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

Autor:	Joel Tellinghuisen
Rok vydání:	2018
Předmět:	Uncertain variable Computation 05 social sciences Monte Carlo method 050301 education General Chemistry Variance (accounting) 01 natural sciences Education Nonlinear system Total variation 0103 physical sciences Data analysis Code (cryptography) 010306 general physics 0503 education Algorithm
Zdroj:	Journal of Chemical Education. 95:970-977
ISSN:	1938-1328 0021-9584
Popis:	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 xi taken as inversely proportional to the variance σxi2. A complication in this method, here called “total variance” (TV), is the need to calculate residuals δi 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 EV2 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 nonli...
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::252787f9eda9245c277a1023120da1ae https://doi.org/10.1021/acs.jchemed.8b00069 Zobrazit plný text záznamu