24 Florida Agricultural Experiment Stations
against
"4 = -- < p 81, ai' k-j-' Aij, Pq i . 8 <"
Individual tests of hypotheses H4 through H7 were performed
by fitting a quadratic regression model of form (C), from which
was omitted, in turn, the set of class constants relevant to the
hypothesis being tested. Then the remainder sum of squares
in each case was compared with the remainder sum of squares
from fitting the original model of form (C), i.e., the model which
included all sets of specified class constants.
A brief explanation of steps involved in testing the signifi-
cance of store constants (H4 : 6, = ) is used to demonstrate the
general procedure. To obtain the remainder sum of squares for
model (C) with the 6; omitted, the zy2 [remainder (1) +
stores]23 was adjusted for the regression of Yik-j- on xw9k-- "ad XlOk-j-.
This required sum of squares of regression was supplied through
the solution of the matrix equations
S7,8,9,10 = [bi7 b8 b9 bl] [ y Tlyx. yx9 Lyxi0 ]
Ex72 1XXg 1KyX tx
7X7 X9 rxgx, rx9 Zx9x10
The solution gave
b, = 2.065742
b, = 2.304440
bs = -4.413188
blo = 1.662648
ASSR7,s,9,1o = 5.992420
Subtraction of ASSR7,8,9,10 from the 2y2, denoted by [Remain-
der (1) + Stores], gave the desired remainder sum of squares
[Remainder (5)] for the special form of model (C), from which
the store constants were omitted. If the remainder sum of
squares from fitting the original model of form (C) were identi-
fied as Remainder (3), obviously, the additional reduction in
sum of squares due to fitting store constants would be the
Line J of Table 2, Appendix III contains the sums of squares and cross
products for all the variables of the model "adjusted" for class variables
other than the 1 "s.