Speculation was a type of educated guess. Speculation was often frowned upon as it could result in incorrect conclusions based on incomplete information and personal biases. To engage in speculation was to speculate.
Starfleet's brig emergency evacuation protocol required convincing the computer's ethical protocols beyond speculation that release would be more likely to ensure a prisoner's survival than keeping the prisoner in captivity. (DIS: "Battle at the Binary Stars")
In 2265, while having a meeting in the briefing room with Lee Kelso, Elizabeth Dehner, and Spock, Captain James T. Kirk explained, "It is my duty, whether pleasant or unpleasant, to listen to the reports, observations, even speculations, on any subject that might affect the safety of this vessel, and it's my science officer's duty to see I'm provided with that." (TOS: "Where No Man Has Gone Before")
In 2267, when Lieutenant Areel Shaw asked Spock not to speculate when he stated that that Captain Kirk could not have possibly done something based on his knowledge of him, Spock replied that Vulcanians did not speculate, that he was in fact basing his conclusion on pure logic. When Shaw questioned this, he elaborated that Humans had certain characteristics, that it was impossible for Kirk to act out of panic or malice, as it was not his nature. (TOS: "Court Martial")
In 2367, Gul Macet argued that Captain Benjamin Maxwell was taking retribution for his losses during the Federation-Cardassian War, with Miles O'Brien countering that this was something that he would never do. Captain Jean-Luc Picard, however, asked that they not indulge in speculation and instead confine their discussion to facts. (TNG: "The Wounded")
In 2372, when Commander Chakotay was captured by a Kazon, the crew of the USS Voyager discovered an ion trail that they believed might be his shuttlecraft, but the warp signature of the radiation was not consistent with that Federation shuttlecraft. Tom Paris questioned if this could mean that someone had blown up Chakotay's shuttle and moved on. Captain Kathryn Janeway described it as speculation, but admitted that it was the only clue that they had to his whereabouts. (VOY: "Initiations")
In 2374, Seven of Nine questioned of Lieutenant commander Tuvok what it meant that Commander Chakotay's face flushed upon seeing Kellin, but he replied that he would rather not engage in speculation, that it was a dangerous pastime. (VOY: "Unforgettable")