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A Study on the Academic Performance of the Students by Applying Multiple Linear Regression Analysis using the method of Least Squares

Many Educational Institutions want their students to be placed in reputed companies and hence they focus on the academic performance of their students. If they could able to know about the student's academic performance, then they can focus more on those students whose academic performance is poor. They can take special care on those students whose academic performance is poor and make them prepare for the placement. In this paper, we present a study on the academic performance of the students of a reputed college by applying multiple linear regression models on the data set consisting of 23 students and evaluate the dependent variable for two given predictor variables. Data Mining is the process of analyzing data available in large data sets and obtains knowledge out of it. The knowledge so obtained is known as the Knowledge Discovery in Databases (KDD). This knowledge helps us in different ways. A data set is a collection of data objects. Each data object represents a record. This data object consists of any number of attributes which specifies the characteristics of the data object. Any Educational Institution consists of students with different categories. We can categorize students based on several properties like attendance, percentage of marks secured, attitude, intelligence etc., to judge their academic performance. In this paper, we present a study on the academic performance of the students based on their aggregate percentage of marks, attendance percentage and number of backlogs. Hence we use multiple linear regression models on the data set of 23 students and evaluate the dependent variable for two given predictor variables. II. Methodology(7) A linear regression model that contains more than one predictor variable is called a multiple linear regression model. This is of the form Y=β0+ β1X1+ β2X2 The above model is linear in the parameters β0, β1, β2 that describes a plane in three dimensional space of Y, X1 and X2. β0 is the intercept of the plane and β1, β2 are considered as partial regression coefficients. Parameter represents the change in the mean response corresponding to a unit change in when is held constant. Parameter represents the change in the mean response corresponding to a unit change in when is held constant. The above model that we consider here is a first order multiple linear regression models. The true regression model is generally never known. It can be estimated by calculating the parameters of the model for an observed data set. The first order regression model applicable to the data set having two predictor variables is Y=β0+ β1X1+ β2X2 Where the dependent variable Y represents the aggregate percentage of marks and the predictor variables X1 and X2 represents the attendance% and number of backlogs. The least square estimates, , can now be obtained: = (X 1 X) -1 X 1 Y