How can I plot the linear variation?

In this attached file, I plot the car price vs mileage and model (year).

in = readtable('FordFocusCMAX.xlsx')
%plot the data as a red asterisks
scatter3(in{:,1}, in{:,2}, in{:,3}, 'o')
xlabel('År');
ylabel('Mil');
zlabel('Pris');

How can I also include the linear variation?

Thanks

[Dyuman Joshi]

I am not sure what you mean/want to do, but try plot3.

Answer 1

[Star Strider]

Calculating the llinear regression was straightforward, however calculating and plotting the regression plane was something of a challenge.

Try this —

in = readtable('FordFocusCMAX.xlsx', 'VariableNamingRule','preserve');

in = rmmissing(in(:,1:3))                                                                   % Remove 'NaN' Values

in = 66x3 table
    Årsm     Mil       Pris   
    ____    _____    _________

     7       3100    1.099e+05
     7       6615    1.059e+05
     6       5600        98500
     8       3300      1.3e+05
     8       3373     1.46e+05
     8       4100    1.399e+05
     3      10145        74500
     4       8500        68900
     7       6885     1.09e+05
     5       6900    1.099e+05
     7       4900    1.299e+05
     7       6770    1.099e+05
     9       1700     1.31e+05
     6      10300        89900
     7       5526     1.07e+05
     7       3552     1.09e+05

B = [in{:,[1 2]} ones(size(in,1),1)] \ in{:,3}                                              % Calculate Linear Regression Parameters

B = 3x1

1.0e+04 * 0.9093 -0.0006 9.0395

[xmin,xmax] = bounds(in{:,[1 2]});
xvc = [xmax; xmin];
[Xx,Xn] = ndgrid(xvc(:,1), xvc(:,2));
Pc = [Xx(:), Xn(:)] * B(1:2) + B(3);
P = reshape(Pc, 2, []);

%plot the data as a red asterisks
figure
scatter3(in{:,1}, in{:,2}, in{:,3}, '*r')                                                   % Plot Data
hold on
surf(Xx, Xn, P, 'FaceColor',[1 1 1]*0.75, 'FaceAlpha',0.75)                                 % Plot Regression Surface
hold off
xlabel('År');
ylabel('Mil');
zlabel('Pris');
% view(-27,30)
axis([xmin(1) xmax(1)  xmin(2) xmax(2)])

EDIT — (29 Feb 2024 at 02:28)

Improved code efficiency.

.

[Sergio]

Thanks @Star Strider, this is quite advanced and very illustrative. The variation must be the distance between each point and the plane. Very nice!

[Star Strider]

As always, my pleasure!

I did not understand how ‘Variation’ was defined. (The formal definition would be ‘Residual’.)

Calcualting the plane values at each ‘Årsm’ and ‘Mil’ data pair is straightforward using the scatteredInterpolant function to create the interpolant, then giving it the appropriate data pairs to calculate the plane value at those points, and then subtracting the ‘Pris’ value from those values to get the desired ‘Variation’ value. (The mean of those values should be 0 within floating-point approximation error, and they should be normally distributed.)

This uses that approach to calculate the ‘Variation’ values, adds them to the existing table, and plots them as green lines from the plane to the ‘Pris’ value —

in = readtable('FordFocusCMAX.xlsx', 'VariableNamingRule','preserve');

in = rmmissing(in(:,1:3))                                                                   % Remove 'NaN' Values

in = 66×3 table
    Årsm     Mil       Pris   
    ____    _____    _________

     7       3100    1.099e+05
     7       6615    1.059e+05
     6       5600        98500
     8       3300      1.3e+05
     8       3373     1.46e+05
     8       4100    1.399e+05
     3      10145        74500
     4       8500        68900
     7       6885     1.09e+05
     5       6900    1.099e+05
     7       4900    1.299e+05
     7       6770    1.099e+05
     9       1700     1.31e+05
     6      10300        89900
     7       5526     1.07e+05
     7       3552     1.09e+05

B = [in{:,[1 2]} ones(size(in,1),1)] \ in{:,3}                                              % Calculate Linear Regression Parameters

B = 3×1

1.0e+04 * 0.9093 -0.0006 9.0395

[xmin,xmax] = bounds(in{:,[1 2]});
xvc = [xmax; xmin];
[Xx,Xn] = ndgrid(xvc(:,1), xvc(:,2));
Pc = [Xx(:), Xn(:)] * B(1:2) + B(3);
P = reshape(Pc, 2, []);

% format longG
% Q = [Xx(:), Xn(:), P(:)]

Fplane = scatteredInterpolant(Xx(:), Xn(:), P(:))                                           % Calculate Interpolant Function For Plane

Fplane = 
  scatteredInterpolant with properties:

                 Points: [4×2 double]
                 Values: [4×1 double]
                 Method: 'linear'
    ExtrapolationMethod: 'linear'

Pv = Fplane(in{:,1}, in{:,2});                                                              % Plane Value At Each Data Pair Coordinate
Variation = in{:,3} - Pv;                                                                   % Calculate 'Variation'

in = addvars(in, Variation)                                                                 % Add 'Variation' To Existing 'in' Table

in = 66×4 table
    Årsm     Mil       Pris       Variation
    ____    _____    _________    _________

     7       3100    1.099e+05      -24583 
     7       6615    1.059e+05     -6405.2 
     6       5600        98500      -11117 
     8       3300      1.3e+05      -12314 
     8       3373     1.46e+05      4146.6 
     8       4100    1.399e+05      2633.7 
     3      10145        74500       20838 
     4       8500        68900     -4233.9 
     7       6885     1.09e+05     -1601.6 
     5       6900    1.099e+05       17578 
     7       4900    1.299e+05      6773.9 
     7       6770    1.099e+05     -1427.2 
     9       1700     1.31e+05      -30502 
     6      10300        89900      9938.2 
     7       5526     1.07e+05      -12176 
     7       3552     1.09e+05      -22631 

%plot the data as a red asterisks
figure
scatter3(in{:,1}, in{:,2}, in{:,3}, '*r')                                                   % Plot Data
hold on
% scatter3(Xx(:), Xn(:), P(:), 200, 'g', 'p', 'filled')
surf(Xx, Xn, P, 'FaceColor',[1 1 1]*0.75, 'FaceAlpha',0.50)                                 % Plot Regression Surface
plot3((in{:,1}*[1 1]).', (in{:,2}*[1 1]).', [Pv in{:,3}].', '-g', 'LineWidth',1)            % Plot 'Variation' At EAch Coordinate Pair
hold off
xlabel('År');
ylabel('Mil');
zlabel('Pris');
title('Data With Regression Plane And ‘Variation’ Distances')
% view(-27,30)
axis([xmin(1) xmax(1)  xmin(2) xmax(2)])

.