multiple linear regression, n-by-n vector of observed responses

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Hi everyone,
I’m new to MATLAB and I need some help.
I have a sample data set containing retunes of companies as well as two predictors variables collected along 5years. Now I need to run a multiple linear regression for the returns of each company. I am using b=regress(Y,X) but it works only with a vector Y (nx1). Having a matrix Y (nxn) (N companies x N time), how can I do it? Do I need a b=regress(Y,X) for every single vector Y or does it exist another way? Thank you very much for your help

Answers (2)

dpb
dpb on 9 Apr 2014
Edited: dpb on 9 Apr 2014
The loop over columns is one way, yes, but you can also do it in "one swell foop" using the "\" backslash operator mldivide for matrix left-divide.
For a set of underdetermined equations, it solves the least squares problem with good internal numerics. Set up your model as in regress excepting write it on an element-by-element basis (meaning use the dot operators) and then write
b=X\Y;
and you'll get a set of coefficients for each column in Y as each column of b.
For example, if your model were just a first order polynomial,
X=[x ones(size(x))];
b=X\Y

Shashank Prasanna
Shashank Prasanna on 9 Apr 2014
Floriano, it appears that you are trying to perform multivariate linear regression. There are several ways to specify this problem. You can use dpb's approach for X\y where X(nxm) y(nxd) for any n,m and d. However if you want full covariance matrix for y (not diagonal) you can use mvregress:
  5 Comments
dpb
dpb on 10 Apr 2014
Presuming, of course, one had the right toolbox at the time...

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