Experimental Pricing As an Approach to Demand Analysis 19
EXAMINATION OF HYPOTHESES FOR SELECTION OF
SPECIFIC MODEL
As previously implied, the choice of a specific model to sum-
marize the experimental demand relationships for orange con-
centrate was to be decided by the application of formal statistical
tests to certain adaptations of the general model. It will develop
that, from these tests, conclusions could be drawn respecting the
particular form, i.e., degree of the logarithmic function relating
quantity and price. Moreover, reasonably justifiable decisions
could be made concerning the retention or omission of certain
class constants. Procedural stages leading to the development
of the final model are dealt with subsequently.
Linear Component.-Attention initially was directed toward
choosing a particular model form. A procedure of first testing
the least complex model and then the progressively more com-
plex alternatives, outlined in the preceding section, appeared to
constitute a logical approach to the problem.
Considering the linear form (A) and allowing the age,
store, weeks and interaction constants to take on any (least-
squares estimated) finite value, the relevant question to be
answered related to the existence of a linear component. Making
use of statistical notation, the hypothesis to be tested was
H1 : 09= 0 against Ql: P9,/ 0.
The method used to choose between the two hypotheses
amounted to testing the reduction in error sum of squares due
to linear regression. Consequently, the testing of H1, given
form (A), required the computation of two new error sums of
squares. These consisted of the remainder after fitting X7 and
Xs and the remainder after fitting X7, Xs and X'9.
Solution of the following matrix equations was required to
obtain the sum of squares (SSRs) for the regression on
X7 and Xs:19
[ 2 1x
[b be] x7 8-I = [yx7 lyx8]
S0.675000 -0.225000
[ J b7 -0.225000 0.675000 .879816 0.932323 ,
The necessary sums of squares and sums of cross products were ob-
tained from line E, Table 2 of Appendix III.