Performance of Post Graduate Students Using Multiple Regression Analysis (Case Study)

The present study is focused to analyze the performance of post graduate students through various statistical parameters. In order to estimate the performance of Post Graduate Students, who are enrolled in different fields of Science, Technology and Humanities at Mehran University of Engineering & Technology (MUET) Jamshoro. The modified model of MLR is used to represent the Number of Degree Holders Students (ND) and would be utilized for those who obtained their master’s degree within time duration or well time to be considered as dependent variable, the initially enrolled student denoted as (NS) number of students and with their obtained CGPA to be considered as independent variable. The result of this research would help to estimate the performance of post graduate students. For this study multiple linear regression model can also be generalized as, With Standard Error of Estimate, Co-efficient of Multiple Determination (R 2 ) and Multiple Correlation.


INTRODUCTION
Postgraduate degree is assumed across the world in universities because it is very precious degree least people enrolled themselves for this degree due that's why degrees considers in research and the procedure for getting admission in this discipline is more different than others because research is based on unique ideas in which candidates knows better solution of the problem from previous one to collect data by reliable resources. With authentication they work in research take out the gap and try to resolve according to data by testing, analyzing and from survey for getting good result so that they can complete their degree in time that's why for testing performance of candidates in this degree M.Phil. Applied Mathematics department was checked which belong to Mehran University of Engineering and Technology (MUET) Jamshoro that how many candidates have secured their degree within time. The word regression analysis is a statistical tool for calculating the connection among the variables and it's done to find out the correlation between more than two independent variables which gives the method to be applied for calculating and prognosticate the independent variable which is known as the value of independent variable.
The connection between the expected value of the dependent and independent variable is known as the line of regression .When the dependence more than one independent variable is known as Multiple Regression. In this study, the performance of students by using Multiple Regression Analysis will be discussed. Many researchers have applied multiple regression analysis to predict student academic performance (Stephen Regression analysis also has supposition of linearity which means that straight line connects between the dependent and independent variable. The linearity between independent and dependent variable for testing by observing scatter plot. Being a linear regression, one desire for testing the significance of the parameters joint for any variables Xi included in a multiple regression model, the null hypothesis tells the co efficient bi=0. The research hypothesis may be one or two sided starting that bi is either less than 0 (i.e bi<0), greater than 0 (i.e bi>0), or simply bi≠0.

METHODOLOGY
The present study is descriptive in nature. In this study the students of the department of Applied Mathematics of batches from 2014-2017. The data was analyzed by applying the statistical tools like variance, mean, standard deviation, multiple linear regression, multiple correlation, standard error of estimate, adjusted R Squared and the independent t-tests were applied to test the significance between the results. A Regression which involves two or more independent variables is called MULTIPLE REGRESSION, the linear multiple regression model formulated as, Y= b 0 +b 1 X 1i +b 2 X 2i +-------------+b n X i +Ԑ Where, Y = Dependent Variable. X i = Independent Variables. b=Parameter.

Ԑ=Error.
The generalized multiple linear regression model for this study formulated as,

TO COMPUTE THE MULTIPLE CORRELATION CO-EFFICIENT:
Where,

TO COMPUTE THE ADJUSTED MULTIPLE CO-EFFICIENT OF DETERMINATION:
Adjusted R-SQUARED is used to compare the model with different number of predictors. The formula of ADJUSTED R-SQUARED is given below, Where k=no: of independent variables. n= no: of observation. (Table 1) representing the mean, standard deviation and variance of the CGPA of students for the three disciplines from Batches 2014-2017. (Table 2) showing the equations of Regression line (Model) in batches from 2014-2017 in three disciplines. (Table 3) showing the test hypothesis values at 95% confidence interval for the difference between means for the results of three disciplines from batches 2014-2017. The table shows that the hypothesis is accepted for all batches. Graph and Bar Chart (1-5), showing the CGPA of students from batches 2014-2017.

Discipline
Batches