General Linear Model

General linear model is used to evaluate the statistical data in both the researches that are social as well as applied. General linear model provides the basis to the T Test, analysis of covariance, analysis of variance, regression lines and also contributed in many of the variant methods like in factor analysis, multidimensional scaling, discriminate factor analysis correlation analysis and many others.  As the model is supportive because of general creation, this model thus plays very significant role in social researches for the students.  To know about the entire knowledge and functions general linear model, some technological statistical training is required.  To attain the actual understanding of general linear model; one should first examine the case of two variables.
The Two Variables Linear Model

In case of the two variables a line is defined by the reference of an equation that is        

Y= b₀ +b₁X + e

In the above equation, the variable Y is the dependent variable that can be articulated in the manner as the function of the constant that is b0 and a slope b1 multiplied by the variable X.  e is denoting the possibilities of errors that occur in the evaluation.  Constant described in the equation is also being known as the intercept and the slope is referred to as the regression co efficient. For example; in case of evaluating the gross percentage average of the students in the university, with the intercept 1, regression co efficient as 0.02 and X is considered as the IQ level that is 130 then the accumulated GPA is taken as 3.6. But in case of more than two variables that are the predictor variables like to evaluate the motivation or satisfaction level there exists multiple number of predictor variables, then their exists multiple  regression coefficients  in the linear equation. That is stated in the following way;

Y= b₀ + b₁X₁+b₂X₂+…..+ b_nX_n + e

In the above equation, n indicates the number of predictors. All the regression coefficients in the equation presents their individuals effect as independent assistance on the dependent variable Y.  It is also examined that the two variables involvement that is X and Y shows a correlation with each other, which in case if X1 is controlling the effect of all other independent variables.This type of correlation is referred to as partial correlation. In 1907, the term partial correlation is used by Yule.

The Extension of Regression to the General Linear Model

From the explained view of two variable cases, the more retrieved form is stated in general linear model. The general linear model is different from the multiple regression models in case of the number of the dependent variables that can be examined. [linkunit]The general linear model steps further to the multivariate regression in order to examine the combination of the number of the dependent variable.  The general linear model in nature is a single dependent variable or also called as univariate model.  In comparison with the multiple regressions, the general linear model evaluates the X variable with non linear independent values.

References

• Rathouz, P.J. (2009), “generalized linear models with unspecified reference distribution.”Vol 10(2). Pp: 205-218. 

• Trochim, W.M.K. (2006), “General Linear Model”, research methods the knowledge base. 

• Dobson, A.J.; Barnett, A.G. (2008). Introduction to Generalized Linear Models (3rd Ed.). Boca Raton, FL: Chapman and Hall