Let Multivariable Regression only fit 1 variable of a "family"

[JrtPec]

I tried something extreme, and the results were too: I generated weather data with solar orientations, tilts, wind directions, ... in total about 1600 variables which resulted in this formula:

Value ~ HDD_13 + GlobalIrradianceO270T90 + HDD_3 + windComponentSquared180 + GlobalIrradianceO265T80 + precipIntensity + windComponent95 + GlobalIrradianceO265T75 + CDD_22 + GlobalIrradianceO275T20 + GlobalIrradianceO260T50 + GlobalIrradianceO40T60 + windComponentCubed145 + GlobalIrradianceO0T0 + GlobalIrradianceO35T90 + GlobalIrradianceO100T55 + GlobalIrradianceO0T85

And got a miraculous RSquared of 1!

I could obviously fix it by reducing the number of variables. But what might also work is this: define certain "families" of variables (for instance, the heating degree days), and make sure the Analysis only uses 1 of them to make its model.
Could just be a list of lists, like

var_structure = [
    [HDD_10, HDD_11, ..., HDD_24],
    [CDD_10, ...],
    [GlobalIrradianceO0T0, GlobalIrradianceO10T10, ...],
    ...
]

@saroele thoughs?

[saroele]

Looks like you had a fun day :-)

This is exactly what @kdebrab mentioned yesterday: with lots of potential dependent variables, you will get a perfect model (R²=1).

Can you post the fit.summary() of the result? I want to have a look at model statistics.

The list-of-list approach to create groups of dependent variables should work, but could again lead to an overfitted model. So preferentially, I'd like to find a way to avoid overfitting in general, without imposing any limits on the combination of variables.