PIE base ‘to move in a straight line’, with derivatives meaning ‘to direct in a straight line, lead, rule’.
Other derivatives include right, realm, anorexia, regimen, rich, rule, royal, direct, correct, rectify, interrogate, adroit, reckon, reckless, and arrogant.
[Pokorny *reĝ-1 ‘to regulate, make just/right; king, reign’, pp. 854–857.]