correlation coefficient
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When you sprinkle dots on a graph — say each person's height against their shoe size — sometimes they line up neatly along a rising slope, and sometimes they scatter into a shapeless cloud. The correlation coefficient is a single number, from minus one to plus one, that says how close the dots come to falling on a straight line.
Written as r, the correlation coefficient measures the strength and direction of a straight-line relationship between two variables. A value near plus one means they rise together in tight lockstep; near minus one means one falls as the other rises, equally tightly; near zero means no straight-line link at all. In a calibration curve, r close to one is reassurance that signal tracks concentration as expected.
It matters because it offers a quick check that two quantities move together as a method assumes, which is why an r value almost always accompanies a calibration line. The serious caveats are two: correlation is not causation, since two things can rise together by coincidence or a shared cause; and r only senses straight-line patterns, so a strong curved relationship can hide behind a deceptively low r.
A calibration set plots instrument signal against five known concentrations. The points fall almost perfectly on a rising line, giving a correlation coefficient of 0.9998 — strong evidence the response is linear over that range.
An r near one signals a tight straight-line fit on a calibration plot.
Squaring r gives the coefficient of determination, r squared, the fraction of the variation explained by the line; analysts often quote r squared rather than r for a calibration curve. A high r does not by itself prove a method is accurate.