[ENH] Scatter Plot: Add ellipse/s

[VesnaT]

Issue

Implements #6734

Description of changes

Add ellipse (similar to regression line).

Includes

• Code changes
• Tests
• Documentation

[codecov]

Codecov Report

Merging #6752 (cef04c9) into master (ba951fa) will increase coverage by 0.05%.
Report is 56 commits behind head on master.
The diff coverage is 100.00%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #6752      +/-   ##
==========================================
+ Coverage   88.13%   88.18%   +0.05%     
==========================================
  Files         322      326       +4     
  Lines       70589    70994     +405     
==========================================
+ Hits        62216    62609     +393     
- Misses       8373     8385      +12     

[VesnaT]

Screen.Recording.2024-03-25.at.13.22.56.mov

[thocevar]

vals, vects = np.linalg.eig(cov)
...
cx = np.cos(m) * np.sqrt(vals[0] * f)
cy = np.sin(m) * np.sqrt(vals[1] * f)

Previously, the stretch of the ellipse was cov[0, 0] which is the variance along each coordinate axis while the stretch should reflect the variance in the direction of the computed eigenvectors. This results in more appropriate shapes. However, the regression line will not be completely in line with the ellipse, because it's minimizing vertical errors and not perpendicular projections.

[janezd]

Lines can also minimize perpendicular distance if you set the plot to treat variables as independent.

[thocevar]

By using the option "treat variables as independent" the regression line actually lines up with the ellipse. Do we want to prioritize this?

[janezd]

By making it a default? Probably not because users expect a regression line. Yet, scatter plot shows relation between two variables, so perpendicular projection should be the default. We never found a good solution to make users aware that there are two possibilities and that they must decide what they want.

[lanzagar]

After the fix everything looks ok.
As discussed we should maybe move this to the base class.

[lanzagar]

Maybe replace with the following reference for HotellingEllipse, from where we took the equation to scale for 95%
https://github.com/ChristianGoueguel/HotellingEllipse/blob/master/R/ellipseCoord.R

[lanzagar]

Use @thocevar 's fix.