The mean value theorem of integration (I have a cross-stitch of this theorem hanging on my wall (between cross-stitches of the central limit theorem and Bayes theorem)) tells us that the area under a curve is equal to the width of the area of interest times the average height of the curve. Often when we want to use the area under a curve in statistics we can just use the average of the y-values generating the curve and it is much simpler.
If the x-coordinates of your points are evenly spaced or are random with a fairly uniform distribution then the mean height of the points will probably be as useful as any curve that you computed and then integrated. If the x-coordinates are not uniformly spread then you may benefit from a weighted average. One option for estimating the integral is to use the trapezoidal rule or Simpson's rule, but if you look at those formulas, they are just a weighted average of the heights again. So, while Yes, R can estimate curves and compute numerical integrals of the curves, there is a good chance that you don't really need to do either. On Thu, Apr 3, 2014 at 9:26 AM, Frances Cheesman <fcheesman...@gmail.com> wrote: > Hi all, > > I have a number of bacterial growth curves I would like to find the > equations for these and then integrate them to find the area under the > curves for me to do stats on later. > > Is there any way I can do this in R? > > Thanks, > > Frances > > [[alternative HTML version deleted]] > > ______________________________________________ > 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. -- Gregory (Greg) L. Snow Ph.D. 538...@gmail.com ______________________________________________ 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.
