Straight-line calibration curves, linear regression

C.I Linear Regression of Straight-Line Calibration Curves... 

A calibration curve is a model used to predict the value of an independent variable, the analyte concentration, when only the dependent variable, the analytical response, is known. The normal procedure used to establish a calibration curve is based on a linear least-squares fit of the best straight line for a linear regression, as indicated in... 

Two x-ray fluorescence spectrometers were used for the analyses a General Electric XRD-6 for iron, copper, tin, and antimony, and a General Electric XRD-5 for nickel, silver, and lead (the latter machine has updated electronics and gave superior results for these three elements). Four certified standards from the National Bureau of Standards were used for each element to obtain a straight line calibration curve using linear regression (10). The experimental conditions used for the determination of each element were given by Carter et al. (10). 

Although the linear model is the model most commonly encountered in analytical science, not all relationships between a pair of variables can be adequately described by linear regression. A calibration curve does not have to approximate a straight line to be of practical value. The use of higher-order equations to model the association between dependent and independent variables may be more appropriate. The most popular function to model non-linear data and include curvature in the graph is to fit a power-series polynomial of the form... 

Not all calibration curves generate a perfect straight line due to indeterminate or random errors. Most scattered points can be corrected using linear regression analysis to... 

One major difference with standard solutions is the requirement to construct what is known as a standard or calibration curve. Ihis is a series of standards of known, but different, concentrations that are used to calculate the concentration of the imknown sample solutions. Ihe caUhration curve is a linear regression plot of peak area versus concentration. Ihe closer the regression line is to a straight line (R = 1), the more accurate is the calculation of the imknown samples. 

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