Is it possible to use 20 variables in a multi regression on MATLAB?

Is it possible to use 20 variables in a multi regression on MATLAB?

[dpb]

Yes.

[Walter Roberson]

In which routine, exactly?

Answer 1

[Sean de Wolski]

doc fitlm

[Kris Janssen]

Not really a constructive answer, or an answer to the question at all. If you feel the urge to contribute something such as this, use the comment function. Better yet, try to provide some real feedback such as some of the others have done, even if you perhaps think the question is not the best one.

[dpb]

I'd disagree with that assessment...it's about all the answer there is to be given, given the question...

[Sean de Wolski]

Kris, the whole point of fitlm is to do multilinear regression in MATLAB. If you run the command (or search "fitlm" in your favorite search engine), this should be clear. I would thus argue that this is more constructive than "Yes" because while still saying "Yes", it tells you how to get started.

If you want more detailed answers, ask more detailed questions!

[dpb]

..."this is more constructive than "Yes"

As my followup indicates, in general I agree. My comment was purposefully what is was, however, to illustrate clearly to the OP "you get only as good as what you ask".

And, of course, since OP didn't say, while it's likely a good starting point, in the event OP doesn't have a linear model in mind that a linear routine won't help at all...simply not enough known about the problem space.

Answer 2

[John D'Errico]

Of course it is possible. In fact, 20 can be a rather small number in some cases, OR wildly too many.

It does depend on how much data you have.

It also depends on whether your data is sufficient to estimate 20 parameters.

[Alexandra Brian]

What would be an approximation of wildly too many?

[Walter Roberson]

If your regression comes down to coefficients of a polynomial, then using order 20 would be far too much in most cases, as that would almost certainly lead to terrible numeric roundoff problems.

[dpb]

As noted, I didn't say anything about "good idea", only the direct answer to the question asked... :)

W/o any other info it's impossible to say much of anything at all useful other than as Walter points out, a 20-order polynomial in x is highly likely to be problematical at best.

One way to get an idea at least is to compute condition number of the X'X design matrix...if it's off the charts, "Houston, we have a problem!" right off the bat that will need some reconsideration...

[John D'Errico]

Wildly too many depends on your problem. If your data supports 10000 unknowns, then it is trivial to solve (in fact, I have code that does this all of the time, with many thousands of unknowns. It is used happily by too many users to count.)

At the other end of the spectrum, if you have what are essentially two data points, then any more than two unknowns becomes wildly too many.

There is no magic number of unknowns, no line in the sand that tells you to go no further, no sign that tells you beyond this point, there be dragons.

There are measures you can use. For example, the condition number of the system can help you to understand when you are getting into dangerous waters. But even there, you need to understand how the extent of ill-conditioning in your matrix will amplify noise in your problem, to the point where any signal in the predicted coefficients is lost.

Essentially, learn what cond tells you. Get used to using it. Even better, learn what svd tells you about the problem, but cond will tell you a lot from just one number.