Subset Selection for Multiple Linear Regression via Optimization

The regression analysis is a statistical methodology for predicting values of response (dependent) variables from a set of explanatory (independent) variables by investigating the relationships among the variables. The regression analysis is used for forecasting and prediction in a variety of areas, from economics to biology. When the relationship among the variables is expressed as a linear equation and the set of explanatory variables has more than one variable, it is termed multiple linear regression. The multiple linear regression model is the most popular model among the various variants of regression analyses. Given a fixed set of explanatory variables, the goal of the multiple linear regression is to find the coefficients for the explanatory variables that minimize the fitting error.