ARS - 2008
Permanent URI for this collectionhttp://repository.kln.ac.lk/handle/123456789/166
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Item Development of a Minitab Macro Program as a Remedy to Overcome Heteroscedasticity in Linear Regressions(University of Kelaniya, 2008) Attanayake, A.M.C.H.; Hewapathirana, T.K.Homoscedasticity in the disturbance terms that appear in a regression function is one of the key assumptions of ordinary least squares analysis. As the developed regression model relies heavily on the model assumptions, violation of the assumptions severely affects the importance of a regression model. Transforming the response variable is one solution to overcome the problem of heteroscedasticity. Today most statistical packages use graphical methods to detect heteroscedasticity. Although a graphical method could be considered as a good starting point, no measure of reliability can be attached to inferences derived from a graphical method. In this study we have developed a Minitab macro to detect heteroscedasticity present in the disturbance terms by the use of graphical as well as statistical methods including the popular White's General Heteroscedasticity test and how to solve the heteroscedasticity problem by applying the alternative form of the Box-Cox power transformation. The alternative form of the Box-Cox transformation is given by: V= Yln(Y) A=O Where lnY= n-'I lnY; Considering the stability of V for minor changes in the power parameter A, the transformed variable, V is chosen for the analysis and useful values of A were found to be in the range [-2, 2]. The program was developed using a Local macro structure and tested on Minitab version 14 and requires Microsoft Windows 2000 or XP operating system to implement this program. The developed macro was tested for many data sets and was found that the program is capable in handling the heteroscedasticity present in the error structure.Item A Univariate Box-Jenkins Model to Predict Relative Humidity Levels in Puttalam at Night(University of Kelaniya, 2008) Attanayake, A.M.C.H.; Hewapathirana, T.K.Humidity is among one of the most important weather conditions that influence salt preparation. Technical processes and treatments carried out in salt factories and laboratories require relative humidity levels to be maintained using control systems. Puttalam is a reputed saltern in Sri Lanka. The knowledge on the fluctuations of relative humidity is paramount for the management of Puttalam saltern, to carry out their activities in a proper manner. This paper presents the results of a study carried out to develop a prediction model for relative humidity during night time in Puttalam saltern, using Box-Jenkins methodology. This study is based on percentage mean relative humidity data collected from the Puttalam weather station from January 1998 to December 2007. Sample autocorrelation functions and sample partial autocorrelation functions are used as the major diagnostic tools in this model building procedure. Model parameters were estimated using the non-linear least squares method. The adequacy of the fitted model was checked by analyzing the residuals. According to the analysis it was revealed that the ARIMA (1, 0, 1) (1, 1, 1\2 model is the best model that could be used to forecast the percentage mean relative humidity at Puttalam saltern during night time. Forecasts can be readily generated using the above model up to a period of twelve months without using any external variables.