@a_wing , I used this profound visual explanation in part presented by @jules at JMP at the introductory segment of this video on the topic of Least-Square means in a training that I provided cross-divisionally this morning. In effect the Least-Square (LS) Means are the means you would get if you had a balanced design. But principally, they correct for the presence of other factor(s) that have have a significant effect on your response and therefore they really should be considered in any physical situation (and any model built to represent that situation) where we know that more than one factor influences our Y response. In the Diamonds Data.jmp example, Price (Y) depends on both Carat Weight (X1) and Color (X2). So if we consider the Means by Color given the effect of Carat Weight (which is highly significant, then we see that the Least Square Means by Color are considerably different that the Overall Means by Color (J and D).
