20 Florida Agricultural Experiment Stations
from which
b7 = 1.984317
bs = 2.042658
The additional reduction in sum of squares due to adjusted re-
gression on X7 and Xs was given by
ASSR8 = [b7 68] [Eyx7 Eyx8]
ASSR7,8 = 3.650251 .
Sum of squares for regression (SSR7ys), when X7, Xs and X'9
were used as regression variates, was obtained by solving the
following matrix equations: 20
E x7 1 x7x8 Zx7x
1X7X9 1X X8X9
[''7 ^s ^l ^a7x 82 8 9 1 yx7 yx8 ryx9
I x7x lx8x9 TEx
ASSR7,8,9 b7 b8 bs ] [yx7 Lyx8 Eyx9 ]
The solution gave
b7 = 2.071092
bs = 2.305635
bg = -0.823312
ASSR7,8,9 = 4.160755
Table 3 illustrates the significant reduction in error sum of
squares associated with the regression of adjusted quantity on
adjusted price. That is to say, after adjustment for the vari-
ation associated with the categorical variables, there existed a
significant regression of quantity on price.
TABLE 3.-TEST OF REDUCTION IN ERROR SUM OF SQUARES DUE TO LINEAR
REGRESSION OF ADJUSTED LOGARITHM OF QUANTITY ON ADJUSTED LOGA-
RITHM OF PRICE.
Source D.F. SS MS F
Remainder (1) ............... 54 4.315089
Reduction due to
fitting X, and Xs ..... 2 3.650251
Additional reduction due
to fitting X'9 ............... 1 0.510504 0.510504 168.71
Remainder (2) .............. 51 0.154334 0.003026
" Sums of squares and sums of cross products were taken from the
remainder line of Table 2, Appendix III.