# Plane Fitting a 3D Scatter Plot

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Sarah on 7 Mar 2019
Commented: Star Strider on 1 Dec 2019
I have a 3D scatter plot that I want to have a planar fit. How do you do this?
x = [14.9 1.7 0.0 10.9 0.0];
y = [11.3 9.1 23.7 12.8 2.9];
z = [5.32787E-17 2.93234E-16 2.09997E-16 5.45E-17 4.55E-16];
scatter3(x,y,z) Star Strider on 7 Mar 2019
A simple linear regression is straightforward:
x = [14.9 1.7 0.0 10.9 0.0];
y = [11.3 9.1 23.7 12.8 2.9];
z = [5.32787E-17 2.93234E-16 2.09997E-16 5.45E-17 4.55E-16];
B = [x(:) y(:) ones(size(x(:)))] \ z(:);
xv = linspace(min(x), max(x), 10)';
yv = linspace(min(y), max(y), 10)';
[X,Y] = meshgrid(xv, yv);
Z = reshape([X(:), Y(:), ones(size(X(:)))] * B, numel(xv), []);
scatter3(x,y,z, 'filled')
hold on
mesh(X, Y, Z, 'FaceAlpha', 0.5)
hold off
view(-120, 35)
title(sprintf('Z = %+.3E\\cdotX %+.3E\\cdotY %+.3E', B))
producing: Star Strider on 1 Dec 2019
You should make the vectors the same length!
It is best for you to post this as a new Question, supplying ‘x’, ‘y’, ‘z’ and ‘Ze’.
Your Comment does not relate to the substance of this thread, so I will delete it (and my Comment here) in a few yours.

KSSV on 7 Mar 2019
x = [14.9 1.7 0.0 10.9 0.0];
y = [11.3 9.1 23.7 12.8 2.9];
z = [5.32787E-17 2.93234E-16 2.09997E-16 5.45E-17 4.55E-16];
nx = 10 ; ny = 10 ;
xi = linspace(min(x),max(x),nx) ;
yi = linspace(min(y),max(y),ny) ;
[X,Y] = meshgrid(xi,yi) ;
F = scatteredInterpolant(x',y',z') ;
Z = F(X,Y) ;
scatter3(x,y,z)
hold on
surf(X,Y,Z)