determining linear independence among two vectors using least square method

hello! I want to determine the linear independence between two columns of a matrix... using the first column elements to fit second column elements using least squares method and also to calculate the error between second column and the estimated vector.. the columns of the matrix are circularly shifted (shifting by one) elements of the first vector.. Thanks in advance !

Answer 1

[the cyclist]

If your two vectors are v1 and v2, then you could use the corrcoef function to calculate the correlation coefficient and its p-value:

[r p] = corrcoef(v1,v2);

You could choose a value of p (perhaps p < 0.05) to say that the linear correlation between the two vectors is unlikely to be from random sampling.

[neha pal]

thankyou for answering but how will this find the linear independency using the least square fit? i will attach what i exactly want to do..

Answer 2

[the cyclist]

If you have the Statistics and Machine Learning Toolbox, then you can use the fitlm function.

[neha pal]

i used it but i dont understand what to with that model.. because i need to form a vector pool of linearly independent vector.. i have no idea of machine learning.. so i am confused

[the cyclist]

I'm confused, too.

I don't understand the page of text that you pasted, possibly because there is not enough context, and I don't recognize the method.

I'm not confident I can help here, but it's possible.

Can you give a little more context about the method/procedure? Does it have a name?

What is "x" in the above text? It would be helpful to understand both conceptually what it is, and have an example. Can you post something in a MAT file?

Similarly, what is p_ini?

[neha pal]

the method is optimal parameter search criterion... for finding the optimal model order for an auto regression process.. to find the breathing rate of the data samples.. x is the data here.. arranged in a time series vector.. Pini is the initial model order assumed.. i have attached the .mat file which has x as the columns..

here is the link to the paper that i need to follow..

https://biosignal.uconn.edu/wp-content/uploads/sites/2503/2018/09/07_Lee_2010_AnnalsBME.pdf