How to develop equation from the database ?

Excuse me every one. I have the scattering data (case selection data) as show in the figure below. I want to develop the equation to predict 'y' value by input the 'x' and 'TH'. The equation shows the typical form like: y = f(x,TH). How to do it ? Thank you very much.

Answer 1

[Saurabh Chaudhary]

You can fit a curve using curve fitting toolbox (enter "cftool" in command window to open it) and obtain the equations and write a small script to select the equation accoding to TH value.

[Lyhour Chhay]

thank you very much sir. I understand your approache. However, my objective is want to generate the exact equation for manual calculation. Is there any alternative approach ?

[Alex Sha]

If possible, upload your data file please.

[Lyhour Chhay]

Dea sir, Alex Sha,

I have upload the database in the excel file. Thank you very much

[Saurabh Chaudhary]

From data you can not get the exact equation. The equation you find from the curve fitting or machine learning it have some error.

[Lyhour Chhay]

Dear Sir, Saurabh Chaudhary,

Thank you very much for your discussion. Therefore, is there any algorithm or approch that I can get it ? How about I create two equation?

[Saurabh Chaudhary]

One is the curve fitting tool and another you can use least square algorithm or machine learning toolbox also can be used.

[Alex Sha]

Refer to the fitting function and result below:

Sum Squared Error (SSE): 0.000562300835691918
Root of Mean Square Error (RMSE): 0.00395214722120885
Correlation Coef. (R): 0.999856659423475
R-Square: 0.99971333939347

Parameter	Best Estimate      
---------	-------------      
p1       	1.60459267721019   
p2       	-0.207764681801805 
p3       	-0.0792360032379987
p4       	5.07935211534004E-5
p5       	9.77939357085156E-5
p6       	-0.101574648932732 
p7       	9.84064177094815 

[Lyhour Chhay]

Dear Sir, Alex Sha,

I really appreciate your kindess. it is really amazing of your equation. Thank you very much.

it would be better if you could tell me how you create this equation. Did you create randomly ? or any suggesting tool ? could you tell me your algorithm to create the equation ?

Best Regards,

CHHAY LYHOUR

[Alex Sha]

Hi, there are some other softwares which can search functions with the better fitting to the data provided, automatically.

You can also use Neural Network to fit your data, the function is much long, but with more better result:

where x1=TH, x2=x;

Sum Squared Error (SSE): 6.15367933063669E-6
Root of Mean Square Error (RMSE): 0.000413443511210577
Correlation Coef. (R): 0.999998431427883
R-Square: 0.999996862858226

Parameter	Best Estimate       
---------	-------------       
p1       	-0.0184998266667526 
p2       	-0.00170324878988054
p3       	0.00105902753507986 
p4       	-8.63188539136108E-5
p5       	13.3141311137491    
p6       	-0.010077245280387  
p7       	-769.681178210069   
p8       	113.441478800875    
p9       	-41.899708039828    
p10      	-46.1202975365195   
p11      	325.53145620631     
p12      	1467.54651172898    
p13      	-22.9188474020333   
p14      	0.975904984363179   
p15      	-4.72158876536306   
p16      	-660.31030174081    
p17      	-6.67856367002313   
p18      	51.8661729374925    
p19      	44.4703308742898    
p20      	22.8349571901207