How do I replicate curve fit figure with an equation?

I would like to replicate the following plane, which was plotted with the curve fitting toolbox.

The toolbox gave me this information for the plane:

%     Linear model Poly22:
%      ans(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2
%        where x is normalized by mean 14.91 and std 0.5073
%        and where y is normalized by mean -7.804 and std 23.72
%      Coefficients (with 95% confidence bounds):
%        p00 =      -3.562  (-3.609, -3.516)
%        p10 =     -0.0439  (-0.1117, 0.02388)
%        p01 =       22.79  (22.72, 22.85)
%        p20 =     0.04982  (-0.08557, 0.1852)
%        p11 =     0.06292  (-0.1923, 0.3182)
%        p02 =       1.543  (1.41, 1.675)

But when I plot it with the code

p00 = -3.562 ; p10 = -0.0439 ; p01 = 22.79 ;
p20 = 0.04982 ; p11 = 0.06292 ; p02 = 1.543 ;
syms x y
z = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2;
fsurf(z, [13.5 16], 'edgecolor', 'none');
xlabel('x'); ylabel('y'); zlabel('z');

I do not get the proper coordinates and end up with this and I'm not sure how to fix it:

I think it has to do with the 'normalized by mean xx and std yy ' but I don't know how it works

Answer 1

[KSSV]

You can use plot to plot the plane you want.

Refer here: https://in.mathworks.com/help/curvefit/fit.html

[MJ]

Sorry the link doesn't have what I'm looking for, this is not what I asked.

[KSSV]

load franke
sf = fit([x, y],z,'poly23') ;
plot(sf)

[MJ]

p00 = -3.562 ; p10 = -0.0439 ; p01 = 22.79 ;
p20 = 0.04982 ; p11 = 0.06292 ; p02 = 1.543 ;
syms x y
z = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2;
fsurf(z, [13.5 16], 'edgecolor', 'none');
xlabel('x'); ylabel('y'); zlabel('z');

This is the code I used, but it is not giving me the same y and z coordinates as the figure that the curve fitting toolbox gave me. I have updated my question.

I think it has to do with the 'normalized by mean xx and std yy ' but I don't know how it works

[KSSV]

How do you got p00, p10... show us the whole code.

[MJ]

It's from the Curve Fitting toolbox that I used with my data. It output this figure (left) and this information with the figure (bottom). I don't know how to implement "normalized by mean xx and std yy" which I think is the issue.

The figure I am getting is on the right, which is clearly different from the figure on the left

[KSSV]

You are messing up with limits of x and y. Check the below example to see how to plot the surface.

load franke
sf = fit([x, y],z,'poly23') ;
sf

     Linear model Poly23:
     sf(x,y) = p00 + p10*x + p01*y + p20*x^2 + p11*x*y + p02*y^2 + p21*x^2*y 
                    + p12*x*y^2 + p03*y^3
     Coefficients (with 95% confidence bounds):
       p00 =       1.118  (0.9149, 1.321)
       p10 =  -0.0002941  (-0.000502, -8.623e-05)
       p01 =       1.533  (0.7032, 2.364)
       p20 =  -1.966e-08  (-7.084e-08, 3.152e-08)
       p11 =   0.0003427  (-0.0001009, 0.0007863)
       p02 =      -6.951  (-8.421, -5.481)
       p21 =   9.563e-08  (6.276e-09, 1.85e-07)
       p12 =  -0.0004401  (-0.0007082, -0.0001721)
       p03 =       4.999  (4.082, 5.917)

% Inbuilt function plot
figure(1)
plot(sf) ;
title('using inbuilt function')
xlabel('x') ; ylabel('y') ; zlabel('z') ;

% My plot
p00 =       1.118 ;
p10 =  -0.0002941 ;
p01 =       1.533 ;
p20 =  -1.966e-08 ;
p11 =   0.0003427 ;
p02 =      -6.951 ;
p21 =   9.563e-08 ;
p12 =  -0.0004401 ;
p03 =       4.999 ;

x = linspace(min(x),max(x)) ;
y = linspace(min(y),max(y)) ;

[x,y] = meshgrid(x,y) ; 

my_sf =  p00 + p10*x + p01*y + p20*x.^2 + p11*x.*y + p02*y.^2 + p21*x.^2.*y.....
    + p12*x.*y.^2 + p03*y.^3 ;

figure(2)
surf(x,y,my_sf) 
title('using surf')
xlabel('x') ; ylabel('y') ; zlabel('z') ;

[MJ]

Thank you for your solution but it still does not output correctly. Your example does not have normalization. How would I implement normalization into the graph?

My curve fit included this information

where x is normalized by mean 14.91 and std 0.5073

and where y is normalized by mean -7.804 and std 23.72

[KSSV]

You can normalize by using:

x = (x - mean_val) /std_val;

[MJ]

I'm still not getting a solution. This is my code and output:

p00 = -3.562 ; p10 = -0.0439 ; p01 = 22.79 ;
p20 = 0.04982 ; p11 = 0.06292 ; p02 = 1.543 ;

xp = (x - 14.91) /0.5073;
yp = (y + 7.804) /23.72;
xp = linspace(min(xp),max(xp)) ;
yp = linspace(min(yp),max(yp)) ;
 
[xp,yp] = meshgrid(xp,yp) ; 
my_sf =  p00 + p10.*xp + p01.*yp + p20.*xp.^2 + p11.*xp.*yp + p02.*yp.^2;
figure(2)
surf(xp,yp,my_sf) 
title('using surf')
xlabel('x') ; ylabel('y') ; zlabel('z') ;

This is the graph I want: