Dear Rich, I think that it's generally a bad idea to give statistical (as opposed to simply technical) advice by email without knowing the context of the research. I think that you'd do well to seek help from a statistician, and not just do what I suggest below.
Interpolating the data only makes sense if there's no random component to the response (mag in your data). Otherwise, it makes more sense to get "predictions" from a statistical model that has an explicit error component for the response. In your case, a simple quadratic model in log(freq) seems to fit the data reasonably well. To see what I mean, try plot(log(freq), mag) mod <- lm(mag ~ poly(log(freq), 2)) summary(mod) points(log(freq), fitted(mod), pch=16) lines(spline(log(freq), fitted(mod))) Some basic regression diagnostics suggest that we can do better by taking the log of mag as well, producing a closer fit to the data and stabilizing the error variance: plot(log(freq), log(mag)) mod2 <- lm(log(mag) ~ poly(log(freq), 2)) summary(mod2) points(log(freq), fitted(mod2), pch=16) lines(spline(log(freq), fitted(mod2))) I have no idea whether this makes substantive sense in the context of your problem. Best, John > -----Original Message----- > From: R-help [mailto:[email protected]] On Behalf Of Evans, > Richard K. (GRC-H000) > Sent: Tuesday, September 26, 2017 10:01 AM > To: Eric Berger <[email protected]>; Fox, John <[email protected]> > Cc: [email protected] > Subject: Re: [R] bowed linear approximations > > My apologies for the typos in the code. > Here is a corrected version you can copy/paste in R to see the issue. > > freq <- c(2, 3, 5, 10, 50, 100, 200, 300, 500, 750, 1000, 1300, 1800, 2450, > 2900, > 3000, 4000, 5000, 6000, 7000, 8200, 9300, 10000, 11000, 18000, 26500, 33000, > 40000); mag <- c(1.9893038, 1.5088071, 1.1851947, 0.9444483, 0.7680123, > 0.7458169, 0.7069638, 0.6393066, 0.6261539, 0.6263381, 0.7053774, > 0.6900626, 0.6953527, 0.7843036, 0.9056359, 0.8867276, 0.8937421, > 0.9492288, 0.9629118, 1.1972268, 1.0010515, 0.9945838, 1.0564356, > 0.8733333, 1.1666667, 1.5366667, 1.4666667, 1.3166667); > plot(freq,mag,type="b",log="x"); for(i in 1:200){ xx <- > exp(runif(1,log(min(freq)),log(max(freq)) )); yy <- approx(freq,mag,xout=xx, > method = "linear"); points(xx,yy$y,col=rgb(1,0,0)); } > > For completeness, I have been puzzling over why the approximated points > don't lie linearly over the original data set (especially prominent in the > bow > between freq=10 and 50). Once I realized (and concurred with) why this bow > exists, I have been struggling with how to make these approximations as > expected.. In my original post, I think I oversimplified it too much by > implying > that my application was just 2 data points. > > Are your suggestions still valid do you think? > -Rich > ______________________________________________ > [email protected] mailing list -- To UNSUBSCRIBE and more, see > 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. ______________________________________________ [email protected] mailing list -- To UNSUBSCRIBE and more, see 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.
