Glossary

Variable-Selection Procedures

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:

F(x₁,…,x_p; x_p+1) =

SSE(x₁,…,x_p) – SSE(x₁,…,x_p, x_p+1)

SSE(x₁,…,x_p)

(n–p–1),

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 x₁,…,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.

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