Every experienced modeler knows that it is important to differentiate between ordered and unordered variables. If a variable X happens to be coded as 1, 2, or 3 but is unordered, then the three possible values are arbitrary labels not intended to convey any sense of order. In other words, the value of X for a record that records X=1 is not necessarily larger nor smaller than the possible values of 2 or 3; it is simply different.

Therefore, were we to run a regression that treated X as continuous, any slope we discovered would be an illusion. Further, X treated as continuous in a regression would embed the notion that a value of “3” for X is not just larger than the value of “1,” but is specifically three times larger.