns have values, so the 9 products without a cost still count in every pair that does not involve margin.

Reading it as a heatmap

Twenty-five numbers are hard to scan, so the matrix is usually drawn as a heatmap: one coloured cell per pair, the number printed inside. Two rules make a correlation heatmap honest:

• A fixed scale from -1 to +1. If the colours stretch to the strongest value in this table, a weak 0.4 is painted as dark as a near-perfect 0.95 would be in another table.
• A diverging palette: one colour for positive, another for negative, pale near zero. Here orange is positive and blue is negative.

On the chart, the darkest off-diagonal cell is price against units sold, in blue.

Strong, moderate, weak

A common rule of thumb: |r| above 0.7 is strong, 0.3 to 0.7 moderate, below 0.3 weak. On Harbor & Pine’s products only two pairs are even moderate: price and units sold (-0.425) and price and revenue (0.375). Everything else is below 0.25, and return rate is barely related to anything.

Rank pairs by the absolute value, then report the sign: “price and units sold have the strongest relationship, a moderate negative one”.

The grain changes the answer

You might expect units sold and revenue to move together strongly. Across products they hardly do (r = 0.14), because a product that sells 900 cheap units can earn less than one that sells 50 sofas. Count the same two numbers per month and r is 0.95: busy months are busy in units and dollars. Per order it is 0.60. A correlation describes the rows you computed it on, so always say what one row is.

Common mistakes

• Sorting by r instead of |r|. Strong negative pairs end up at the bottom.
• Counting pairs twice and keeping the diagonal. Use only the cells above the diagonal.
• Letting the colour scale float. Fix it at -1 to 1.
• Writing “causes”. A matrix shows which columns are associated; say “is associated with” or “tends to go with”, and check the scatter plot before anything else.