Advances in Regression: Use of Models in Spectroscopic Data Analysis
Abstract
Regression analysis or the method of least squares is one of the oldest methods of statistical data analysis, which provides a general approach to extracting underlying relationships from data, including the parameters which describe the relationship between points and the uncertainties in those parameters. Regression methods have their roots in the method of maximum likelihood which assures that the parameter estimates are unbiased and efficient. Regression analysis of spectroscopic data will be presented, with emphasis on using models to describe the correlations which are expected in the data, on proper weighting of observations, and on determining uncertainties in estimated parameters. While this approach is particularly powerful for multidimensional, hyphenated spectroscopic methods (time-resolved fluorescence, GC-MS, LC-UV, etc.), the theory of regression methods will first be developed with examples from measurements of lower dimensionality. The basis of regression methods for multidimensional data in the simple statistics of estimating a mean and standard deviation provides an intuitive basis for understanding more powerful analysis procedures, while extending our background simple statistics into methods for manipulating spectroscopic data.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1989
- Accession Number
- ADA210541
Entities
People
- A. L. Wong
- J. M. Harris
- P. E. Poston
- S. D. Frans
Organizations
- University of Utah