 R2 application

 R2 application calculate the linear fit of plotted CSDs ( Crystal Size Distribution ) by applying the ordinary least squares fit method, considering asraw data the data in the ln[n(L)], L space. The method of least squares assumes that the best-fit curve of a given type is the curve that has the minimum sum of deviations squared from a given set of data. Let (xi,yi) be the n points representing our input data, where x is the independent variable, i.e., the sampled diameter L, and y is the dependent variable, i.e., ln[n(L)]. We sought a linear function f(x)=mx+q, where m and q are the adjustable parameters we wish to determine and which, in turn, best approximate our data points. According to the ordinary least squares method, the best fitting curve is determined by minimization of the sum S of squared residuals. The quality of the fit was assessed using the coefficient of R2 determination, which can be used as an indicator of how well a line fits the data points. Note that 0≤ R2≤1 and an R2 equal to 1 indicates that the regression line fits the data perfectly. The R2 is calculated for all possible linear fit of the CSDs. The R2 distribution for each sample is then presented as a grid of R2 valuesPlease if you use this application in scientific publication and/or congress posters and oral presentation cite:  Fornaciai A., C. Perinelli, P. Armienti, M. Favalli, (2015) Crystal size distributions of plagioclase in lavas from the July-August 2001 Mount Etna eruption. Bulletin of Volcanology 77:70. DOI 10.1007/s00445-015-0953-8http://link.springer.com/article/10.1007%2Fs00445-015-0953-8  Instructions1) Prepare the input txt file containing the following information (as an example)# l           ln 2.24        -6.62 1.78        -5.1 1.42        -3.82 ...  the # at the first line is mandatory (for the processing software to skip the line) or alternatively the first line can be missing:  2.24        -6.62 1.78        -5.1 1.42        -3.82 ...  2) Save the input file as “input.txt”  3) Compile the form and upload the file  (link is below)  4) Download the output at the link provided in the e-mail the system will send to you.  Output data output_plot.png  Plots of crystal size distributions. Vertical axis represents the natural logarithm of the population density, horizontal axis crystal size  output_R2_cut_at_0.XX.png  Distribution of the square of the correlation coefficient (R2) between the dependent variable ln[n(L)], representing the natural logarithm of the population density, and the independent variable L for simple linear regression.R2 indicates how closely the CSD data points fit the regression line. R2 equal to 1 indicates that the regression line fits the data perfectly. X and Y are the first and the last node of the interval for which the R2 is calculated. Node count starts from 0. 0.XX is the lower threshold value in plot legend. To make the R2 diagrams images more readable, we have removed the original pixelation by linear interpolation to a higher resolution.  Users’ comments and suggestion how to improve this help and the R2 web-application are particularly welcome.Team:   Alessandro Fornaciai     alessandro.fornaciai(at)ingv.it , Massimiliano Favalli   massimiliano.favalli(at)ingv.it ,   Luca Nannipieri   luca.nannipieri(at)ingv.itGO TO  ==>   R2 APPLICATION FORM