The Regression With Additive Error Sampling Method can be used to define the uncertainty in a parameter that has a dependency linkage to another parameter in the analysis. The sampling process is defined by selecting an Independent Parameter which will become the basis for generating the sampled value at this parameter. In order for a regression element to be selected, a parameter with an independent sampling method (i.e., simple distribution, monthly distribution or specified parameters) must be created first. A Regression Relationship is defined between the two parameters. The calculation process proceeds for a sample by first accessing the value computed for the independent parameter. Then the regression is applied to calculate the preliminary parameter value for this parameter. An epsilon error term is then calculated using one of the eight available probability distribution choices. The sampled epsilon error is added to the preliminary parameter value to produce the value used for a sample. From sample to sample, the values that vary are the sampled value for the independent regression parameter and the error term. For realization of regression parameter xi, user-specified slope m, user-specified intercept b and value sampled from the specified error distribution εi, the sampled parameter value Yi is:

An Epsilon Error Term is added to the preliminary parameter value calculated from the regression parameter and the linear or semi-logarithmic relationship. The epsilon term represents the error in the fitting relationship between the regression parameter and this parameter. You may choose any one of the nine analytical probability distributions to represent the error term. Based on the selected distribution, parameter coefficients must be entered to define the distribution.  You may also select a constant value (for example, 0).  This means that the relationship between the two variables is deterministic, with uncertainty in both parameters completely controlled by the sampling of the regression element.