Qualitative regression models-some applications

We know that regression model is a mathematical representation of the problem under consideration, to measure of average relationship between a dependent variable and one or more independent variables. Generally a linear model Y_nx1 = X_nxkβ_kx1 + ε_nx1 may be estimated through ordinary least squares method with some usual assumptions. Depending upon the statistical significance of individual OLS estimates of the parametric vector β and significance of complete regression respectively, we can test the influence of regressors individually and jointly on the dependent variable of the problem under study.

In regression analysis the dependent variable is frequently influenced not only by the quantitative variables but also by the variables that are qualitative in nature. Qualitative variables indicate presence or absence of quality that take values 1 or 0 and called dummy variables. Regression models which contain all regressors exclusively dummy are called ANOVA models. And regression models containing a mix of quantitative and qualitative regressors are called ANCOVA models.

The purpose of this paper is to present some ANOVA and ANCOVA models with some specific examples which can be adapted to any similar situations in any area of interest for the purpose of regression analysis of data with exclusively qualitative and qualitative along with quantitative variables as regressors.