making an equation from data

seraphimvc

hi guys any help would be great!thank you in advance!

basically i run this experiment 3 times meaning i take readings(n=1,n=2,n=3) according to different temperature.

Temp n=1 n=2 n=3
25 162 100 136
15 162 90 102
10 375 157 176
5 496 193 760

i can easily measure the mean,standard deviation ,plot a graph (it will be a ugly curve)from the data.

my question is,i would like to make an equation to sum up the experiment - making a trendline of the curve,comes out with an equation of the trendline which can allow me to predict what temperature will give the theorical readings.it will definitely not accurate but as soon as it can represent something i am happy with it.maybe i can use the standard deviation for the error correction by adding some plus/minus at the end of the equation.how can i work it out?

the reason i am looking at this is currently doing some self study in summer while i have no idea how the person of this paper comes out with some equation.

hope you guys can shed me some light.

2Scoops

You can get a simple line equation in any spreadsheet program. In Excel, you can choose the trendline that best fits the data and then just display the line equation in the options. You can calculate standard error about the regression line too but I'm not sure how easy that would be for anything that's not linear (and this isn't linear).

Or you could do confidence intervals about each condition/temp.

Michael Collins

The process you're trying to do is known as modelling, or curve fitting. It's quite doable - to varying levels of accuracy - usually the complexity of the function goes up quite a bit with accuracy. In other words, if you want a simple function, you will have to accept a certain (possible large) level of error.

But before I go into that, could you give me a bit more detail about what the readings actually are? They seem to vary wildly between n = 1, n = 2 etc? For the modelling to make any sense, the readings have to be repeatable, and it looks like what you're reading is quite unpredictable, particularly for Temp = 5.

seraphimvc

gladly to get response so quickly!

i knew i could do the curve and the trendline equation from excel,but i hope i can do it manually,trying to get to know more of the method so that i can fitting it with some error correction or some way to play with the equation.(i have only learnt how to make linear equations and the highest level of my maths knowledge is basic calculus of 3 variables,a 2nd yr college subject which i took it as personal interest)

and for michael,yes,the data is funny in my eyes too tbh,but the fact that these biology thingy is vary different everytime you do the experiment

this is one of the exercises i got now.for the other case,i actually make up 2 equations for different range(1-9 is polynomial trendline equation,above 10 use a power trendline equation)since the curve is coincidentally showed 2 huge differences,the 2 different trendlines fit well on the curve.but then i have no idea how to fit in the error correction (to making the equations more persuasive) and what will i do next time if i get a new question?

DublinDilbert

If its a linear system you should be able to use a "least squares estimator" LSE....

Its fairly easy in matlab to calculate the LSE for a given set of input/output data.

When you say your looking for a formula for the system, what sort of formula do you need? A discrete time (digital) input / output equation?

seraphimvc

DublinDilbert wrote: »

If its a linear system you should be able to use a "least squares estimator" LSE....

Its fairly easy in matlab to calculate the LSE for a given set of input/output data.

When you say your looking for a formula for the system, what sort of formula do you need? A discrete time (digital) input / output equation?

sorry for the late reply.i kinda work the thing out with excel,using the trendline tool,managed to get acceptable fit curves as i mention above.

defo not a linear system i say?since they are curves.we are looking at something like y = ax^2+ bx +c?power/exponential/log etc trend on the curve.

i have got a copy of sigma plot,anyone know about this software?seems really complicated