"Scots" and "Scotland" proper would not emerge as unified ideas until centuries later. In fact, the Roman Empire influenced every part of Scotland during the period: by the time of the End of Roman rule in Britain around 410, the various Iron Age tribes native to the area had united as, or fallen under the control of, the Picts, while the southern half of the country was overrun by tribes of Romanized Britons. The Scoti (Gaelic Irish raiders) who would give Scotland its English name, had begun to settle along the west coast. All three groups may have been involved in the Great Conspiracy that overran Roman Britain in 367. The era saw the emergence of the earliest historical accounts of the natives. The most enduring legacies of Rome, however, were Christianity and literacy, both of which arrived indirectly via Irish missionaries.
I would add, rule of law, structure of government, and infrastructure around Italy and Europe.
The Picts were whipped, badly, by Agricola, and by S.Severus. Agricola's campaign in Caledonia was so devastating it permanantly weakened the Picts, and made Scotland possible after the Roman era. IF there had been anything of any value in Scotland, the expense of conquering it might have looked attractive. Instead, the Roman army replaced an earlier barrier with the one seen today.
There's a modern nationalistic and anachronistic need for a resistance myth; in Germany it's the one battle won by Arminius; in Britain it's the mass-murdering Boudicca and her gullible horde, who were annihilated by a legion and a half and some cavalry; in France it's the utter defeat of Vercingetorix at Alesia by Julius Caesar; in Scotland it's, well, the Scots were in Ireland, so usually it's "look at Hadrian's Wall" which mostly follows the line of a natural geographic barrier, and isn't even the longest Roman barrier found in the Empire. Mostly it served as a barrier against infiltration and to control trade. It greatly reduced the garrison needed to rule Britain for over 350 years.
The Angles, Saxons, and Jutes came in a series of waves and overwhelmed the formerly Roman Britain, were (like Scotland and Ireland and the islands) fighting the Scandinivians for centuries after that (btw, thanks Vikings for 35% of my DNA), and eventually one of Alfred the Great's descendants and successors whipped the Scots, Welsh, and the Kdm of Strathclyde (along with Danes and Vikings from Northhumbria and overseas) in a single short series of battles in the first half of the 10th c.
After the Normans (who also had Scandinavian roots) conquered England they got invited over as mercs by one of the Irish kings who needed some extra muscle, and wound up staying in either part or all of Ireland until, well, the present day. Similarly, beginning in the early 12th c, and thanks to the Normans, Scotland was on-and-off under English rule and after the death of Eliz I a descendant of Henry VII was crowned monarch of the United Kingdom. The disastrous "Farty-five", the 1745 rising led by Bonnie Prince Charlie, was the last serious threat, unless one wants to count the attempt at Scottish exit that failed at the ballot box despite considerable support among English voters. :^)