Analysing Four Factor Second Order Models Using Response Surface Methodology with Application in Germination of Melia volkensii
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 cases 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 included 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 obtained. 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.
References
Dilute Acid Pretreatment Using Response Surface Methodology for Bioethanol Production from Cellulosic Biomass of Rice Polish. Pakistan Journal of Botany. 44(1). 169-176 Box, G. E. P., and Wilson, K. B. (1951), On the Experimental Attainment of Optimum Conditions, Journal of the Royal Statistical Society, Series B, 13, 1–45.
Hill W.J., Hunter W.G. (1966), A review of response surface methodology: a literature review. Technometrics, 8, 571–590.
Hussain I. and Uddin M. B. (2012). Optimization effect of germination on functional properties of wheat flour by response surface methodology. International Research Journal of Plant Science. 3(3). 31-37
Hussain I., Uddin M. B. and Aziz M. G. (2011).Optimization of antinutritional factors from germinated wheat and mungbean by Response Surface Methodology. International Food Research Journal. 18(3).957-963
Krishnaa D., Krishnaa K.S., Padma Sreeb R. (2013). Response Surface Modeling and Optimization of
Chromium (Vi) Removal From Aqueous Solution Using Borasus Flabellifer Coir Powder. International Journal of Applied Science and Engineering. 11(2). 213-226
Madamba P. S. (2002). The Response Surface Methodology: An Application to Optimize Dehydration Operations of Selected Agricultural Crops. Food Science and Technology. 35(7), 584–592
Mead R., Pike D.J. (1975), A review of response surface methodology from a biometric viewpoint. Biometrics, 31, 803–851.
Montgomery, D.C. (2005). Design and Analysis of Experiments (5th Edition), John Wiley and Sons
Myers R.H., Khuri A.I., Carter W.H. (1989), Response surface methodology : 1966-1988. Technometrics, 15,
301–317.
Pishgar-Komleh S.H. , Keyhani A. , Mostofi-Sarkari M. R. and Jafari A.(2012).Application of Response
Surface Methodology for Optimization of Picker-Husker Harvesting Losses in Corn Seed. Iranica Journal of Energy & Environment. 3(2).134-142
Zainal S., Nadzirah K. Z., Noriham A. , Normah I.(2013). Optimisation of beef tenderisation treated with bromelain using response surface methodology (RSM). Agricultural Sciences 4(58). 65-72
