Level 1 · Do pricier products sell less?

What a correlation measures

The correlation coefficient r is a number from -1 to 1 that says how closely two columns move along a straight line:

• close to 1: when one is high, the other is high, almost on a rising line;
• close to -1: when one is high, the other is low, almost on a falling line;
• close to 0: no straight-line pattern.

In pandas it is one call on two Series of the same length:

per_product["unit_price"].corr(per_product["units_sold"])   # -0.425

Across Harbor & Pine’s 120 products, r is -0.425: pricier products sell fewer units, but the points are far from a tidy line. A common rule of thumb calls 0.1 weak, 0.3 moderate and 0.5 strong, but the number alone never tells you the shape. Look at the chart.

When Pearson undersells a curve

Pearson’s r (the default .corr()) rewards a straight line. The dots in the chart bend: units fall steeply from $11 bowl sets and vases to $200 lamps, then barely change from $800 dining chairs to the $1,659 loveseat. The dashed best-fit line misses both ends, so r looks only moderate.

A rank correlation (Spearman’s) asks a looser question: as price goes up, do units go down, whatever the shape? Replace each value with its rank (1 = cheapest) and correlate the ranks:

per_product["unit_price"].rank().corr(per_product["units_sold"].rank())   # -0.694

-0.694 is a strong negative relationship. With SciPy installed, .corr(method="spearman") gives the same number; ranking first works everywhere, including this browser.

What r does not tell you

• Not the slope. r = -0.7 does not mean “each extra dollar costs 0.7 units”. The size of the effect is a regression question (level 3).
• Not the cause. The cheap end is kitchenware, decor and textiles, which far more customers shop for; the expensive end is furniture and outdoor sets. Price is tangled up with what the product is, so this chart cannot say what a price cut would do to units.
• Not robust to outliers. One product with huge sales can move r a lot. Ranks are much less sensitive.

Common mistakes

• Reporting r without the scatter plot. Very different shapes can share the same r.
• Calling a moderate r “no relationship”. Here r = -0.43 hides a strong, curved pattern.
• Mixing grains. Correlating price with units per order line instead of per product counts popular products hundreds of times. Decide what one row is (here: one product), build both columns in one DataFrame at that grain, then correlate.