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Least-Squares Analysis of Data with Uncertainty in "y" and "x": Algorithms in Excel and KaleidaGraph
Tellinghuisen, Joel – Journal of Chemical Education, 2018
For the least-squares analysis of data having multiple uncertain variables, the generally accepted best solution comes from minimizing the sum of weighted squared residuals over all uncertain variables, with, for example, weights in x[subscript i] taken as inversely proportional to the variance [delta][subscript xi][superscript 2]. A complication…
Descriptors: Chemistry, Least Squares Statistics, Data Analysis, Spreadsheets
Tellinghuisen, Joel – Journal of Chemical Education, 2016
The method of least squares (LS) yields exact solutions for the adjustable parameters when the number of data values n equals the number of parameters "p". This holds also when the fit model consists of "m" different equations and "m = p", which means that LS algorithms can be used to obtain solutions to systems of…
Descriptors: Least Squares Statistics, Computer Software, Graphs, Chemistry
Tellinghuisen, Joel – Journal of Chemical Education, 2015
The method of least-squares (LS) has a built-in procedure for estimating the standard errors (SEs) of the adjustable parameters in the fit model: They are the square roots of the diagonal elements of the covariance matrix. This means that one can use least-squares to obtain numerical values of propagated errors by defining the target quantities as…
Descriptors: Least Squares Statistics, Error of Measurement, Error Patterns, Chemistry
Peer reviewed
Tellinghuisen, Joel – Journal of Chemical Education, 2005
The method of least squares (LS) is considered as an important data analysis tool available to physical scientists. The mathematics of linear least squares(LLS) is summarized in a very compact matrix rotation that renders it practically "formulaic".
Descriptors: Data Analysis, Least Squares Statistics, Monte Carlo Methods, Scientific Research
Peer reviewed
Tellinghuisen, Joel – Journal of Chemical Education, 2005
Several data-analysis problems could be addressed in different ways, ranging from a series of related "local" fitting problems to a single comprehensive "global analysis". The approach has become a powerful one for fitting data to moderately complex models by using library functions and the methods are illustrated for the analysis of HCI-IR…
Descriptors: Goodness of Fit, Data Analysis, Models, Evaluation Methods