Marwan A.

asked • 07/01/18

find the equation of set of points

I have set of points of (x,y) as follow
-2000000    0.616,
 
-199700      1.742,
 
-63190         3.28,
 
-5631           8.130,
 
-1845           9.123,
 
-577             9.492,
 
0                  9.68,
 
310.7          9.778,
 
497              9.836,
 
618              9.875,
 
700.5          9.9,
 
759.4          9.92,
 
882             9.959,
 
969.98       9.987,
 
983.98       9.992,
 
991.74      9.994,
 
9.999        9.997,
 
1007.5     9.999,
 
1009.9     10,
 
1009.97   10,
 
1010         10,
 
I will be gratfule if tell me the type of this function and is it possible to find it's equation.

1 Expert Answer

By:

Paul M. answered • 07/01/18

Tutor
5.0 (39)

Learn "how to" do the math and why the "how to" works!
About this tutor ›
About this tutor ›
In my opinion, the way to attack this problem is to graph the points first, even approximately.
Looking at the data, I would hazard a guess that is it approaches 0 toward -infinity and 10 toward positive infinity.
That suggests it will have a point of inflection somewhere far out on the negative x axis.
One common function which has sort of that shape is tan x.
Also most probability distribution functions have this general shape.
Good luck!
Upvote • 1 Downvote
More
Report

Paul M.

tutor
Correction:
In my original answer I suggested that tan x had a shape somewhat like the data; I should have said arctan x.
Report

07/01/18

Marwan A.

Thanks for you reply and correction.
Actually I have another question if you do not mind.
Suppose I have equation in the form of  y=ax^m-bx^n+cx^o-dx^p+ex^q
Where a b c d e and m n o p q
Are unknown for you and I knew this equation and I provid you with set of points of (x,y) and I asked you to find the equation. 
Is it possible to find this equation?
Report

07/02/18

Paul M.

tutor
Maybe!
The problem is the exponents.
With 10 points you will get 10 equations in the 10 unknowns.
The problem is that the exponents will make  the equations non-linear...and they may make it at least difficult if not impossible to solve the system.
Report

07/02/18

Marwan A.

I do know if you received my second question or not.
Any way I will send it again.
The question as follow:
 
Assume I have equation in this form
Y=aX^m-bX^n+cX^o-dX^p-eX^q
Where a b c d and m n o p q  Are unknown and I provide you with set of points of (x,y). So can you find the equation of this function?
Report

07/02/18

Marwan A.

What I understand that you can find the unknowns a b c d e but you will face problem to calculate the power m n o p q.
Can you you tell me why?  And there is no any way to extract each parameter alone rather than 
Report

07/02/18

Marwan A.

 
Report

07/02/18

Marwan A.

I am really apologise for inconvenient and thank you for your support.
Report

07/02/18

Marwan A.

 
Report

07/03/18

Marwan A.

Dear Paul , do you have any feedback regards my last question.
Report

07/03/18

Marwan A.

 
Report

07/04/18

Paul M.

tutor
The usual way to do curve fitting of this sort is to plug the points into the equation you wish to fit.
That way you wind up with a set of simultaneous equations in the parameters of the equation you wish to fit.
When the parameters are the coefficients, the system you get is linear and soluble, especially since even large systems can be solved by matrix inversion on big computers,
The system you envision will involve he parameters in the exponent, i.e. the system will be non-linear and you cannot generally solve such a system by using only arithmetic operations.
If you had only a single term such as y = axn, you could convert to logarithms to solve it, but with multiple additive terms that won't work.  I am not saying it cannot be done, but I do not know how to do it.
I suggest that you write the system down for yourself & see if you can imagine a way to solve.  Good luck.
Report

07/04/18

Marwan A.

 Thank you very much Paul ,
In fact I asked this question just to make sure that there is no way to solve this type of equation which consist of 5 terms only and i think the solution will be more complecated or impossible if we have more than 5 terms (6,7,8,...).
so that mean we still have problem to solve the non linear equation of multiplt terms even if we know the system equation ( equation formula).
But i do not know how they use the non linear regression solution to fit curve even if they do not know the system equation. Is that true?
 
Report

07/04/18

Marwan A.

Is there any relation between the rational function and the sgmoid function? Or in other word can we convert the rational function to sgmoid function.
Report

07/14/18

Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.
Most questions answered within 4 hours.

OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.