Multivariate calibration. An important aspect of creating multivariate calibrations is selection of which and how many features (for example, wavelengths or wavenumbers) should be used to construct the calibration model.
a. The spreadsheet in Figure 19-4 is available on SaplingPlus or at macmillanlearning.com. Insert a random guess in cells 115:117, and use Solver to minimize the sum of squares in cell J11 by varying cells 115:117. Your spreadsheet should now appear as in Figure 19-4. Calculate the relative errors for the determinations given that the true concentrations are 2.43 M 2.43 M xylene, 3.80 M 3.80 M dichloroethane, and 1.40 M  1.40 M toluene.
b. Add the absorbances at 2 971.5 2 971.5 and 2 868.8 cm-12868cm^-1 to the original five sets of data in your spreadsheet. Use Solver to revise the calculated concentrations of the three components. What are the relative errors in the three concentrations?

c. Replace the absorbances at 2 971.5 2 971.5 and 2 868.8 cm- 12 868,8 cm^-1 with those at 3 124.5 3 124.5 and 2 780.6 cm -1.2 780.6 cm^-1. Use Solver to determine the concentrations of the three components. What are the relative errors?
d. Why did addition of absorbance information at two additional wavenumbers have different effects in (b) and (c)?

Figure 19-4

Wavenumbers (cm-1) Wavenumbers (cm) 2971.52 971.5 2868.82 868.8 3124.53 124.5 2780.62 780.6 Xylene 0.5700.570 0.5690.569 0.0330.033 0.0190.019 Absorbance of standards C2H4C12CH4Cl 0.5950.595 0.1070.107 0.0270.027 0.0180.018 Toluene 0.2730.273 0.2440.244 0.0310.031 0.0060.006 Absorbance of mixture 1.4431,443 1.0971.097 0.1180.118 0.0690.069