Weighted linear fit of model to data using multivariate input

What is the best matlab functionality to use that allows weighted linear fit of data y using multiple predictors x, where each predictor is likely to have a different predictive power in the model, hence requiring weights, and there is a large amount of noisy data with weak correlation?

For example, for y with size 100,000 x 1 and x of size 100,000 x 3 it is possible to do this:

[b,int,r,rint,stats] = regress(y,x);

predicted = x * b;

However, this does not account for the fact that the the columns in x may require different weighting to produce optimal outcomes, eg does not produce weightings for b.

What is the best matlab function / approach for finding a weighted linear model, with the weights being for the columns (coefficients), not the datapoints?

If there is a nice tool that allows different types of low-dimensional models (eg non-linear but with only a few coefficients) to be compared as well, great!

The goal is to produce a model that makes predictions of future data with minimum least-squared error (on a validation data test set) after fitting the model on a sub-sample training set pulled from the data.

Answer 1

[Benjamin Thompson]

Look at the features in the System Identification Toolbox.

[CdC]

Thanks very much for your suggestion.

I have spent some time with the System Identification Toolbox, which looks like it has some fantastic functionality.

However, unfortunately, I have not yet been able to figure out how to use it to make actual future predictions for a timeseries, which is my requirement per the question above. I created a new question on this topic. I thought you might know the answer, and that this follow-on question might also be useful for others who come to this question in the future, so I'm linking it here:

https://www.mathworks.com/matlabcentral/answers/1642755-how-to-predict-a-future-time-point-in-a-time-series-using-a-predictive-model-created-with-the-syste?s_tid=srchtitle

[Benjamin Thompson]

If you have a model of past system behavior you can use that to extrapolate into the future as well.