# of measurments in order to find parameters

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In summary, the minimum number of measurements needed to fit a known function to a measured data is determined by the order of the polynomial representing the function. For a first degree polynomial, two measurements are needed, while for a second degree polynomial, three measurements are needed. This follows the pattern of n+1 measurements, where n is the order of the polynomial.
  • #1

ted1986

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Hi,

I've got a question about fitting a known function to a measured data.

Suppose I want to find X parameters by fitting a curve to some measurments - What is the minimum number of measurements needed?
Someone has told me that I need X+1 measurments, (because one degree of freedom), but I didn't understand it...
Could someone tell me if its true, and why


Thanks!

Ted
:-)
 
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  • #2
Well, I am no expert on curve-fitting, but let's think about it...

if you knew that your function is a straight line (order 1 "polynomial": ax+b), how many measurements would need to make? Well...you would just need to make 2 measurements so that you could put together 2 equations and 2 unknowns and solve for a and b...that was n+1, where n was the order of the "polynomial" representing your function (1 in this case...this is the highest power for x in the equation).

Now, if you knew that your function was a parabola (ax^2+bx+c)...how many measurements would you need to determine a, b, and c? You would need 3 values for x, plug them in the equation above and form a system of 3 equations and 3 unknowns and solve...that was n+1=3 measurements for a 2nd degree "polynomial"..

...starting to get the picture?

my 2 cents
 

1. How many measurements do I need to take in order to find parameters?

The number of measurements needed to find parameters depends on the complexity of the system being studied and the level of accuracy desired. Generally, more measurements will lead to more accurate results, but there is no specific number that applies to all situations.

2. Can I use existing data or do I need to collect new measurements?

In some cases, existing data may be sufficient to find parameters. However, if the existing data does not accurately represent the system or if the parameters being studied are highly specific, new measurements may be necessary.

3. How do I determine the appropriate number of measurements for my study?

This will depend on several factors such as the specific parameters being studied, the level of accuracy desired, and the resources available. Consulting with other researchers or conducting a pilot study can help determine the appropriate number of measurements.

4. Do I need to take the same number of measurements for each parameter?

Not necessarily. Some parameters may require more measurements to accurately determine, while others may only need a few. It is important to consider the significance of each parameter and allocate measurements accordingly.

5. Is there a specific method for determining the number of measurements needed?

There is no one-size-fits-all method for determining the number of measurements needed. It will depend on the specific research question, the system being studied, and other factors. Consulting with other researchers or conducting a literature review can provide insight on the appropriate number of measurements for a particular study.

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