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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

Alex Sha
on 21 Sep 2020

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

Vinai Datta Thatiparthi
on 16 Sep 2020

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!

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