linear_regression: add fit_intercept argument

[mathause]

This PR adds fit_intercept to mesmer.core.linear_regression.

train_gt_ic_OLSVOLC uses fit_intercept=False therefore this needs to be added to _fit_linear_regression_xr before we can refactor this code path.

mesmer/mesmer/calibrate_mesmer/train_gt.py

Line 264 in f63fbeb

linreg_gv_volc = LinearRegression(fit_intercept=False).fit(

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Open question - how should intercept be saved when fit_intercept=False?

1. Omit intercept from the result
2. As scalar (this is what sklearn does)
3. The same shape as the predictors (this is the current solution)

See details for an example.

(1) would look like this:

<xarray.Dataset>
Dimensions:        (cell: 3)
Data variables:
    tas            (cell) int64 0 1 2
    fit_intercept  bool False

(2) would look like this:

<xarray.Dataset>
Dimensions:        (cell: 3)
Data variables:
    intercept      int64 0
    tas            (cell) int64 0 1 2
    fit_intercept  bool False

(3) would look like this:

<xarray.Dataset>
Dimensions:        (cell: 3)
Data variables:
    intercept      int64 0 0 0
    tas            (cell) int64 0 1 2
    fit_intercept  bool False

I went for 3 because it's easiest. I would probably go for (2) if it did not involve changing a ton of tests.

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Remark: I use LinearRegression().fit(..., fit_intercept=False) while sklearn uses LinearRegression(fit_intercept=False).fit(...). I think this makes more sense (here) because I want to be able to do res = LinearRegression(), res.params = params (i.e., assign the params).

cc @znicholls

[codecov-commenter]

Codecov Report

Merging #144 (cd5d69f) into master (cc766d4) will increase coverage by 0.05%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #144      +/-   ##
==========================================
+ Coverage   79.19%   79.25%   +0.05%     
==========================================
  Files          30       30              
  Lines        1389     1393       +4     
==========================================
+ Hits         1100     1104       +4     
  Misses        289      289              

Flag	Coverage Δ
unittests	79.25% <100.00%> (+0.05%)	⬆️

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Impacted Files	Coverage Δ
mesmer/core/linear_regression.py	90.78% <100.00%> (+0.51%)	⬆️

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[znicholls]

I went for 3 because it's easiest

+1 for me, also because then you have the same shape array as when fit_intercept is True which just makes things simpler downstream.

I think this makes more sense (here) because I want to be able to do res = LinearRegression(), res.params = params (i.e., assign the params).

Agree

[znicholls]

Very nice (not sure if more to come but I took a quick look)