I am writing an essay which briefly discusses linear models as well as models with fixed and random effects. I am googling since ages to find a reference which says who first introduced linear models and especially later mixed effects models. I found on wikipedia that in 1918 Ronald Fisher introduced random effects models to study the correlations of trait values between relatives. Also, as far as I can see Laird, Nan M.; Ware, James H. (1982). "Random-Effects Models for Longitudinal Data". was the first one who applied those models to longitudinal data. My data is also of type longitudinal and I therefore can use that reference later on. However, it would be great to found evidence of who first introduced linear models as wells the fixed effets models.
There is a "Brief History of LMMs" in "Linear mixed Models - A Practical Guide Using Statistical Software" (West, Welch, Galecki).
They say: "First known formulation of a one-way random-effects model" was in 1861 by Airy. Sadly there is no more precise information about the corresponding paper/book/whatever.
According to my understanding: least squares was proposed by Legendre in 1806. The linear model (simple linear regression) was introduced by Galton in 1895. Multiple linear regression was formulated formally by Pearson in 1938.
See 1st and 8th chapters of Stigler (1986) and Stanton (2001) for references. BTW, if you're interested in history of statistics, Stigler is a beautiful book.