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To validate the accuracy of this established prediction formula, error analysis is conducted by normality and homoscedasticity tests, standardized residual and prediction formula application.
The precision of the system in bringing the needle to target (needle placement error) was calculated for each target site using the formula: Error = √[(X-X') + (Y-Y') + (Z-Z')].
After editing was complete, we calculated the error rate for each batch with the following formula: Error rate = Number of edits (Number of variables on form ) × (Number of forms in batch ) Similarly, we summed errors and forms over all batches to derive an error rate for each type of form.
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The proposed neural network system presents a maximum error lower than 15%, while existing design formulae errors are over 20%.
The error-added TACs for simulation were generated according to the following formula [18]: Error ‒ added C i = C i + Rand × σ C i, σ C i = ϵ C i Δ t i × exp - λ t i, (2).
Thirdly, by applying the generalized Taylor's formula, some error analysis is provided.
Furthermore, we obtain a formula with error term for the reconstruction of the potential.
HSIAO [9] extrapolated that the effect formula of error on the beam's width, which provided a very beneficial and applicable supplement to extant theories on antenna gain loss.
To calculate the confidence intervals for family studies we used the formula standard error (log odds ratio)=√(1/T+1/U) (see web extra appendix 3 for a fuller explanation).
The quadrature formulas and error expansions of (3.1) have been given in the front part of this section.
More about quadrature formulae and error estimations (from the point of view of inequality theory) can be found in the monographs [11] and [12].
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