least-squares regression
/ ree-GRESH-un /
Least-squares regression is the math that draws the single best straight line through a scatter of data points. Imagine pinning a taut thread through a cloud of dots so it sits as close to all of them as it can — not touching every one, but balanced fairly among them. That fair-as-possible line is what least-squares finds.
It works by a clear rule: for each point, measure how far it sits above or below the line, square that distance, and add up all the squares. The best line is the one that makes this total as small as possible — hence "least squares." Squaring keeps positive and negative misses from cancelling and penalizes big misses more, pulling the line toward the bulk of the data.
It matters because a calibration curve is rarely drawn by eye — squinting at the points invites bias. Least-squares gives an objective, repeatable equation for the line, complete with its slope (the sensitivity) and intercept, and lets you estimate the uncertainty in a concentration you read back from it. A common caution: it assumes the scatter is similar at all concentrations, which is not always true.
Six calibration points are fed into a spreadsheet's regression function, which returns the line absorbance = 0.098 × concentration + 0.004, with a correlation coefficient of 0.9997 — the objective best fit to the data.
The fit gives an objective slope and intercept instead of an eyeballed line.
A high correlation coefficient shows the points lie near a straight line, but it is not proof that the calibration is correct — a curved data set can still give a high value over a narrow range. Always inspect the residuals and check for points that bend away from the line.