Calibration curve and regression analysis

As the response of many detectors is linear as a function of the measured variable, taking account of the differences due to experimental conditions as well as of the instrument, the goal is to find the parameters of the straight line that best fits. 

The least squares regression line is the line which minimizes the sum of the square or the error of the data points. It is represented by the linear equation y = ax + b. The variable x is assigned the independent variable, and variable j is assigned the dependent variable. The term b is the y-intercept or regression constant (the value of when x = 0), and the term a is the slope or regression coefficient. 

Coefficients a and h, as well as the standard deviation on a, may be given by several formulae and specialized software. 

Moreover, the dimensionless Pearson correlation coefficient R gives a measure of the reliability of the linear relationship between the x and y values. If i = 1 it exists an exact linear relationship between x and y. Values of R close to 1 indicate excellent linear reliability. If the correlation coefficient is relatively far away from 1, the predictions based on the first order relationship, y= ax+ b will be less reliable. 

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