Special Teams Percentage vs Special Teams Face-off Percentage

Is there a relationship between PowerPlay face-off percentage and PowerPlay success percentage?

Does the same relationship exist for Penalty Kill?

The following visual shows the relationship between the two for each team, including games thru 1/20/20:

This data was taken directly from the Stats section of NHL.com

What we see from this visual is that for both the PowerPlay and the Penalty Kill there is a small positive relationship between the face-off percentage and the success rate.

For Powerplay:

PP%=0.2975* (PP FOW%) + 3.5886

R^2=0.0720

For Penalty Kill:

PK%=0.1484*(PK FOW%) + 73.2336

R^2=0.0176

For PowerPlay, face-off percentage and success rate have a higher positive correlation than Penalty Kill, albeit a small positive correlation. Winning a face-off on the PowerPlay is better for PowerPlay success than winning a face-off on the Penalty Kill is for Penalty Kill success.