Help finding a best fit to an angular distribution

[chloealex88]

Hi all,

I have a set of data that is number of counts - vs - angle. I need one angle for a calculation. I think need to find the best fit instead of an average. What would be the best way of doing this? Maybe perform a least sq calculation? The function is non-linear.

Thanks in advance,

Chloe

 

[chiro]

Hey chloealex88 and welcome to the forums.

As you have alluded to, the idea of best fit seems good for your purpose.

There are a variety of statistical packages that do all kinds of regression modelling including linear and non-linear fits and its pretty much just a click of a button to do this automatically.

The most important that needs to be asked is essentially: "What are the important characteristics of your process?"

It's not really hard to click a button to generate a best-fit with a high correlation but again if you don't have any understanding of your process and just blindly extrapolate a value beyond your data based on the fit it may be so wrong as to be useless for your purposes.

So apart from the first question the next question to ask is if the value you are trying to predict is 'close' to your data or 'far away'?

Here is what I mean for the above. Imagine you have 2D data for value of A going from [0,10] and you want to predict a value of B for A = 10.5: that would be considered 'close'.

If however you wanted to predict a B value for A = 20 that would be very dangerous and is considered 'far'.

It's not a hard and fast definition but the idea of using fit data to predict a value that close with no detailed idea of the process is very different than doing the same thing for a 'far' value and its important you be aware of this.

 

[chloealex88]

Hey chloealex88 and welcome to the forums.

As you have alluded to, the idea of best fit seems good for your purpose.

There are a variety of statistical packages that do all kinds of regression modelling including linear and non-linear fits and its pretty much just a click of a button to do this automatically.

The most important that needs to be asked is essentially: "What are the important characteristics of your process?"

It's not really hard to click a button to generate a best-fit with a high correlation but again if you don't have any understanding of your process and just blindly extrapolate a value beyond your data based on the fit it may be so wrong as to be useless for your purposes.

So apart from the first question the next question to ask is if the value you are trying to predict is 'close' to your data or 'far away'?

Here is what I mean for the above. Imagine you have 2D data for value of A going from [0,10] and you want to predict a value of B for A = 10.5: that would be considered 'close'.

If however you wanted to predict a B value for A = 20 that would be very dangerous and is considered 'far'.

It's not a hard and fast definition but the idea of using fit data to predict a value that close with no detailed idea of the process is very different than doing the same thing for a 'far' value and its important you be aware of this.

Thank you that was very interesting. The will be a more probable scattering angle. The function itself is similar to a cosine function. I have found a good non-linear fitting program. I will know it has work because there is a theoretical trend to the calculation I will perform.