22 Florida Agricultural Experiment Stations
(C) is a special case, provides a representation of a quadratic
model which would allow the regression parameters to vary with
price "age." In contrast, it will be noticed that form (C) as-
sumed the regression of quantity on price to be independent of
price "age."
TABLE 4.-TEST OF H : /10 = 0.
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', --...........-- 1 0.510504
Additional reduction due
to fitting X'o .............. 1 0.046823 0.046823 21.778
Remainder (3) ............... 50 0.107511 0.002150
To determine if a distinct regression were associated with
each price "age," the hypothesis
H3 : P = 2 = P3
P4= P5= P6
was tested against
"3 : < ik-i-' P1' P2' P3' P4' P5' 6' P7' PS<8
As with the preceding tests, the procedure involved a statisti-
cal appraisal of the additional reduction in the remainder sum
of squares resulting from the fitting of form (D) rather than
form (C).
The sum of squares for regression (SSR1,2,3,4,5,6,7,8) for form
(D) was obtained by solving the matrix equations 21
[B]' [G] = 1,2,3,4,5,6,7,8
[B]' [. =[G]
[B]' bl . b8]
xl2 ......... IXlX8
A =
Zxlx8 ........ Zx2
[G] '=[yx .. yx8]
"The elements of [A] and [G] were obtained from line E, Table 2,
Appendix III.