## 3 Results and Discussion
### Comparison of Raman and MIR Spectroscopy  
Based on the data of three fermentations, the time-dependent concentration curves of a fourth fermentation can be predicted. Depending on the choice of fermentations, which are used for  
Figure 5: Predicted time-dependent concentration courses of glucose, ethanol, and biomass during batch-fermentation of _S. cerevisiae._ (**A**) 2D MLR, (**B**) 4D MLR, (**C**) PLS without pre-processing (PP), (**D**) PLS with PP. Comparison of real-time measurement data by Raman and MIR-ATR with off-line reference values (HPLC, gravimetry). the model building and for the prediction, the quality parameters RMSEC and RMSEP can vary considerably. Through the permutation of the predicted yeast fermentation, while the other three fermentations were used for model building, four quality parameters were generated for a given analyte (glucose, ethanol, biomass), multivariate model (2D MLR, 4D MLR, PLS without PP, PLS with PP), and applied spectroscopic method (Raman, MIR-ATR). Averaging over these four values led to statistically more stable quality parameters and secured statements. For the comparison of Raman and MIR-ATR spectroscopy, the averaged RMSEC and RMSEP values (in g L\({}^{-1}\)) for each analyte and multivariate method are given in Table 2A. Dividing these values by the maximum concentration of the corresponding analyte, the relative calibration and prediction error for the determination of an analyte were obtained (Table 2B). It can be seen in Table 2 that Raman and MIR spectroscopy exhibited similar quality parameters (RMSEC and RMSEP values) for a given analyte and multivariate regression model. The same applies for the comparison of 4D MLR, PLS without PP, and PLS with PP for a given analyte and spectroscopic method. In contrast, the calibration and prediction errors applying the simple 2D MLR models were approximately twice as high as for the other three multivariate methods. For example, the standard error of prediction for glucose in case of Raman spectroscopy and applying 2D MLR was 1.86 g L\({}^{-1}\) (relative error 6.2%), whereas 4D MLR, PLS without PP, and PLS with PP yielded 1.08 g L\({}^{-1}\) (3.6%), 0.92 g L\({}^{-1}\) (3.1%), and 0.76 g L\({}^{-1}\) (2.5%), respectively. The larger inaccuracies of the 2D MLR models are also indicated by the stronger fluctuations of the concentration curves in Figure 5. However, the extension of the 2D MLR models by two more channels to 4D MLR models significantly improved the results. By the selection of four analyte-specific optical channels, the simple 4D MLR could reach the performance of the more sophisticated PLS evaluation of Raman and MIR spectra. Within the studies mentioned in the Introduction, the relative errors, with respect to the maximum glucose and ethanol concentrations, ranged between 0.2% and 6.0%. Only [PERSON] et al. [17] obtained bigger errors using Raman spectroscopy for the determination of glucose (11.9%) and ethanol (12.3%) concentrations during a lignocellulosic bioethanol production in conjunction with an internal standard and linear regression. The smallest relative errors for glucose (0.4%) and ethanol (0.2%) were found by [PERSON] et al. [18] in conjunction with a PLS-PCA model. [PERSON] et al. [19] achieved relative errors of 5% for glucose and 2% for ethanol with the aid of a PLS evaluation. Similar relative errors of 5% for glucose