CHEM312 Problem Set:
Multiple Linear Regression Modeling of UV Absorbance Data from PAH Mixtures
Tables 5.1 of the
Brereton text contains UV absorbance spectra obtained at 27 wavelengths from 25
different mixtures, each having varying concentrations of ten different polynuclear aromatic hydrocarbons (PAH’s). Table 5.2 contains the ten PAH concentrations
present in each of the 25 mixtures. The
two data tables are included in the Brereton
Text data sets.
Requirements:
- Download the
data tables and paste them into separate excel worksheets that are clearly
labeled.
- Handwrite the
matrix equations used to calculate measured absorbances
from concentrations and molar absorptivities
- Clearly label
the number of rows and columns of each matrix and state what each
represents.
- Clearly derive
and write the final equation used to determine the matrix of molar absorptivities
- Clearly derive
and write the final equation used to determine the matrix of mixture
component concentrations
- Copy the data
into Matlab and write a set of commands to:
- Calculate
the molar absorptivity matrix
- Calculate
the predicted concentration matrix
- Calculate
the residual matrix
- Calculate
the root mean square error of calibration (RMSEC)
- Calculate
the relative % error by comparing the RMSEC to the average concentration
for each component.
- Paste the
specific set of MATLAB commands that you successfully used into a clearly
labeled separate worksheet section of your spreadsheet
- Paste the
calculated molar absorptivity matrix into the
spreadsheet
- Paste the
calculated concentration matrix into the spreadsheet
- Paste the
calculated residual error concentration matrix into the spreadsheet
- Compare your
results with the predicted PAH concentrations listed in Table 5.8 of your
text.