**Variable-Selection Procedures:**

In regression analysis, variable-selection procedures are aimed at selecting a reduced set of the independent variables - the ones providing the best fit to the model.

The criterion for selecting is usually the following F-statistic:

where n is the total number of data points, SSE is the sum squares due to error - that is, the sum of squares minimized by the least squares method. If adding the variable x_{p+1} to variables x_{1},...,x_{p} does not improve (or deletion of the variable x_{p+1} does not worsen) the fit significantly, this statistic follows an F-distribution; otherwise, the statistic tends to take on larger values.

There are several methods for variable-selection procedures. Some of them are step-wise regression, forward selection, backward elimination.