Linear regression uses the method of least squares to determine the best linear equation to describe a set of x and y data points. The method of least squares minimizes the sum of the square of the residuals - the difference between a measured data point and the hypothetical point on a line. The residuals must be squared so that positive and negative values do not cancel. Spreadsheets will often have built-in regression functions to find the best line for a set of data.

A common application of linear regression in analytical chemistry is to determine the best linear equation for calibration data to generate a calibration or working curve. The concentration of an analyte in a sample can then be determined by comparing a measurement of the unknown to the calibration curve.

Linear Regression Equations

For the linear equation: y = mx + b

Useful quantities:

Slope:

Intercept:

Standard deviation of the residuals:

Standard deviation of the intercept:

Standard deviation of the slope:

Standard deviation of a unknown read from a calibration curve:

Where:

N is the number of calibration data points.
L is the number of replicate measurements of the unknown.
and is the mean of the unknown measurements.