Halliday And Matthiessen (2014: 679):
Projection is thus dispersed across different grammatical environments. But the different manifestations of projection are not, of course, synonymous. The ideational manifestations make explicit the orientation of the assessment: the logical manifestation is explicitly subjective (e.g. I regret) whereas the experiential manifestation is explicitly objective (e.g. it’s regrettable). In contrast, the interpersonal manifestation leaves the orientation implicit:
ideational, logical – nexus: explicit orientation: subjective (I regret)
ideational, exper. – 2 clauses: explicit orientation: objective (it’s regrettable)
interpersonal – 1 clause: implicit orientation (regrettably)
The difference between ‘subjective’ and ‘objective’ orientation in the ideational manifestation follows from the general difference between a projecting ‘mental’ or ‘verbal’ clause with a Senser or Sayer and a ‘relational’ clause without such a ‘projector’. When the assessment is explicitly ‘subjective’, the Senser or Sayer has to be the speaker I if the clause is ‘declarative’ or the addressee you if it is ‘interrogative’ (as in Do you regret that it’s taken so long for you and your dad to get to work together?). If it is a person other than the speaker or addressee, the clause will still be a projecting one; but it will not be agnate with an interpersonal assessment.