With only two coefficients, it's just a linear equation to get the concentration from absorbance at that wavelength.

Personally, I would use known standards and develop a calibration curve. Or at least a zero blank and a couple of known concentrations to check the calibration.

P.S. So, yes, it's just Beer's law if it's linear. They left room for additional coefficients in case the calibration has some curvature for some analytes.

Beer's law is associated with two forms of linear calibration: the classical least squares and the inverse least squares.

In classical least squares framework, y variable is the intensity and the x variable is the analyte concentration.....here the

regression model is used to predict the value of y given x .... the observed y value from the unknown sample is plugged into the linear regression equation and corresponding value of x is taken as the estimate of analyte concentration.

In inverse least squares, the y variable is the analyte concentration and the x variable is the intensity, here the linear regression model directly predicts the concentration of analyte in unknown sample, using the linear regression equation so obtained, by plugging in the value of the intensity observed for the unknown sample.

For discussion on Classical and Inverse least squares methodologies of multivariate spectroscopic Calibration and Prediction, I would recommend the following books:

1. Quantitative spectroscopy by Brian. C. Smith

2. Mathematical analysis of Spectral Orthogonality by Kalivas and Lang.

However, when we consider a general spectroscopic instrument, the Beer's law is not the functional form of relationship that relates Absorbance A, to concentration C and Path length L at every considered wavelength... for an arbitrary chosen wavelength say d, the Absorbance A is in general, a non-linear function of C and L, as follows:

A= f(C, L), a special case of which is the Beer's law form.

Thus, when we choose to calibrate the analyte concentration with respect to instrument response, at an arbitrary wavelength: the general approach is to keep the path length constant and build a polynomial response function that directly predicts the analyte concentration C based on the observed instrument response: the absorbance value A.... this is achieved by considering a Polynomial linear regression framework ( the model is linear because it is linear with respect to the model parameters) which utilizes the powers of the Absorbance variable A as the explanatory variables and the analyte concentration C as the dependant variable. . . . such type of models are probably being considered in the slides that you have shared.

Debopam Ghosh intuitive and explicit explanation, thanks, sir.

Apparently they use linear regression. The higher order coefficients are 0.