How are least square means calculated for different groups in the context of regression models?

Question

In essence, what are least square means? I understand the overall concept of least squares for regression, but not least square means.

Answer 1

Let ei = m - xi
ei^2 = (m - xi)^2
∑ei^2 = ∑(m - xi)^2
∑ei^2 = ∑(m^2 - 2mxi + xi^2)
∑ei^2 = nm^2 - 2m∑xi + ∑xi^2
∂(∑ei^2)/∂m = 2nm - 2∑xi = 0 for min ei^2
nm = ∑xi
mx = (1/n)∑xi
my = (1/n)∑yi
so least square means appear to be simply the means of the data.

Answer 2

Well it's least mean squares (lms) for short. I used have this crap all down when I did control systems. For an explanation go to this site. It says more than I would ever want to read again!

http://en.wikipedia.org/wiki/Least_mean_squares