Improve regression to reduce RMSE

Hi everyone :D

Sorry for another question :(

I'm fitting some 4D data with linear regression, and the ideia is to have something like that: T = D + Ax + By + Cz

At the moment, my RMSE is 15%, but i need to reduce that to 5%, or something like that.

Any ideia how can i do this?

Thanks

Answer 1

[dpb]

Only by improving either one or both of

1. the model (incorporating other terms or the like), or
2. the data itself to be more representative of the chosen model

Have you done the obvious of testing for lack of fit, plotting residuals looking for patterns that don't appear random, etc., etc., etc., ...?

[Luis Meneses]

I'm trying to plot the residuals.

Do you know how to do it?

[dpb]

Depends a little on how you did the fitting -- do you have the Curve Fitting Toolbox and used it or some other method? It has some methods built in the user interface tool and/or can return the residuals as one of optional outputs. If used the backslash operator and a specific model, then you evaluate that model at the inputs.

With the multi-dimensional data you'll have to plot various variables as "one at a time" for fixed values of the others or use 2D/3D plotting for multiple.

Unfortunately, Matlab isn't as strong as it could be in the evaluation end of things; afaik there is no place that does actually give a classic ANOVA table and all in a neat output format. It's a major shortcoming I was expecting that the Curve Fitting Toolbox would have solved but it doesn't seem to address it much at all, unfortunately.

You can get confidence and prediction limits that help but it is disjointed and have to do it separately rather than an integrated output a la SAS, say. (I will admit I've not used the Curve Fitting Toolbox much yet, maybe there are other facilities for output/post processing I'm unaware of, but if so they are pretty well disguised).