4. Regression Analysis

Regression analysis is a very important concept which is used not only in Engineering but other disciplines as well. Engineering problems of the present scenario are quite challenging to solve mainly due to their analytical complexities that requires numerical modeling approach. This chapter deals on the use of surrogate models for handling the solution of large-scale and high-dimensional computation intensive real-life problems. In large-scale high-dimensional computational problems, to evaluate the system response/behavior the majority of computation is involved in the repetitive function calls. To adhere to the quality of solution which depends on the system response estimation, the high-fidelity models are used to get accuracy in results. Their use of incorporates the conventional techniques a.k.a., the evolutionary algorithms require a great number of such high-fidelity function calls. To this end, a much-appreciated low-cost surrogate models or metamodels, which approximates the original model mathematically by reducing the computation cost for a desired accuracy level in an optimization solution is well accepted. During training, the surrogate model requires a minimum number of evaluations of the original model at support points and an efficient design of experiment can be performed for that. This chapter discusses in detail various regression models like linear, non-linear, multiple linear and Equivalent linear. The Equivalent Linear Regression model is extremely useful in real life as it has lot of practical applications.