Least-Squares Analysis of Data with Uncertainty in "y" and "x": Algorithms in Excel and KaleidaGraph

Autor/in	Tellinghuisen, Joel
Titel	Least-Squares Analysis of Data with Uncertainty in "y" and "x": Algorithms in Excel and KaleidaGraph
Quelle	In: Journal of Chemical Education, 95 (2018) 6, S.970-977 (8 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Tellinghuisen, Joel)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0021-9584
DOI	10.1021/acs.jchemed.8b00069
Schlagwörter	Chemistry; Least Squares Statistics; Data Analysis; Spreadsheets; Graphs; Monte Carlo Methods; Computation; Problem Solving; Equations (Mathematics) + Suchen Sie Ihr Suchwort? Chemie; Auswertung; Spread sheet; Spredsheets; Spreadsheet; Tabellenkalkulation; Grafische Darstellung; Monte-Carlo-Methode; Problemlösen; Equations; Mathematics; Gleichungslehre
Abstract	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 in this method, here called "total variance" (TV), is the need to calculate residuals [delta][subscript i] in every uncertain variable. In "x-y" problems, that means adjustments must be obtained for "x" as well as for the customary "y." However, for the straight-line fit model, there is a simpler procedure, a version of effective variance (EV) methods, that requires only the residuals in y and agrees exactly with the TV method. Furthermore, Monte Carlo calculations have shown that this EV[subscript 2] method is statistically comparable to the TV method for many common nonlinear fit models. This method is easy to code for computation in Excel and programs like KaleidaGraph, as is illustrated here for several examples, including implicit nonlinear models. The algorithms yield estimates of both the parameters and their standard errors and can be used as well for more traditional problems requiring weighting in "y" only. (As Provided).
Anmerkungen	Division of Chemical Education, Inc and ACS Publications Division of the American Chemical Society. 1155 Sixteenth Street NW, Washington, DC 20036. Tel: 800-227-5558; Tel: 202-872-4600; e-mail: eic@jce.acs.org; Web site: http://pubs.acs.org/jchemeduc
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01