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A STUDY ON MULTIPLE LINEAR REGRESSION USING MATRIX CALCULUS

In spite of accessibility of a large number of imaginative tools in Applied Mathematics the most important tool of the Mathematician is always the linear model as it involves uncomplicated and apparently most restrictive properties namely linearity ,constancy of variance ,normality and independence. Linear models and the methods connected to it are remarkable, flexible and powerful. Since almost all advanced statistical tools are generalizations of linear models proficiency in linear models is a prerequisite to studyadvanced statistical tools. This research article primarily focuses on the specific forms of Simple Linear Regression Model, Multiple Linear Regression Model, LSE of its parameters and the properties of LSE.Furthermore an innovative proof of Gauss-Markov theorem has been proposed by means of Principles of Matrix Calculus. In addition to these the concept of BLUE has been depicted.