Multiple linear regression predicted value, response

Usually, the linearity of a NIR spectroscopic method is determined from the multiple correlation coefficient (R) of the NIR predicted values of either the calibration or validation set with respect to the HPLC reference values. It may be argued that this is an insufficient proof of linearity since linearity (in this example) is not an independent test of instrument signal response to the concentration of the analyte. The analyst is comparing information from two separate instrumental methods, and thus simple linearity correlation of NIR data through regression versus some primary method is largely inappropriate without other supporting statistics. 

From the experimental data, a linear correlation was found between the responses of the different sensors of e-nose system and rancidity parameters obtained by biochemical assays. Therefore, multiple regression analyses were carried out to develop three linear regression equations to predict the FFA value, PV value and TEA value (individually) of the cookies as a function of responses of four metal oxide gas sensors (TGS 830, TGS 2600, TGS 2610 and TGS 2626), which are provided below. 

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