Weighted linear fit of model to data using multivariate input
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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.