# Linear Regression

## Introduction

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.

## Related topics:

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