～ようだ・みたいだ
Curiosity
When you infer from clues you directly observe, as in "it seems someone came (from the traces)," what does Japanese use? How does it differ from sou da / rashii?
Intuition
you da is the speaker's own inference from clues they grasped directly, grounded in sensory evidence. It also serves as a simile, "as if like" (marude yume no you da). In conversation, mitai da carries the same meaning more casually.
Visualization
furu → furu you da (it seems it will rain). Casual: furu mitai da. With a noun, you da takes no (gakusei no you da ↔ gakusei mitai da).
Essence
Plain form + you da (furu you da). Nouns/na-adjectives take ~no you da / ~na you da; casual mitai da attaches directly to a noun (gakusei mitai da). Use you da when the basis is direct observation; rashii or hearsay sou da when the information was received. It conjugates as you ni (adverb) and you na (adnominal).
Examples
Mini-quiz
Which fits "the lights are off; it seems no one is here (direct observation)"? (inai)