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Artificial Intelligence Algorithms have been used in recent years in many scientific fields. We suggest
employing flower pollination algorithm in the environmental field to find the best estimate of the
semi-parametric regression function with measurement errors in the explanatory variables and the
dependent variable, where measurement errors appear frequently in fields such as chemistry, biological
sciences, medicine, and epidemiological studies, rather than an exact measurement.
We estimate the regression function of the semi-parametric model by estimating the parametric
model and estimating the non-parametric model, the parametric model is estimated by using an
instrumental variables method (Wald method, Bartlett’s method, and Durbin
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