How to specify a specific constant for a multiple linear regression?

I would like to know if it is possible to specify a certain constant to a multiple linear regression abd how?

[jean claude]

would you clarify your question with an example that we can help ?

[Khaled Ahmat]

I have a multiple linear regression using three predictor variables, say x1,x2,x3 the resulting equation is y=43-1.4x1+3.8x2-1.1x3 due to some presentation reasons I want to force the constant to be 30 instead of 43; so that the resulting equation becomes y=30-ax1+bx2-cx3;

is this possible in MATLAB?

Answer 1

[Image Analyst]

See John's answer. https://www.mathworks.com/matlabcentral/answers/274980-linear-fit-to-data-with-intercept-at-origin#answer_214651

You can fit y-43 instead of y, then do the fit and add back in the 43 to get yFitted .

[John D'Errico]

Actually, if you want to force the constant term to be 30, then fit the model as

y - 30 = a*x1 + b*x2 + c*x3

Thus estimate a 3 term model with no constant term, but subtract the constant you want in there from y.

I think that is what you meant, but you said to fit it as y-43.

[Image Analyst]

Right (didn't read it carefully enough). Thanks for the correction.

[Jan]

@Khaled Ahmat: Please use flags only to inform editors and admins about contributions, which might conflict with the terms of use e.g. by rudeness. Thanks.

[Khaled Ahmat]

so sorry about this mistake!

Answer 2

[Khaled Ahmat]

Thank you very much for your suggestion; my next question is how to run a Multiple linear regression without a constant in MATLAB? Is it the same function Regress(y,x) or there is another function for regression without a constant? Thank you in advance

[Image Analyst]

I thought a*x1 + b*x2 + c*x3 was a multiple linear regression. What formula are you thinking about?

[Khaled Ahmat]

Yes it is a Multiple linear regression, but my question is how to make it with a zero constant in MATLAB

[Image Analyst]

But we already solved that in the first answer. If you don't know how to do it, then just attach vectors x1, x2, x3, and y in a .mat file.

Answer 3

[Khaled Ahmat]

The m.file along with the data file is attached. Thank you for your effort

[Image Analyst]

Not familiar with regress(). Why didn't you use the method of John D'Errico?

[Khaled Ahmat]

Actually I liked the method he which proposed y-30= ax1+bx2+cx3; and I am sure that there is a function in MATLAB for linear regression without a constant but now I am not able to get the function in MATLAB! This my Challenge now. If Mr John D'Errico can give us a clue about the function or an example it would be great

Answer 4

[Image Analyst]

I'm not sure I've got the columns correct for x1, x2, x3, and y, but this is essentially how you'd do it (again, thanks to John D'Errico):

% Read in data file.
data = importdata('Data_case1.txt')
% Extract columns into separate variables.
% Make sure the column numbers are the correct ones!!!!
x1 = data(:, 1);
x2 = data(:, 2);
x3 = data(:, 3);
y = data(:, 4);

% Construct x matrix
x = [x1, x2, x3];
% Construct y
y = y - 30;

% Get the cofficients:
coefficients = x \ y;   % Estimate Parameter: x*coefficients = y

% Get fitted values for y.  Be sure to add back in the 30 we subtracted!
y_estimated = x*coefficients + 30;

% Print them out
fprintf('  x1        x2        x3        y        y_estimated\n');
for row = 1 : length(x1)
  fprintf('%8.4f, %8.4f, %8.4f, %8.4f, %8.4f\n', ...
    x1(row), x2(row), x3(row), y(row), y_estimated(row));
end

Answer 5

[Khaled Ahmat]

It worked, thank you very much! Really appreciate it.