Size requirements for "best" King response at end of level?

[apocalyptech]

I don't suppose anyone knows what the size requirements are to get the "best" response from the King... The one which is worded:

We are moved to tears by the sheer size of this thing. This is so incredible! Happy, happy, so happy. We want to turn it into a star right now!

After finishing the game I've been going through and trying to get that message for each level, but I've gotten stuck on Make A Star 5 for awhile now. The best I've gotten personally is 2.67, which isn't enough to trigger it. I saw a youtube vid which completed Star 5 at 2.9something, and seemed very nearly 100% complete on the level, so I'd assume that would probably do it (though the video stops before getting to the King dialogue), but I'm curious how close I am.

I was thinking originally that maybe it was 2x the goal, but it looks like it's probably less than that (and if it were 2x, then getting that response on Star 5 looks practically impossible, given that video I watched).

[Pesky]

It's difficult to assess them for the 'make a star' levels. At the end of those the star is given a name indicating the size. So you might get one which says "green" "park" "meadow" or "jungle" depending on the size of your Katamari. But I don't know whether there's anything bigger than "jungle".

It's easier for the constellations because at the end of the level it fills in more stars of the constellation. If you go to the constellation display you can see how many stars are filled in for each constellation.