On 20/02/2011 18:52, David Winsemius wrote:
On Feb 20, 2011, at 1:27 PM, Ben Ward wrote:
However, the
Y ~ X + Y^2
Produces the best fitting line - it is pretty much on the data points
- I'm trying to make a standard curve, with which to take readings
from a spectrophotometer off of. Rather than what I would normally
use models for - such as hypothesis testing and analysis of data from
experiments.
I thought we were leaving behind the model that had the dependent
variable on both sides of hte equation. Can you explain how you would
construct a chart or a function that will turn those results into
something useful?
Sorry for any confusion, I am indeed leaving behind the Y ~ X + Y^2
model, I was only mentioning that it had a higher R squared than
anything else I had done.
I'll explain exactly what the chart/function is made from and is for, to
remove any mystery or highlight anything important: The curve I'm trying
to produce, is from readings from a spectrophotometer, from series of
standards called the MacFarland Scale - tubes of solution which were
made up to simulate different known numbers of bacteria in a liquid
sample: the standards are of different intensities of coloudy-ness, and
they represent different numbers of bacteria in a liquid medium. The (X)
axis is % light transmission as measured by the spectrophotometer, the
cloudier the standard, the lower this value, and the Bacterial Counts on
the (Y) axis, are higher, the cloudier a sample (or the standards) are,
thus it is higher with lower % Light Transmission. This is a negative
curve, which never goes below 0, because you cant have less than no
bacteria. This curve/function, which has been made from the standards of
known numbers, will then be used to estimate the numbers of bacteria
present in proper samples, rather than known standards. I would take the
% Light Transmission Readings the spectrophotometer gives me for those
standards, and then using the curve - or working through the function,
calculate the (Approximate) number of bacteria present in my samples. I
took 5, % Light Transmission readings for each standard to make sure the
machine wasn't giving me wildly different readings (it' wasnt), and used
them to try and construct a curve.
Hence my comment about Y ~ X + Y^2 giving me a better fit (R-Squared).
I need a good fit to make reliable predictions. However, since then,
I've added an extra standard from the scale (There are about 10/11
standards to the scale, but I've got 9, because the last few can't be
made up accurately without introducing error or the lab tech's running
into difficulty doing it by hand), and the Y ~ X + Y^2 curve is no
longer sufficient after this.
I followed a suggestion (I think by you) to try a GLM, with the poisson
distribution, as I mentioned in my last email that went around, which
wasn't closely fitting as I would like, it's my first experience with
GLM, but to my understanding, the Residual Deviance, was orders higher
than the residual degrees of freedom. So under instruction of a
textbook, I tried with a quasi-poisson, but still got the same result.
Then (again textbook suggestion) tried with a negative binomial
distribution, and got a much lower AIC value and a residual deviance
much much closer to the residual degrees of freedom (the R print outs of
them are on the previous email I sent around).
I hope this has explained when you asked "Can I explain how I would
construct a chart or a function that will turn those results into
something useful?"
Thanks,
Ben.W
Thanks,
Ben.
On 20/02/2011 11:53, nzcoops wrote:
model<- lm(Approximate.Counts~X..Light.Transmission +
I(Approximate.Counts^2), data=Standards)
Might not be addressing the problem, don't you have Y ~ X + Y^2
here? That's
a violation of the assumptions of an lm isn't it?
Also for plotting CI on a curve look into ggplot2::geom_ribbon, it's
much
nicer than just plotting lines and is easy to use. had.co.nz should
set you
right for setting this up.
David Winsemius, MD
West Hartford, CT
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