fit line to 3D scatterplot

I'm trying to add a linear fit to my 3d scatterplot, is there an easy function that let's me do this? Thanks!

Here's my code:

sessions = [12
            12
            12
            12
            12
            12
            12
            12
            21
            21
            21
            21
            12
            12
            12
            12];

VASdelta = [50.5
            50.5
            50.5
            50.5
            9
            9
            9
            9
            50
            50
            50
            50
            40
            40
            40
            40];

relPower = [NaN
            13.39162848
            -5.151906173
            22.74039589
            -6.608297044
            -11.53044932
            -8.162916339
            -9.332208193
            9.440958586
            44.6072671
            NaN
            NaN
            -2.527864912
            9.2589486
            -11.9690337
            -27.36570581];

personC = [[0.9 0.1 0];
           [0.9 0.1 0];
           [0.9 0.1 0];
           [0.9 0.1 0];
           [0 0.5 0];
           [0 0.5 0];
           [0 0.5 0];
           [0 0.5 0];
           [0 0 1];
           [0 0 1];
           [0 0 1];
           [0 0 1];
           [0 0 0];
           [0 0 0];
           [0 0 0];
           [0 0 0];       
           ];

scatter3(VASdelta,relPower,sessions, 50, personC, 'filled');
xlabel("Change in VAS scores")
ylabel("Change in relative delta band power (%)")
zlabel("Number of sessions")

scatter(VASdelta,relPower,(sessions/21)*50, personC, 'filled');
xlabel("Change in VAS scores")
ylabel("Change in relative delta band power (%)")

Answer 1

[Askic V]

I'm not really sure what you want to achieve here, but if you have X and Y data and want to do a linear fit, then you can construct a line, but if you have a 3D data, then you can construct a plane to be a linear fit in case

Z = function (X,Y).

This is a small example how to construct plane as a result of linear square fit method:

clear; clc; close all
% Input random data
X = randi(10,1,10); % Replace x1, x2, ..., x10 with the actual x values
Y = randi(10,1,10); % Replace y1, y2, ..., y10 with the actual y values
Z = randi(5,1,10); % Replace z1, z2, ..., z10 with the actual z values

% Perform least squares fit
A = [X(:), Y(:), ones(10, 1)];
coefficients = lsqlin([X(:), Y(:), ones(10, 1)],Z(:))

coefficients = 3×1

0.0351 0.2803 0.6492

% Extract the calculated parameters

a = coefficients(1); b = coefficients(2); c = coefficients(3);
% Generate points as a mesh grid
x_data = linspace(min(X), max(X), 100);
y_data = linspace(min(Y), max(Y), 100);
[X_data, Y_data] = meshgrid(x_data, y_data);
Z_line = a*X_data + b*Y_data + c;

% Plot the data points and the line
scatter3(X, Y, Z, 50, 'filled', 'MarkerFaceColor', 'b');
hold on;
mesh(X_data, Y_data, Z_line, 'EdgeColor', 'r');
xlabel('X'); ylabel('Y'); zlabel('Z'); zlim([0 10]);
title('3D Linear Fit');
grid on;
hold off;