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I have 3 variables speed, dp,eff and I used the following code to 3d scatter plot the data. The scatter plot is attached. My question is how to find the best fit line for the scatter data on scatter plot. I tried curve fitting tool box but not working great. Help me find out the solution. i.e to find out the best fit line( eqn) and draw that line of scatter plot.

Thank you

load TEAVG_0Dafterconversion.mat

scatter3(speed,dp,eff)

xlabel('Speed')

ylabel('Dp')

zlabel('Eff')

Alex Sha
on 17 Sep 2020

Hi, Chetan, if you don't mind the length of the fitting equation, refer to follow:

x1=Speed, x2=Dp, y=Eff

y = b0+b1*x1+b2*x1^2+b3*x2+b4*x2^2+b5*(exp(-sqr(x1/100)))+b6*(exp(-sqr(x1/100)))^2+b7*(exp(-sqr(x2/1.4)))+b8*(exp(-sqr(x2/1.4)))^2+b9*x1*x2*(exp(-sqr(x1/100)))+b10*x1*x2*(exp(-sqr(x2/1.4)))^2+b11*x1*x2^2*(exp(-sqr(x2/1.4)))+b12*x1*(exp(-sqr(x1/100)))*(exp(-sqr(x2/1.4)))^2+b13*x1^2*x2*(exp(-sqr(x1/100)))+b14*x1^2*x2*(exp(-sqr(x2/1.4)))^2+b15*x1^2*x2^2*(exp(-sqr(x2/1.4)))+b16*x1^2*(exp(-sqr(x1/100)))*(exp(-sqr(x2/1.4)))^2+b17*x2*(exp(-sqr(x1/100)))*(exp(-sqr(x2/1.4)))+b18*x2*(exp(-sqr(x1/100)))^2*(exp(-sqr(x2/1.4)))^2+b19*x2^2*(exp(-sqr(x1/100)))^2*(exp(-sqr(x2/1.4)))+b20*x1*x2*(exp(-sqr(x1/100)))*(exp(-sqr(x2/1.4)))^2+b21*x1*x2^2*(exp(-sqr(x1/100)))*(exp(-sqr(x2/1.4)))+b22*x1*x2^2*(exp(-sqr(x1/100)))^2*(exp(-sqr(x2/1.4)))^2+b23*x1^2*x2*(exp(-sqr(x1/100)))^2*(exp(-sqr(x2/1.4)))+b24*x1^2*x2^2*(exp(-sqr(x1/100)))*(exp(-sqr(x2/1.4)))^2

Sum of Squared Residual: 0.0118621810316654

Correlation Coef. (R): 0.962793830997943

R-Square: 0.926971961007696

Parameter Best Estimate

---------- -------------

b0 15.310755982188

b1 -0.132958264716742

b2 -0.00156128206992743

b3 10.4211565559291

b4 4.65796095967851

b5 -48.3481150500531

b6 -22.8688433790466

b7 36.3660070659581

b8 19.7901689881374

b9 0.059559167138516

b10 0.387826626201331

b11 -0.0133030524719128

b12 0.107006174136916

b13 -0.00233928422236141

b14 -0.00258023255196725

b15 0.000880324623195984

b16 -0.00696504324693559

b17 -19.2013564945072

b18 8.53997897435642

b19 34.4260175482625

b20 -0.410840827168776

b21 -0.0126076476622779

b22 0.0759466046214045

b23 0.00332686217055514

b24 -0.000562931147662027

Alex Sha
on 17 Sep 2020

Hi, the fitting function is in the form of y = f(x1,x2)

where x1=Speed, x2=Dp, y=Eff

It is same as you wanted: Eff = f(Speed, Dp)

Of course, the function is very long, although the r-square reach 0.926971961007696

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