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The regression estimation of a cost function is a mathematical representation relating how a cost changes with changes with the level of activities relating to the cost. In this research, this estimation process examines the effects of extreme values and observations where there is a relationship between cost and the cost drivers. The regression estimation methodology uses several types of single and multi criteria loss functions.

The needs for cost functions occur as a result of economies of scale, quantity discounts, resources increase in lot sizes not in individual units, labor hours consumed decrease as workers learn their jobs, and downstream activities market and distribution.

The need for accurate cost estimation is a significant problem in financial management.

Cost estimations are clearly key inputs to such financial analysis as net present value or internal rates of return.

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