Prediction, Linear Regression and the Minimum Sum of Relative Errors

Abstract

When linear regression is used for prediction purposes, the minimization of the sum of relative errors (MSRE) is proposed as an alternative criterion to the minimization of the sum of squared errors (MSSE) and the minimization of the sum of absolute errors (MSAE). The problem is formulated as a linear programming problem and a solution procedure is given. The problem of subset selection with the MSRE criterion is also considered and results illustrated with an example.

KEY WORDS:

• Prediction
• Regression Analysis
• Minimization
• Squared Error
• Absolute Error
• Relative Error
• Subset Selection
• Linear Programming
• Primal Problem
• Dual Problem