I need some help getting pointed in the right direction for creating a regression model in R with data that looks like this.

This is my first foray into this. So using Excel's trend line equation as my reference, I was able to create a logarithmic trend line for another set of data which matched between the two applications.

However, with this specific example, I'm not sure how to formulate the model or even if I should be using non-linear vs linear regression with transformation. Below is an example of the data in the plot.

x = c(0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1)
y = c(0.008,0.004,0.0025,0.0024,0.0023,0.0022,0.0021,0.002,0.0018,0.0005,0.012,0.006,
z = c(1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2)

df = data.frame(x, y, z)

plot(df$y ~ df$x, type="p", pch=20, col=df$z)

Sample Data

  • $\begingroup$ try lm(y ~ -log(x)) $\endgroup$ – Aksakal Feb 3 '15 at 15:49
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    $\begingroup$ This looks more like a deterministic sequence than a set of stochastic data. What are these data? $\endgroup$ – gung - Reinstate Monica Feb 3 '15 at 15:49

Use nls() to fit any curve. It takes a user-defined function as an argument. In your case you have two inflection points, so a cubic might work. You could also define a higher-order polynomial.

rhs <- function(x, b0, b1, b2, b3) {
    return(b0 + b1*x + b2*x^2 + b3*x^3)

model <- nls(y ~ rhs(x, intercept, linear, quadratic, cubic), data=df, 
             start=list(intercept=0.015, linear=-.001, quadratic=0, cubic=0.01), trace=T)

If your start values are at all reasonable you will get a good fit.

  • $\begingroup$ Thanks. I had experimented with that, but wasn't getting the right result. How would you modify your function to incorporate for Z? Would I add a +b4*z into the function? (Assuming Z shifts the series up linearly). $\endgroup$ – ElPresidente Feb 3 '15 at 16:07
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    $\begingroup$ Any function you can write will work. You just need to supply arguments from your dataframe. You'll get back the fitted values. See css.cornell.edu/faculty/dgr2/pubs/list.html#pubs_m_R item 11 Rossiter, DG 2005. Technical Note: Fitting rational functions to time series in R. Technical Report ITC, Enschede, NL. Version 1, December 2005. 15 pp. for some ideas, $\endgroup$ – 罗大伟 Feb 3 '15 at 16:25
  • $\begingroup$ Note that a polynom is not non-linear in its parameters. It would be better practice to use lm(y ~ poly(x, degree = 3), data = df). Or possibly lm(y ~ poly(x, degree = 3, raw = TRUE), data = df) $\endgroup$ – Roland Feb 4 '15 at 8:27

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