TABLE OF CONTENTS The least squares method of linear regression [4] , [6] [8] is used to fit the best straight line to a set of calibration data such as that shown in Table 4.8. (Chapter 3, Section 3.11 describes the statistical principles underlying the method of linear regression).
The best straight line is that which minimises the sum of the squares of the residual distances of the individual calibration points (measured on the y-axis, i.e. instrument signal axis) from the calculated best straight line. This is referred to as the regression of y on x and Figure 4.9 illustrates the residual distances of the calibration points from the calibration line.
The important parameters of the regression line are:
the slope of the line and its uncertainty
the intercept of the line and its uncertainty
These parameters are readily calculated using an appropriate software package and a personal computer. For background information, the formulae for the calculations of the uncertainty estimates (as standard deviations) of the slope and intercept of the line are given below. In Eqs. 4.9 and 4.10, s m is the standard deviation of the slope and s c is the standard deviation of the intercept respectively.
The parameter rsd is the residual standard deviation (also known as the residual standard error and the standard error of the estimate).
