Saman Babaie-Kafaki - Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
Mahdi Roozbeh - Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran
Monireh Manavi - Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran

As known, outliers and multicollinearity in the data set are among the important difficulties in regression models which badly affect the least-squares estimators. Here, we suggest a nonlinear mixed-integer programming model to simultaneously control inappropriate effects of the mentioned problems. The model can be effectively solved by popular metaheuristic algorithms. To shed light on importance of our optimization approach, we make some numerical experiments on a classic real data set.

Condition number, Linear regression, Penalty method, Metaheuristic algorithm, Nonlinear mixed-integer programming.