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Re: [Phys-l] How to print logarithmic graphics in A4 size ?

On 09/06/2007 12:40 PM, Richard L. Bowman wrote:

I know this is a complicated problem,

Agreed, complicated.

and I don't have time
to pursue it now. However, my sense is that when we "eye-ball" a good
straight-line to the data on a log-log plot, we are in fact doing an
imprecise least-squares fit to the log-log data

Agreed, imprecise.

and not to the raw data.

Agreed, definitely the same as not fitting the raw data.

With the very high R-squared values (and what does that mean
for log-log plots?) that we usually work with in undergraduate labs,
probably none of these concerns make a large difference in the
constants of the defining relationship.

I wouldn't say that. It is easy to come up with examples
where fitting to the log of the data introduces disastrous
bias.

In particular, if the raw (i.e. non-log) data has symmetrical
error bars, the log data will have asymmetrical error bars.
The problem gets worse the larger the raw error bars are as
a percentage of the raw data ... and the problem becomes
infinitely bad if the scatter in the raw data ever extends
as far down as the zero contour.

In situations like this (even remotely like this) it is
imperative to fit the data in non-log space. Then, for
clarity of presentation you have the option of taking
the log of the data and of the fitted function. OTOH
there are sometimes other ways of achieving clarity of
presentation.
-- One option, rather than plotting the log data at
all, is to plot the fitted function on scale, and
then plot the *residuals* on another scale.
-- Another option if you have a lot of data is to do
some preliminary data reduction on the raw data,
perhaps "averaging" them in groups of 100, so as
to create some half-raw data with sqrt(100) less
scatter.

It's complicated. There are lots of ways to do it wrong.
OTOH, don't despair, there are a few ways of doing it right.
This is why you study, to be able to handle situations like
this.