Is there a maths genius on the forum?

AndyT said:
It's not linear, it's quadratic. A linear relationship would be of the form y = mx +c
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it is a linear model - both linear models and non linear models can be used to fit curves

in this case there is a constant and two parameters multiplying the predictor variables, that one of the predictor variables is simply the square of the other doesn't matter, the model is still linear in the parameters and still takes the standard form:

Screen_Shot_2017_03_03_at_19_07_11.png


resulting plot looks like this:

Screen_Shot_2017_03_03_at_12_04_58.png


so the OP has a bit of a problem if he's trying to predict values for the independent variable using the dependent variable
 
Linear and non linear models can be used, but when it comes to a science experiment and using standards to determine stuff, you have an issue when using a non linear model. The source of error can be rather large.
 
shredgodxp said:
Linear and non linear models can be used, but when it comes to a science experiment and using standards to determine stuff, you have an issue when using a non linear model. The source of error can be rather large.
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Not sure what you mean by that?
 
dowie said:
Not sure what you mean by that?
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Experimentally, when you increase the concentration of something, the absorbance should increase in a linear fashion and it does, up to a certain point. All methods have a linearity range, set by either the detector you're using or some other factor.

What we usually do, is determine results in the linear (straight line) portion of the graph.

eDlRRvG.png


So the above graph is a typical conc vs signal (in this case absorbance) for calibration and result determination.

LoD is limit of detection (how low your concentration can be to actually see it practically), LoQ is quanitification (at what level you can accurately determine a result). It gets interesting at the LoL (limit of linearity) where you lose the signal to concentration relationship where it eventually levels off. Often this is due to the detector (in this case UV-Vis) being overloaded and you no longer see a signal increase when you increase the concentration.

You can and often do get quadratic curves but the above applies, the Limit of Linearity is where the curve starts to become non linear. To deal with this you just don't include the higher concentration points that make it non linear overall.

Hope that makes some sense.

Edit: Just saw that OP is doing work with proteins, these get messy and quite often you do work with 2nd or 3rd order calibrations. Is a pain though.
 
That makes some sense, but seems to have gone off open a tangent somewhat to talking about some experiments you're used to where you have issues with some equipment.

Your previous post mentioned linear vs non-linear models and some ambiguous comment about errors, so I'm guessing if the next post is the explanation then you weren't really talking about any general issues between linear and non-linear models after all but just some issue with some experiments you're used to.

Also, please not, as per my post further up, linear models can be used to fit curves.
 
The point about errors is that a polynomial only gives an approximation of the modelled function unless the number of exponential terms (the order of the polynomial) matches that of the underlying functon and the linear weights of each term are accurate and precise.
 
Tuppy_Glossop said:
The point about errors is that a polynomial only gives an approximation of the modelled function unless the number of exponential terms (the order of the polynomial) matches that of the underlying functon and the linear weights of each term are accurate and precise.
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Pretty much any model only gives an approximation of the real world.
 
Motion? - you can't know the position of every possible atom that could affect say air resistance etc.. your model is going to be an approximation.

Anyway this doesn't have much relevance to what was posted earlier - the other poster made some ambiguous comment about errors in linear vs non-linear models and you've followed up with a random unrelated comment that polynomials of different order will will produce different errors.
 
You 'explained' another posters post by posting about something rather different. I'm not sure what else to say to that aside from politely pointing out that it isn't really relevant.
 
This is Laplace's view of determinism, and is refuted by 20th century science.

However, this is beside the point you're making. You're asserting the perfection of [insert model], whilst simletaneously acknowledging the impossibility of testing any model to arbitrary order. For reference, each of the models you mentioned are verifiably inaccurate within appropriate regimes.
 
I think this needs to be emphasised more at school:

https://en.wikipedia.org/wiki/All_models_are_wrong

Although the aphorism seems to have originated with George Box, the underlying idea goes back decades, perhaps centuries. For example, in 1960, Georg Raschsaid the following.[13]

… no models are [true]—not even the Newtonian laws. When you construct a model you leave out all the details which you, with the knowledge at your disposal, consider inessential…. Models should not be true, but it is important that they are applicable, and whether they are applicable for any given purpose must have course be investigated. This also means that a model is never accepted finally, only on trial.
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Tuppy_Glossop said:
Show me a quantum car made of wave matter that doesn't obey Newton's laws and I'll consider your point.
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I'm not sure what your point is - no one is saying that newton's laws aren't good approximations. You however seemed to be under the impression that they're perfect, they're not.

Tuppy_Glossop said:
dowie said:
Pretty much any model only gives an approximation of the real world.
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I disagree. We have perfect models of many real world processes: motion, forces, electromagnetism, thermodynamics, etc.
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