There are a couple of points to keep in mind when doing a log-transform of an
exponential model, such as --
y = a*exp(b*x)
1. The implicit statistical model is multiplicative in the error. The
implied
statistical model of the log transform is --
log(y) = log(a) + b*x + u
which implies --
y = a*exp(b*x)*exp(u)
A linear regression in the log transform is not a least-squares fit in
the
original model, which implies a statistical model like --
y = a*exp(b*x) + u
This may be OK, but it should be recognized. The least-squares fit in
this
untransformed model requires a nonlinear fit.
2. If y is distributed log-normal, its expected value is --
E(y) = exp(logy.hat + 0.5*var(u))
not exp(logy.hat) as one might expect. Here logy.hat is the predicted
value of the log of y in the log-linear regression, and var(u) is the
error variance around the fitted line of the log-linear regression.
3. If your model contains an intercept term --
y = a + c*exp(b*x)
You need nonlinear least-squares or maximum likelihood to fit it.
Larry Hotchkiss
-----------------------------------------------------------------------------------
Date: Sun, 10 Jan 2010 16:44:02 -0500
From: "Murray Cooper" <myrm...@earthlink.net>
To: "chrisli1223" <chri...@austwaterenv.com.au>,
<r-help@r-project.org>
Subject: Re: [R] R exponential regression
Message-ID: <1fa457dc6fe04de4ab2541d89d2d0...@ownerc86c2419d>
Content-Type: text/plain; format=flowed; charset="iso-8859-1";
reply-type=original
Chris,
I haven't seen anyone post a reply yet so thought I'd
throw in my thoughts. I'm no R expert!
When you talk about an exponential trend line are you
refering to:
1) y=ax^b
or
2) y=ae^(bx)
If 1) then take base10 logs of y and x and then fit them
with simple linear regression. Then calculate the antilog
of the residulas and plot these as your trendline.
If 2) then take natural logs of y and x and follow the rest
of the procedure described in 1).
Hope this helps.
Murray M Cooper, Ph.D.
Richland Statistics
9800 N 24th St
Richland, MI, USA 49083
Mail: richs...@earthlink.net
----- Original Message -----
From: "chrisli1223" <chri...@austwaterenv.com.au>
To: <r-help@r-project.org>
Sent: Thursday, January 07, 2010 10:33 PM
Subject: [R] R exponential regression
>
> Hi all,
>
> I have a dataset which consists of 2 columns. I'd like to plot them on a
> x-y
> scatter plot and fit an exponential trendline. I'd like R to determine the
> equation for the trendline and display it on the graph.
>
> Since I am new to R (and statistics), any advice on how to achieve this
> will
> be greatly appreciated.
>
> Many thanks,
> Chris
> --
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