Absolute error mathematical modeling

The objective of any modeling exercise is to place a calculated line (based on some relevant mathematical model) as close to the data collected as possible. The difference between individual data points and the calculated line (in a vertical direction— no error in the x terms) is called the residual. The sum of residuals could be zero even with very large residuals for individual points if the negative residuals canceled the positive values. An absolute residual might solve this problem, but more usefully, the squared residual will also achieve the desired result. This is the least-squares criterion. An extension of this is to weight each data point by the inverse of the estimated variance. This term is the objective function, WSS, shown in Eq. (1), calculated for n data points ... 

Majumdar and Majumdar [12] tried to develop the mathematical and statistical model to predict the breaking elongation of cotton ring spun yam. Along with the fiber properties from HVl testing, they also use yam twist multiplier for mathematical model. In this study, they have concluded that prediction power of statistical model was better than the mathematical model. The correlation coefficient and mean absolute error was 0.870 and 6.696%, respectively for statistical model and 0.731 and 10.05%, respectively for mathematical model. 

---