I am trying to interpolate data from a data set. each data point depends on two variables. I wish to interpolate data inbetween them but not sure which function to use.

X(variable 1) ranges between 0 to 30.69 and Y (variable 2) has two values 0.06 and 0.015. corrresponding values of the function depdendant on x and y are given in matrix format below. I wish to interpolate points for the X values when the corresponding Y value is 0.03(between 0.06 and 0.015)

 
                 6.00E-02      1.50E-02     
 
  0               0                 0 
 
  1                 19.7627      44.421 
 
  2                 20.4254      46.964 
 
  3                21.0881          49.507 
 
  4                  21.7508           52.05 
 
  5.02656      21.52675         54.66054 
 
  7.495802     23.79959  60.93982 
 
  10.07348      25.82133   67.49487 
 
  12.57828       27.59128  73.86457 
 
  15.08343      29.61274  80.23518 
 
  17.6245      31.38282  86.6971 
 
  20.05641     32.90098  92.88145 
 
  22.77898         34.7975  99.80494 
 
  25.13765      35.81236  105.803 
 
  27.85968         37.3316  112.7252 
 
  30.18262        38.7236  118.6324 
 
  30.69034        38.72549  119.9235 

[KSSV]

You need to explain us data and also don't attach data as image snippet. Attach it as text.

[Tania Hari Madhavi]

Thanks for letting me know. Just corrected it.

[Alex Sha]

Hi, Tania, using the fitting function below for your data:

z = ((1+p1*x+p2*y)/(p3+p4*x+p5*y))*x^p6;

Root of Mean Square Error (RMSE): 0.289317492463695
Sum of Squared Residual: 2.84595678914633
Correlation Coef. (R): 0.999961722670218
R-Square: 0.999923446805589

Parameter	Best Estimate
----------	-------------
p1	0.0789662121293465
p2	22.3733549538477
p3	0.00158106317969181
p4	-2.06920975585446E-6
p5	2.02328157880142
p6	0.00480045399978579

When y=0.03, the corresponded z will be:

0
28.1027419119399
29.4695871486962
30.8027482616138
32.1229094712084
33.4712089275956
36.7002709522503
40.0613990097622
43.3235655146164
46.5845879608778
49.8918606433028
53.0571541956126
56.6012692450567
59.6723118101152
63.2173415594977
66.2434433614816
66.904958155618

Answer 1

[Vinai Datta Thatiparthi]

Hey Tania,

Since you have 2 independent variables, the scenario that you describe seems to be a curve-fitting problem. Based on the knowledge of what 'X' & 'Y' represent, you may have to estimate the relationship between the output data (F(x,y)) and the 2 input independent variables (X & Y). Once you get the relationship, you could then use that to evaluate F(x,0.03). Note that in theory, there could be multiple curves that could pass through the given set of points.

These following links may have the information needed to establish the relationship:

• Example on fitting a non-linear function to given data
• Curve Fitting App to interactively fit data
• System Identification Toolbox

Hope this helps!

[Tania Hari Madhavi]

Thanks ! Thank helps.