Abstract:
Second order models are useful in situations where there are curvilinear effects present
in the true response function. Such models have real life applications in a wide variety
of fields such as agriculture, biology,
and
business among others. In such cas
es the
problem is twofold. First is to fit a model for the relationship between the dependent
variable and the explanatory variables. Second is to find the values of the predictor
variables that optimize the response. The objectives here
were
to fit second
order
models involving four independent variables as well as to obtain values for the
explanatory variables that optimize the dependent variable. Response surface
methodology (RSM) is used both to fit the models as well as to analyze the fitted
surfaces.
The data obtained by simulation
were
from a four factor rotatable central
composite design (CCD). Results include
d
the fitted models and the tests of adequacy of
fit for the models. Optimal values for the independent variables
were
also given.
Contour and
surface plots are presented to give a pictorial view of the nature of the
response surface. As an application a model for the germination of Melia volkensii
experiment
was
fitted and optimal values of temperature, soil pH and chemical
concentration obtaine
d. The work in this paper can be directly applied in many
instances where an investigator studies the relationship between four predictor
variables and a response. With some relevant adjustments this can be extended to any
number of explanatory variables.
