Linear Regression

Introduction

Linear regression uses the method of least squares to determine the best equation describing a set of x and y data points.

Linear Regression Equations

For the 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 y_c (bar) is the mean of the unknown measurements.