18 Florida Agricultural Experiment Stations
straightforward. It may be recalled that these categorical vari-
ables consisted of stores, weeks (within age) and the interaction
of stores and age. Price was considered as a continuous co-
variable, i.e., a logarithmic function containing both linear and
quadratic components was intended to summarize the relationship
between price and quantity.
ALTERNATIVE FORMS OF THE GENERAL MODEL
The general model purposely was constructed broad enough
to accommodate several visualized sets of possible demand cir-
cumstances. Below are some of the adaptations that might ap-
propriately describe the demand relationship in question and, at
the same time, include the parameters and variables required to
estimate the missing observations. For instance, if
P1 = P2 P3 and P4 = P5 = 6 ='
the model would reduce to
Y'k-i- = ik-j-+ P7X7k-- + PXBk-- + 9X9ik-- + 'k-j- (A)
where Pp PI = 2 =
In the event that P 2 0 P3 but 4 = 5 = P6 = 0, it would become
Yki- = Ik-j- lik-j-+ P2X k-- + Pa k-j- (B)
+ P$X7k-i-+ PB ik-i- + 'Ik-i-
Should p1 = P2 = P3 and 4 = P5 = 6. the model could be written
Y;k-j- = Ak-j- + 7X71k-i- + BX8k-i-
(C)
+ PX91ik-j- + P1B lk-i- + e;k-j-
where P9= P1= 02= P3 and Pl0 = P4 = 5 = P6
Or if P0 / 22, P3 and If P4 P5 / P6, the model would revert to the original general
form,
Ylk-- = Ak-- + PIXlk-j- + P2X'2k-j-+ P3X3k-j- + 4X4k-- (D)
+ PB5Xilk-j- + P6XAik-- + P7X71k-j- + P8X81k-- + 'k-ij-
It should be noted that in all of the model forms,
"Ak-i- = PO + ai + 6 + k + A;l. Furthermore, it should be apparent
that these expressions are all particular forms of the general
model. Other forms of the model could be written by systemati-
cally omitting in turn each of the categorical variables.