Fitting method with multiple response variables (y1, y2, y3).

Assuming I have the following data representing water level trends at different stations in this area:

X = linspace(0, 10, 100)';

Y1 = 2X.^2 - 3X + randn(size(X))*0.5;

Y2 = 2.5X.^2 - 3X + randn(size(X))*0.5;

Y3 = 4.1X.^2 - 3X + randn(size(X))*0.5;

These data are self-generated, and I want to create a fitting line or regression line in Matlab using the fitlm command to represent these three sets of data. Chatgpt has suggested the following code to solve my problem:

Y1 = 2X.^2 - 3X + randn(size(X))*0.5;

Y2 = 2.5X.^2 - 3X + randn(size(X))*0.5;

Y3 = 4.1X.^2 - 3X + randn(size(X))*0.5;

% Create tables of the sea level data for each region

data1 = table(X, Y1, 'VariableNames', {'X', 'Y'});

data2 = table(X, Y2, 'VariableNames', {'X', 'Y'});

data3 = table(X, Y3, 'VariableNames', {'X', 'Y'});

% Merge the data for all regions merged_data = [data1; data2; data3];

% Fit a linear trend to the data model = fitlm(merged_data, 'Y~ X');

% Plot the results plot(model);hold on % plot(X ,mean_Y) legend({'Region 1', 'Region 2', 'Region 3', 'Overall Trend'}, 'Location', 'Northwest');

However, I am not sure about the instruction "merged_data = [data1; data2; data3];" in the code. Can fitlm fit the data in this way?

Also, what does "YX" in "model = fitlm(merged_data, 'Y X');" mean?

[Torsten]

You want to fit 6 parameters (two for each data set) or only 4 (one parameter for each X.^2 (= 3) and the same parameter for the X (= 1)) ?

[peter huang]

I want to fit a fitted line representing these three trends (y1 y2 y3)

Answer 1

[Torsten]

rng("default")
X = linspace(0, 10, 100)';
Y1 = 2*X.^2 - 3*X + randn(size(X))*0.5; 
Y2 = 2.5*X.^2 - 3*X + randn(size(X))*0.5; 
Y3 = 4.1*X.^2 - 3*X + randn(size(X))*0.5;
A = [X.^2 X];
sol1 = A\Y1

sol1 = 2×1

1.9942 -2.9563

sol2 = A\Y2

sol2 = 2×1

2.5075 -3.0601

sol3 = A\Y3

sol3 = 2×1

4.0979 -2.9944

%or
sol = A\[Y1,Y2,Y3]

sol = 2×3

1.9942 2.5075 4.0979 -2.9563 -3.0601 -2.9944

If you really want to fit a linear function to the quadratic data, use

A = [X ones(size(X))];

instead of

A = [X.^2 X];