iosr-Jm   Volume-10 ~ Issue-4 ~ July-August 2014

Abstract: This study is aimed at employing the methodology of concomitant order statistics in the analysis of poultry feeds data. The purpose is directed toward finding the distribution of maximum and minimum concomitant order statistics of the cholesterol level given the egg weight. It was estimated on the basis of sample of 96 chickens, which were classified into two groups of 48 chickens each. One group was fed with in-organic copper salt combination while the second group with organic copper salt combination. The estimate of the probability of obtaining both the highest and the lowest are given using numerical approach to solve the integral obtained.

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Abstract: This paper concerns with the study of constructing a special family of 3-tuples (a,b,c) such that the product of any two elements of the set added with k-times their sum increased by 4 2 k  is a Perfect square.
Keywords: Diophantine triple, Gaussian integer.2010 Mathematics Subject Classification: 11D99

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Abstract:In this article, we consider the perturbed controlled linear system described by the difference equation , and the corresponding output , we suppose that ω is a disturbance which infects the system. Obliged to take into account the undesirable perturbation ω, we investigate also in this work a feedback control which allows to eliminate or to attenuate the effects of ω. To illustrate the obtained results, various examples are presented.
Keywords: Discrete-time systems, perturbation analysis, stability, pole placement controllability, Ackermann's theorem, Milman's theorem, tolerance

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Abstract: This research was set to examine the effect Multicollinearity has, on the standard error for regression coefficients when it is present in a Classical Linear Regression model (CLRM). A classical linear regression model was fitted into the GDP of Nigeria ,and the model was examined for the presence of Multicollinearity using various techniques such as Farrar-Glauber test, Tolerance level, Variance inflation factor, Eigen values etc and the result obtained shows that Multicollinearity has contributed to the increase of the standard error for regression coefficients, thereby rendering the estimated parameters less efficient and less significant in the class of Ordinary Least Squares estimators. Tolerance levels of 0.012, 0.005, 0.002 and 0.001 for𝛽1, 𝛽2, 𝛽3 ,and 𝛽4 respectively clearly shown a very low tolerance among all the explanatory variables with very high Variance Inflation Factors of 84.472, 191.715,502.179 and 675.633 respectively. A Coefficient of determination (R- Square) of 99%, though signaled a very high validity for the CLRM but it is equally an indications of a very high degree of Multicollinearity among the explanatory variables. The Eigen values of 0.431, 0.005, 0.002 and 0.000 for 𝛽0, 𝛽1, 𝛽2, 𝛽3 ,and 𝛽4 respectively clearly shown a very low Eigen value among the explanatory variables, which are closer to zero with very high Condition index of 30.983, 49.759 and 100.810 for 𝛽2, 𝛽3 ,and 𝛽4 respectively which indicate that the Multicollinearity present is due greatly to the influence of regressors X2, X3, and X4..

Keywords: Eigen values, Multicollinearity, Standard Errors , Tolerance Level ,Variance Inflation Factor

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