Linear fit over multiple Rows without using Loops (or polyfit)?

Hello, I have a matrix of data

I=[1.8,3,3.6,4.2,4.7,5.3,5.5;3.3,4.2,4.8,5.3,5.8,6.3,6.6;4.5,5.6,6.3,6.8,7.3,7.9,8.2;6.1,6.9,7.5,8,8.6,9,9.4]

I =

    1.8000    3.0000    3.6000    4.2000    4.7000    5.3000    5.5000
    3.3000    4.2000    4.8000    5.3000    5.8000    6.3000    6.6000
    4.5000    5.6000    6.3000    6.8000    7.3000    7.9000    8.2000
    6.1000    6.9000    7.5000    8.0000    8.6000    9.0000    9.4000
    

I would like to get the gradient of a straight line fit through each row.

i.e. I was just going to loop over all the rows something like this:

    x = 1:7
    
    1     2     3     4     5     6     7
    
    y=I(1,:)
    
    p=polyfit(x,y,1)
    

I then just want to average all those gradients (m's)

I was wondering if there was a better way to do this rather than use polyfit and loops?

Answer 1

[Image Analyst]

No, I don't think so. That way is fine.

I = [1.8,3,3.6,4.2,4.7,5.3,5.5;3.3,4.2,4.8,5.3,5.8,6.3,6.6;4.5,5.6,6.3,6.8,7.3,7.9,8.2;6.1,6.9,7.5,8,8.6,9,9.4]

I = 4×7

1.8000 3.0000 3.6000 4.2000 4.7000 5.3000 5.5000 3.3000 4.2000 4.8000 5.3000 5.8000 6.3000 6.6000 4.5000 5.6000 6.3000 6.8000 7.3000 7.9000 8.2000 6.1000 6.9000 7.5000 8.0000 8.6000 9.0000 9.4000

[rows, columns] = size(I)

rows = 4

columns = 7

x = 1 : columns;
coefficients = zeros(rows, 2);
for row = 1 : rows
    coefficients(row, :) = polyfit(x, I(row, :), 1);
end
coefficients % Let's see them in the command window:

coefficients = 4×2

0.6000 1.6143 0.5393 3.0286 0.5964 4.2714 0.5429 5.7571

% Compute means
meanSlope = mean(coefficients(:, 1))

meanSlope = 0.5696

meanOffset = mean(coefficients(:, 2))

meanOffset = 3.6679

[Jason]

I've been trying to see if Regress will work:

[y, x] = find(I)
B=reshape(I,1,[])
[x,y,B']    %View the matrix "unfolded"
scatter3(x,y,B','filled')

%Taken from the Regress help page
% https://uk.mathworks.com/help/stats/regress.html
X = [ones(size(x1)) x y x.*y]
b = regress(B',X)
x1fit = min(x):10:max(x);
x2fit = min(y):10:max(y);
YFIT = b(1) + b(2)*X1FIT + b(3)*X2FIT + b(4)*X1FIT.*X2FIT
mesh(X1FIT,X2FIT,YFIT)

But this mesh gives me an error:

Error using mesh

Z must be a matrix, not a scalar or vector.

[Image Analyst]

Are you sure you replied to the correct thread?

[Jason]

Yes, sorry, this is also more of a visualisation part.

[Jason]

My mistake was this

x1fit = min(x):10:max(x);

should be this

x1fit = min(x):1:max(x);