I would like to calculate the line of organic correlation, so that I can use it for record extension for a stream gauging station. Below is a description (1) and then my first attempt with R code (2). Thanks in advance for any help.
Stephen Sefick The LOC minimizes the sum of the areas of right triangles formed by horizontal and vertical lines extending from observations to the fitted line (figure 10.8). By minimizing errors in both directions it lies between the two OLS lines on a plot of Y versus X (see figure 10.7). The slope of the LOC line equals the geometric mean of the Y on X and X on Y OLS slopes: b1'' = sqrt(b1*b1') = sign[r] • sy/sx where b1'' is the slope of the LOC line Yi = b0'' + sign[r] • sy/sx • Xi So the correlation coefficient in the equation for OLS slope is replaced by the algebraic sign (+ or −) of the correlation coefficient with LOC. The magnitude of the LOC slope b1'' is determined solely by the ratio of standard deviations sy/sx. Performing LOC of X on Y will give the identical line as does the LOC of Y on X . I have written this code so far #line of organic correlation find out how to calculate "slope" loc <- function(x, y){ cor.xy <- cor(x,y) sign.xy <- sign(cor.xy) sd.ratio <- sd(y)/sd(x) Yi <- "slope" + sign.xy*sd.ratio*x } I don't know how to calculate "slope" for the predicted line. Maybe This is to simple of an approach? -- Stephen Sefick Let's not spend our time and resources thinking about things that are so little or so large that all they really do for us is puff us up and make us feel like gods. We are mammals, and have not exhausted the annoying little problems of being mammals. -K. Mullis ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.