On 2011-03-29 06:57, Walter Anderson wrote:
Hello,I need to regress data like the example below. The data points represent friction factors derived from observed trip length data. The function used to describe this data is a gamma function of the form, f(t) = a * t^b * e^(c*t) and I need to regress the data to obtain the a,b, and c coefficients. The gamma function can also be expressed in the log-linear form, ln[f(t)] = ln[a] + b * ln[t] + c*t, which may be easier to perform a regression on. I have performed a search for information on the subject, and have found a few possibly related sites, I can not figure out how to perform the regression in R. Any help/guidance would be appreciated. Walter t f ln(f) 1 1 952893 13 2 2 951077 13 3 3 945991 13 4 4 942358 13 5 5 939452 13
[... more data snipped ...] This looks like easy grist for the nls() mill. I would usually use the log form to get reasonable starting values for the nls interations: ## assume that your data are in a data.frame DF; fm1 <- lm( log(f) ~ log(t) + t, data = DF ) coef(fm1) # (Intercept) log(t) t # 13.81370501 0.18469223 -0.05955323 startvec <- c( aa=exp(14), bb=0.2, cc=-.06 ) fm2 <- nls( f ~ aa * t^bb * exp(cc*t), data=DF, start=startvec ) #summary(fm2) coef(fm2) # aa bb cc # 9.093841e+05 2.294895e-01 -5.951806e-02 ## plot the data plot( f ~ t, data=DF ) lines( fitted(fm2) ~ t, data=DF ) I wouldn't trust the model for small t. Peter Ehlers ______________________________________________ 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.
