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Factor levels are the values of the factor utilized in the experiment.
To assess the importance of a single factor, we compared the mean square error (MSE) values of the validation data both before (MSEi) and after (MSE*i) randomly permuting the values of the factor for each tree [48].
(3) and (5) respectively, considering the material parameters of Table 4, are summarised together with the values of the factor ( left(sqrt{E{varepsilon}_{e rtr}/{R}_e}right) ) in Table 9 (for the cortical bone considered as semi-ductile material) and in Table 10 (for the cortical bone considered as ductile material).
Note that μ 0 > 0 so 1 2 ( μ 0 + 1 μ 0 ) ≥ 1. Since, by assumption, the real part of μ is positive, it holds | φ | ≤ φ 0 < π / 2. A computation shows that the values of the factor 1 1 + 1 2 ( α μ + 1 α μ ) are located in a disc in the complex plane with center at δ / 2 and radius δ / 2, where δ = 1 / ( 1 + cos φ 0 ).
To assess the importance of a single factor, we compared the mean square error (MSE) values of the validation data both before (MSEi) and after (MSE*i) randomly permuting the values of the factor for each tree [ 48].
Here the importance of a predictor to the RFML model was assessed by randomly permuting the values of the factor within a validation dataset, and processing the validation data through the regression trees.
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The values of the factors were kept constant during the entire processes described in this article.
The values of the factors and responses were exposed to multiple regressions to derive a second-order polynomial equation used to predict the values of optimized dependent variables (responses).
The estimation of the PR, however, requires a more complicated mathematical expression that relates the effects and the values of the factors of interest.
The model provides the value of the Factor of Safety for a given slope and soil depth.
To deal with this instability, we apply regularization techniques to minimize the value of the factor (frac{1}{mu_{n}}) for large n.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com