Linear models

TABLE 4.3. YIELDS OF 6 PLANTS Treatment Variety 1 2 y111, y112 9121 WN - #211 V/221 represents the yield of the kth plant of variety i that received treatment j. We will now write these out, using 5 dummy (0, 1) variables and 5 regression coefficients corresponding to the 3 varieties and the 2 treatments. The re- gression coefficients for the 3 varieties will be denoted by 1, @, and a, and those for the treatments will be , and By. Furthermore, the intercept term in the regression, previously denoted by bo, will now be written as u. Thus the vector of parameters b' will be b' = [M 21 82 23 P1 B2]. [This notation clearly distinguishes between regression coefficients for varieties (@'s) and those for treatments (S's) and, in contrast to using b's as elements of b, avoids double subscripting which could then provide that clarity.] With this notation the regression equation for yik is where the x's and x*'s are dummy (0, 1) variables. Thus for the observation on variety 1 and treatment 2, 121,1 = 1, 121.2 = 0 and 2121,3 = 0; and 21 = 0 with 2* = 1. In this way the regression equations for the yields in Table 4.3 are ym = / + (1) + x2(0) + x,(0) + B,(1) + Pz(0) + em yna = / + , (1) + x2(0) +