Spectroscopy: Multiple Linear regression Problem
This is my first post on this forum and I would appreciate any feedback you all can provide. I am a graduate student in Texas. The problem below can be solved with very expensive proprietary software that frankly we cannot afford. I have tried to solve the problem in MatLab but have so far been unsuccessful.
Here is an abbreviated description of my problem:
I am trying to calculate a coefficient ?vector? that will be multiplied by each time point for many spectra (with a large number of data points) that is calculated by summing the result of coefficient X spectra value for each time point of a particular spectra that approaches a final number. The coefficient file will correlate to many spectra predicting their final number at a 0.95 R-squared level (or lower if indeed the spectra do not return an easy solution.
An example that might help:
Time Spectra 1 Spectra 2 Spectra 3
0 58.1213 68.1243 75.0123
1 58.0124 68.0457 74.9856
2 57.9854 68.0012 74.9754
... ...... .... .....
10000 2.1242 1.2144 0.2121
Spectra 1 has 0.4 grams of oil, spectra 2 has 0.5 grams of oil, and spectra 3 has 0.6 grams of oil. The spectra are not linear and will have many peaks and valleys (it is an NMR spectra to be more specific).
A sample coefficient file calculated will a provide a value for each time point. This coefficient file will be calculated by trying to match each spectra's final number with the highest confidence of fit versus actual final value (i.e. the grams of oil):
Time Coefficient value
The resulting Spectra 1 file is calculated
Time Coefficient X spectra data point = result
0 0.00005 x 58.1213 = 0.0029
1 0.00005 x 58.0124 = 0.0029
2 0.00004 x 57.9854 = 0.0023
... ..... x ...... = ........
10000 -0.0001 x 2.1242 = -0.0002
The sum of all the results for this spectra will equal 0.4 grams of oil.
I am not sure if this can be solved by ?multiple linear regression, or matrix algebra. I have some experience in MatLab (and some other math programs) and have no problem downloading recommended software. I can provide full length and example data (and results) if anyone is more interested.