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.