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I have a small dataframe that has a exponentially decreasing trend. I would like to extract a formula based on the data in my dataframe? Is this possible, and if so, how can I go about extracting the formula?

Nick
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    Hi nick - R can certainly do this for you, and SO can help. However - nobody can really provide any guidance without seeing what your data looks like. Here's a tutorial on how to ask a great question: http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example. Please update your question and I bet you'll get some high quality answers. – Chase Aug 26 '11 at 01:09
  • Sounds like you need some sort of polynomial fit: [http://en.wikipedia.org/wiki/Curve_fitting](http://en.wikipedia.org/wiki/Curve_fitting) – O_O Aug 26 '11 at 00:44

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To get a best fit exponential curve, you'll want to basically convert an the curve to a linear one, and find the "linear fit" and then convert it back. For example, here's data decreasing exponentially. 

t <- c(0,2,4,7)
y <- c(25,11,4,3)

Then take the log of y.

y2 <- log10(y)

Then model y2 as a function of time.

lm(y2~t)

You'll get the slope and intercept in usual linear equation form (y = mx + b), but using log(y). To get the exponential equation of the line, put the slope and intercept into the following form:

y = A*r^t

Where A = 10^intercept and r = 10^slope.

For these data, your equation will be:

y = 20.77304*0.7333309^t

If you want to plot them together, define: 

expLine <- function(t) 20.77304*0.7333309^t

Then plot(t,y) and curve(expLine,0,7,n=101,add=TRUE).

Amyunimus
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  • If you want to plot them together, define: `expLine <- function(t) 20.77304*0.7333309^t`. Then `plot(t,y)` and `curve(expLine,0,7,n=2000,add=TRUE)`. – Amyunimus Aug 26 '11 at 18:30
  • or `with(as.list(coef(lmfit)),curve(t*x+#(Intercept)#,0,7,add=TRUE))` (**note**, you'll have to replace # with a back-tick (single back-quote), comment syntax can't handle it). `n=2000` is overkill for this problem; the default value of `n=101` should be fine. By the way, @Amyunimus -- you're allowed and indeed encouraged to edit your question (this time I went ahead and did it for you ...) – Ben Bolker Aug 26 '11 at 19:03