Multicollinearity and regression analysis

In regression analysis it is obvious to have a correlation between the response and predictor(s), but having correlation among predictors is something undesired. The number of predictors included in the regression model depends on many factors among which, historical data, experience, etc…. At the end selection of most important predictors is something objective due to the researcher. Multicollinearity is a phenomena when two or more predictors are correlated, if this happens, the standard error of the coefficients will increase. Increased standard errors means that the coefficients for some or all independent variables may be found to be significantly different from 0. In other words, by overinflating the standard errors, multicollinearity makes some variables statistically insignificant when they should be significant In this paper we want to focus on the multicollinearity and reasons and consequences on the reliability of the regression model

Islamic mathematics

The present doldrums position and state of decadence, internal differences, external aggression (geographical and ideological), lack of self-confidence and dependence, illiteracy, political instability, economic disaster, lack of knowledge and wisdom, back benchers in science and technology, education, medicine, trade and business, banking system and defensive incapability of Muslim World prompted me to look at our principal sources of inspiration, which are, the Qur’an, Sunnah of the Prophet (SAW), and examples of the “enlightened Caliphs” and see what is Islam’s view about seeking knowledge, technology and inventions in general and mathematics’ education in particular. We will discuss the nature of mathematics and its scientific status. We will highlight the position of mathematics in Islamic classification of knowledge. We will also discuss the current state of mathematics and future suggestions. We have gathered together some of these impressions; these are all tentative, nothing final about them, but these are here nonetheless

Al-Razi's understanding and curing of smallpox and measles

The objective of this study is an attempt to introduce the role of the Muslim scholar, namely AI-Razi, in establishing treatment for smallpox and measles clinical observations. The methodology of this chapter uses the book written by AI-Razi about smallpox and measles in Arabic language as a reference. In 1970, the World health Organization (WHO) praised AI-Razi for the originality and accuracy in his writings in this subject (Amoozaneh & Ashtiyani, 2010). Smallpox and measles have been known through the decades as prominent killers destroying millions of lives as they pass through towns and villages, though vaccines for both diseases were develope

Statistics and its importance in validating research findings

Researches in life constitute a chain where every ring of it should be verified and validated. Statistics and its tools are widely used in researches regardless to the area of application. Nowadays, we can hardly find any research work without using statistical packages or tool to reach a result and interpret them. The objective of this paper is to touch on a serious problem in validating the research findings. This problem is, in fact, when using statistics and its tool without enough knowledge of how a certain statistical process is working and its requirements, which will result in wrong interpretation, and consequently affecting the validity of the obtained results. The danger comes when these results are used by other researchers as verified and validated facts to build on. This means that, any not validated result will break the chain of research and results in what is called broken link. It is almost impossible to have an exact or approximate statistics on research works that have not been validated due to various reasons. Most serious concern is when these (wrong) findings used by other researchers to conduct new researches. We are trying to give some humble guidelines to avoid or minimize broken links in researches

Islamic mathematical sciences

In Islam Mathematics is seen as an important tool for life. The Qur’an considers the rules of mathematics to be a pathway to discover God’s will. This Paper discusses some of the contributions made in mathematics by some Muslim scholars. These remarkable inputs are due to the fact that mathematics is one of the renowned physical sciences which started right from antiquity. The inputs worth discussing in this paper include those of Al–Khawarizmi, Al–Kashi, Al–Khayyam and Al–Khazin. All have invented some vital concepts used in modern day mathematics

Statistical optimization of fermentation conditions for cellulase production from palm oil mill effluent

Palm oil mill effluent discharged by the oil palm industries is considered as the mixed of high polluted effluent which is abundant (about 20 million tonnes year-1) and its effect contributes to the serious environmental problems through the pollution of water bodies. Approach: The aim of this study was to identify the potential of low cost substrate such as Palm Oil Mill Effluent (POME) for the production of cellulase enzyme by liquid state bioconversion. The filamentous fungus Trichoderma harzianum was used for liquid state bioconversion of POME for cellulase production. Statistical optimization was carried out to evaluate the physico-chemical parameters (factors) for maximum cellulase production by 2-level fractional factorial design with six central points. The polynomial regression model was developed using the experimental data including the effects of linear, quadratic and interaction of the factors. The factors involved were substrate (POME) and co-substrate (wheat flour) concentrations, temperature, pH, inoculum and agitation. Results: Statistical analysis showed that the optimum conditions were: Temperature of 30°C, substrate concentration of 2%, wheat flour concentration of 3%, pH of 4, inoculum of 3% and agitation of 200 rpm. Under these conditions, the model predicted the enzyme production to be about 14 FPU mL-1. Analysis Of Variance (ANOVA) of the design showed a high coefficient of determination (R2) value of 0.999, thus ensuring a high satisfactory adjustment of the quadratic model with the experimental data. Conclusion/Recommendations: This study indicates a better solution for waste management through the utilization of POME for cellulase production that could be used in the industrial applications such as bioethanol production

Stochastic models of heredity rhesus factor

We consider linear and nonlinear stochastic models of transmission Rhesus factor from parents to their offspring and show that in long run behavior the frequency of Rhesus factor be the same

Al-Battani contributions in astronomy and mathematics

This chapter is talking about one of the famous and greatest Islamic astronomers and mathematicians around the world; AI-Battani has great and significant contributions in astronomy and mathematics. In astronomy, he has astronomical observations for more than forty years. In addition, he did some corrections upon Ptolemy's results and made some new tables of the Sun and the Moon. Moreover, he determined the length of solar year. In mathematics, he innovated new relationships in trigonometric, and created a table of cotangents, and made some formulas in spherical trigonometr