On Feb 19, 2011, at 1:08 PM, Ben Ward wrote:
Hi Graham,
Thanks, that does explain lots. I've been playing with making log's of
data in models to make the relationship linear, which it does, which
suggests to me that lm() is the right way to go, however, after if
try
to predict after y values after about 60% on the x axis for light
transmission, the y value, for bacterial numbers, crosses the axis and
gives me negative values for y, which on a practical level isn't
possible, as one can't have less than no bacteria in a culture.
Once you have your estimated parameter in the transformed "analysis"
scale, you need to apply the inverse transformation, in this case
exp, to return the estimate to the measured scale. You also need to
consider that in the process of transforming the values, performing an
additive estiamtion, and transforming back to the "natural" scale, you
will have estimated a multiplicative model, since exp(log(x)+log(y)) =
x*y.
Had you used log(x) inside the lm call and then used predict, the
predictions would be correct.
You might want to consider glm models with family="poisson".
--
David.
On a
practical level, when I include the cirve in my appendix I could say
anything above around 60% is 0, and mention the negative results from
the standard curve's prediction capabilities are not literal, and to
say
turn any negative bacterial count obtained as a result of the curve to
0.
I wouldn't. The informed observer would know you were flailing around.
I've not had to deal with such pleatauing curves before. The values I
have for the curve don't go above 50%, so anything above it is
prediction, and my experiment probably won't result in x values above
50% as the death of the culture proceeds slowly, but that depending on
relative amounts of culture and antimicrobial I use the rate 'could'
go
faster or slower, so could go above 50%. I was wondering if non-linear
regression is better for such a thing, but I'm hesitant to go into
it in
more detail for now because of the danger of drastically increacing
complexity, if on a practical level, what I currenly have, works and
is
very accurate, within the range I will most likely be using it.
Thanks,
Ben.
On 19/02/2011 15:39, Graham Smith wrote:
Ben,
Does this help.
http://r-eco-evo.blogspot.com/2011/01/confidence-intervals-for-regression.html
Not sure if it will work with your particular model, but may be worth
a try.
Graham
On 18 February 2011 23:29, Ben Ward <benjamin.w...@bathspa.org
<mailto:benjamin.w...@bathspa.org>> wrote:
Hi, I wonder if anyone could advise me with this:
I've been trying to make a standard curve in R with lm() of some
standards from a spectrophotometer, so as I can express the curve
as a formula, and so obtain values from my treated samples by
plugging in readings into the formula, instead of trying to judge
things by eye, with a curve drawn by hand.
It is a curve and so I used the following formula:
model <- lm(Approximate.Counts~X..Light.Transmission +
I(Approximate.Counts^2), data=Standards)
It gives me a pretty decent graph:
xyplot(Approximate.Counts + fitted(model) ~ X..Light.Transmission,
data=Standards)
I'm pretty happy with it, and looking at the model summary, to my
inexperienced eyes it seems pretty good:
lm(formula = Approximate.Counts ~ X..Light.Transmission +
I(Approximate.Counts^2),
data = Standards)
Residuals:
Min 1Q Median 3Q Max
-91.75 -51.04 27.33 37.28 49.72
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.868e+02 2.614e+01 37.75 <2e-16 ***
X..Light.Transmission -1.539e+01 8.116e-01 -18.96 <2e-16 ***
I(Approximate.Counts^2) 2.580e-04 6.182e-06 41.73 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 48.06 on 37 degrees of freedom
Multiple R-squared: 0.9956, Adjusted R-squared: 0.9954
F-statistic: 4190 on 2 and 37 DF, p-value: < 2.2e-16
I tried to put some 95% confidence interval lines on a plot, as
advised by my tutor, to see how they looked, and I used a function
I found in "The R Book":
se.lines <- function(model){
b1<-coef(model)[2]+ summary(model)[[4]][4]
b2<-coef(model)[2]- summary(model)[[4]][4]
xm<-mean(model[[12]][2])
ym<-mean(model[[12]][1])
a1<-ym-b1*xm
a2<-ym-b2*xm
abline(a1,b1,lty=2)
abline(a2,b2,lty=2)
}
se.lines(model)
but when I do this on a plot I get an odd result:
They looks to me, to lie in the same kind of area, that my
regression line did, before I used polynomial regression, by
squaring "Approximate.Counts":
lm(formula = Approximate.Counts ~ X..Light.Transmission +
I(Approximate.Counts^2), data = Standards)
Is there something else I should be doing? I've seen several ways
of dealing with non-linear relationships, from log's of certain
variables, and quadratic regression, and using sin and other
mathematical devices. I'm not completely sure if I'm "allowed" to
square the y variable, the book only squared the x variable in
quadratic regression, which I did first, and it fit quite well,
but not as good squaring Approximate Counts does:
model <- lm(Approximate.Counts~X..Light.Transmission +
I(X..Light.Transmission^2), data=Standards)
Any advice is greatly appreciated, it's the first time I've really
had to look at regression with data in my coursework that isn't a
straight line.
Thanks,
Ben Ward.
David Winsemius, MD
West Hartford, CT
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