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Potential Project Description for 2011-12

 

Title: Uncertainties in Chemical Measurements Resulting from Least Squares Regression
Domain Expert: Paul Jackson (Chemistry, Environmental Studies) and Mary Walczak (Chemistry)

Analytical Chemistry is replete with instances where a calibration is performed by measuring a signal (y) for known concentrations (x). This calibration curve can be linear or non-linear. Most frequently the method of least squares is used to derive the relationship between the two variables; the resulting equation is used subsequently to determine the concentration (x) for a signal (y) resulting from analysis of an unknown solution. Analytical chemists are keenly interested in knowing the quality of the least squares fit to the data and the uncertainty in the determined concentration. It is this set of uncertainties that establishes the level of confidence in the result.

In this project, we will work on statistical methods to determine the uncertainty in the independent variable x as a function of linear or quadratic least squares fitted functions. There is interesting literature to explore regarding the “calibration problem”, where we use an equation to estimate x rather than y as is typical. Potential outcomes of the project include a written guide to linear and quadratic regression analysis and a spreadsheet-based computational tool to determine uncertainties.