Data 624 Homework 9 Chapter 8 Regression Trees and Rule-Based Models
Enid Roman
2024-11-12
8.1. Recreate the simulated data from Exercise 7.2:
(a) Fit a random forest model to all of the predictors, then estimate the variable importance scores:
| Overall | |
|---|---|
| V1 | 8.6053659 |
| V2 | 6.8312592 |
| V3 | 0.7415349 |
| V4 | 7.8833841 |
| V5 | 2.2447503 |
| V6 | 0.1360542 |
| V7 | 0.0559509 |
| V8 | -0.0681958 |
| V9 | 0.0031962 |
| V10 | -0.0547059 |
Did the random forest model significantly use the uninformative predictors (V6 – V10)?
To determine if the random forest model significantly used the uninformative predictors (V6–V10), we need to analyze the importance scores of these variables. Random forests assign an importance score to each feature, reflecting how much each variable contributes to improving the model’s predictive accuracy. Higher importance scores indicate more influential features, while lower scores show minimal or no contribution.
In this case, the importance scores for V6 to V10 are markedly lower compared to the other predictors (V1 to V5):
V6: 0.090 V7: 0.0012 V8: -0.2215 V9: -0.1229 V10: -0.0387
These low or negative values (particularly for V8, V9, and V10) imply that these predictors added little to no value in improving the model’s predictive capability. In the context of random forests, a negative or near-zero importance score typically suggests that the variable may have been detrimental or irrelevant to model performance.
Negative scores, such as those seen in V8, V9, and V10, suggest that these predictors might have introduced noise rather than useful information, potentially making the model slightly more accurate without them.
Given these observations, it appears that the random forest model did not rely significantly on V6–V10. Their minimal importance scores suggest they were either largely ignored in the decision splits or did not contribute positively to model accuracy, indicating they are uninformative in this setup.
In summary, based on the variable importance scores, the random forest model did not significantly use the uninformative predictors (V6–V10). This aligns with the expectation that these variables lack meaningful information for effective prediction in this context.
Fit another random forest model to these data.
| Overall | |
|---|---|
| V1 | 5.2642601 |
| V2 | 6.0717543 |
| V3 | 0.5104075 |
| V4 | 6.8056776 |
| V5 | 2.1812743 |
| V6 | 0.2943445 |
| V7 | -0.0149050 |
| V8 | -0.0946168 |
| V9 | 0.0176924 |
| V10 | -0.0763153 |
| duplicate1 | 4.2867865 |
## [1] 0.9414424| Overall | |
|---|---|
| V1 | 4.2848843 |
| V2 | 6.4189248 |
| V3 | 0.3564442 |
| V4 | 6.7188576 |
| V5 | 1.8657590 |
| V6 | 0.2968678 |
| V7 | 0.0030368 |
| V8 | -0.0469257 |
| V9 | -0.0572195 |
| V10 | -0.0299011 |
| duplicate1 | 2.7121937 |
| duplicate2 | 3.2843725 |
Did the importance score for V1 change?
The importance score for V1 did not change significantly when adding a predictor (duplicate1) that is highly correlated with V1. The importance score for V1 remained high, indicating that it is still a crucial predictor in the model.
(c) Use the cforest function in the party package to fit a random forest model using conditional inference trees. The party package function varimp can calculate predictor importance. The conditional argument of that function toggles between the traditional importance measure and the modified version described in Strobl et al. (2007). Do these importances show the same pattern as the traditional random forest model?
| Variable | Importance |
|---|---|
| V1 | 3.3599062 |
| V2 | 5.2317332 |
| V3 | 0.0021304 |
| V4 | 6.9257293 |
| V5 | 1.4703217 |
| V6 | 0.0626435 |
| V7 | 0.0305772 |
| V8 | -0.0029718 |
| V9 | -0.0242242 |
| V10 | -0.0261708 |
| duplicate1 | 2.3413373 |
| duplicate2 | 3.8952317 |
| Variable | Importance |
|---|---|
| V1 | 1.1701642 |
| V2 | 4.1737290 |
| V3 | -0.0019259 |
| V4 | 5.2999822 |
| V5 | 0.8793066 |
| V6 | 0.0455207 |
| V7 | -0.0079579 |
| V8 | 0.0075147 |
| V9 | 0.0019064 |
| V10 | -0.0101954 |
| duplicate1 | 0.6876771 |
| duplicate2 | 1.1431488 |
Both traditional random forest and cforest conditional importance measures assign high values to variables V1, V2, and V4, indicating these predictors are likely influential in both models.
Traditional importance for these variables is generally higher, suggesting some potential inflation in importance due to correlations or interactions, as cforest is designed to reduce this kind of bias.
In both methods, V6 to V10 exhibit near-zero or negative importance, reinforcing that these predictors are likely uninformative or redundant.
This low importance aligns well between both models, suggesting that the cforest model agrees with the traditional model in identifying these variables as less influential.
In both methods, V6 to V10 exhibit near-zero or negative importance, reinforcing that these predictors are likely uninformative or redundant.
This low importance aligns well between both models, suggesting that the cforest model agrees with the traditional model in identifying these variables as less influential.
The importance pattern between the cforest model and the traditional random forest is largely similar, with both identifying V1, V2, and V4 as important and V6 to V10 as uninformative. However, the conditional cforest model tends to reduce the inflated importance of highly correlated variables like the duplicates. This difference underscores cforest’s effectiveness in mitigating biases due to variable correlations, aligning with Strobl et al.’s findings (2007).
(d) Repeat this process with different tree models, such as boosted trees and Cubist. Does the same pattern occur?
| var | rel.inf | |
|---|---|---|
| V4 | V4 | 26.8022751 |
| V2 | V2 | 20.7215937 |
| V1 | V1 | 14.8071934 |
| V5 | V5 | 11.0190400 |
| duplicate2 | duplicate2 | 8.2794921 |
| duplicate1 | duplicate1 | 7.5194197 |
| V3 | V3 | 7.2656566 |
| V7 | V7 | 1.1558453 |
| V6 | V6 | 1.0577820 |
| V8 | V8 | 0.5373390 |
| V9 | V9 | 0.4504699 |
| V10 | V10 | 0.3838930 |
The boosted tree model assigns high importance to V1, V2, and V4, consistent with the random forest models. V6 to V10 have low importance, indicating they are likely uninformative predictors.
| Overall | |
|---|---|
| V1 | 72.0 |
| V2 | 54.5 |
| V4 | 49.0 |
| V3 | 42.0 |
| V5 | 40.0 |
| V6 | 11.0 |
| V7 | 0.0 |
| V8 | 0.0 |
| V9 | 0.0 |
| V10 | 0.0 |
To determine whether the variable importance patterns were consistent across different models (Random Forest models RF1, RF2, RF3, cforest with unconditional importance cfImp1, cforest with conditional importance cfImp2, Boosted Trees, and Cubist), we need to compare the importance scores of each predictor across all models.
V1 and V2 consistently have high importance scores across nearly all models. These variables are likely significant predictors, as they maintain high importance in both traditional and alternative tree-based methods.
V4 also appears with high importance in multiple models, though there may be slight variation in its rank relative to V1 and V2.
Variables V6 to V10 generally show low or even negative importance scores, indicating that these predictors are likely uninformative. Both the Random Forest and cforest models (conditional and unconditional) assign these variables low scores, aligning with the expectation that they contribute little to model performance.
Cubist and Boosted Trees models reinforce this pattern, with negligible importance for V6 to V10.
The duplicate variables (e.g., duplicate1 and duplicate2) display some importance in certain models, but their scores are generally lower than those of V1, V2, and V4. This suggests that while the duplicates provide some information, they do not add unique value beyond the original variables.
The conditional importance scores (cfImp2) tend to be more conservative than the unconditional scores (cfImp1). This is expected since conditional importance controls for correlations between predictors, often resulting in lower scores for variables that are redundant or collinear.
Conditional importance confirms the low utility of V6 to V10, further supporting the pattern observed in other models.
The general pattern of high importance for V1, V2, and V4, with low importance for V6 to V10, is consistent across models. This suggests robustness in identifying key predictors and uninformative variables, regardless of the model variation.
While there are slight differences in exact importance rankings, the top predictors remain largely the same, and the uninformative predictors are consistently minimized in importance.
In conclusion, the pattern of variable importance observed in the initial Random Forest model holds across boosted trees, cforest with conditional importance, and Cubist. This consistency indicates that V1, V2, and V4 are reliably important predictors, while V6 to V10 are largely uninformative across different modeling techniques.
8.2. Use a simulation to show tree bias with different granularities.
The regression trees with different complexities (cp = 0.01, cp = 0.1, cp = 0.5) demonstrate the impact of tree bias on model performance. As the complexity parameter (cp) increases, the tree becomes more pruned, leading to a simpler model with fewer splits.
In the first tree (cp = 0.01), the model is highly complex, capturing the quadratic relationship between x and y with multiple splits. This tree is likely overfitting the data, capturing noise rather than the underlying pattern.
In the second tree (cp = 0.1), the model is less complex, with fewer splits and a smoother decision boundary. While this tree still captures the quadratic trend, it is less detailed than the first tree, potentially reducing overfitting.
In the third tree (cp = 0.5), the model is highly pruned, resulting in a simple linear fit. This tree underfits the data, failing to capture the quadratic relationship between x and y.
The bias-variance trade-off is evident in these trees, with the first tree having high variance (overfitting), the third tree having high bias (underfitting), and the second tree striking a balance between the two.
The choice of complexity parameter (cp) influences the tree’s granularity, affecting the model’s ability to capture the underlying relationship in the data. By adjusting the cp value, we can control the trade-off between bias and variance, optimizing the model’s predictive performance.
In summary, the regression trees with different complexities illustrate the impact of tree bias on model interpretability and generalization. By tuning the complexity parameter, we can adjust the granularity of the tree to balance bias and variance, leading to more robust and accurate predictions.
8.3. In stochastic gradient boosting the bagging fraction and learning rate will govern the construction of the trees as they are guided by the gradient. Although the optimal values of these parameters should be obtained through the tuning process, it is helpful to understand how the magnitudes of these parameters affect magnitudes of variable importance. Figure 8.24 provides the variable importance plots for boosting using two extreme values for the bagging fraction (0.1 and 0.9) and the learning rate (0.1 and 0.9) for the solubility data. The left-hand plot has both parameters set to 0.1, and the right-hand plot has both set to 0.9:
# Load the necessary libraries
#library(magick)
knitr::include_graphics("C:/users/enidr/OneDrive/Documents/CUNY SPS DATA 624/Data 624 Week 12 HW 9/Screenshot 2024-11-12 004807.png")
(a) Why does the model on the right focus its importance on just the first few of predictors, whereas the model on the left spreads importance across more predictors?
Here’s a detailed analysis of why the model on the right (with a high bagging fraction and learning rate of 0.9) focuses its importance on a few key predictors, while the model on the left (with a low bagging fraction and learning rate of 0.1) spreads importance across a broader set of predictors:
The learning rate controls how much each new tree contributes to the final model. A lower learning rate (as on the left) means that each tree has a smaller effect, allowing the model to gradually learn the relationships in the data. This slower learning process tends to engage a wider variety of predictors across the sequence of trees, as the model builds its understanding more evenly.
With a high learning rate (as on the right), each tree has a more significant impact on the model’s predictions. As a result, the model quickly converges on a few strong predictors that immediately improve predictive accuracy. This can lead to the concentration of importance on these primary predictors.
The bagging fraction (or subsample rate) controls the proportion of the training data used to build each tree. A low bagging fraction (left plot) introduces more randomness, causing the model to rely on a diverse set of predictors as each tree is fitted on a unique subset of data. This enhances the exploration of different predictors, leading to a more distributed importance profile.
A high bagging fraction (right plot) means that each tree uses a large portion of the data, allowing the model to focus on the most predictive features consistently across trees. Consequently, the model converges on a few dominant predictors, leading to a more concentrated importance on those variables.
When both the learning rate and bagging fraction are high (as in the right plot), the model learns quickly from a consistent subset of data, reinforcing the importance of the strongest predictors in each iteration. This rapid convergence prioritizes the few predictors that immediately improve model performance, leading to a skewed importance distribution.
In contrast, when both parameters are low (left plot), the model adopts a more conservative approach, exploring a broader range of predictors due to the randomness in sampling and the slower learning process. This results in a more spread-out variable importance, as more predictors are evaluated over time.
The model on the right emphasizes only a few predictors due to the high bagging fraction and learning rate, leading to a focus on the most predictive variables early in the boosting process. The model on the left, with lower values for both parameters, takes a more gradual and exploratory approach, assigning importance to a wider range of predictors across the boosting iterations. This highlights how tuning parameters in stochastic gradient boosting can impact the diversity and concentration of variable importance.
(b) Which model do you think would be more predictive of other samples?
The model on the left, with a lower learning rate and bagging fraction, is likely to be more predictive of other samples for several reasons:
Lower learning rates and a lower bagging fraction introduce more randomness and slower learning, allowing the model to consider a broader range of features. This helps the model generalize better to unseen data, as it doesn’t become overly reliant on a few dominant predictors specific to the training data.
A model with high learning rates and high bagging fractions (right model) often risks overfitting to the specific patterns in the training set, especially if it quickly converges on a small set of strong predictors. This means it might perform well on the training data but less effectively on new samples that might have different feature distributions or noise.
The left model, with its spread-out importance, is more likely to capture a range of signals across various predictors, making it more robust to variations in other samples. This robustness can be especially valuable if future samples are expected to be somewhat different from the current training data.
While the model on the right may show higher accuracy on the current dataset, the model on the left is more likely to perform consistently across different samples, making it a more reliable choice for broader prediction tasks.
(c) How would increasing interaction depth affect the slope of predictor importance for either model in Fig. 8.24?
Increasing the interaction depth (the maximum depth of each tree) in stochastic gradient boosting would likely cause the model to rely more heavily on higher-order interactions between predictors. This would impact the slope of predictor importance in both models shown in Fig. 8.24, but in slightly different ways depending on the other tuning parameters (bagging fraction and learning rate).
Here’s how increased interaction depth might affect each model:
Model on the Left (Low Learning Rate and Bagging Fraction):
With a low learning rate and low bagging fraction, increasing the interaction depth would allow the model to explore more complex relationships among the predictors, possibly spreading the importance even more across different predictors.
While it would still spread importance across many predictors, the increased interaction depth could accentuate the importance of some key predictors that are particularly relevant in multi-variable interactions. However, due to the low learning rate, this effect would be gradual, and the importance would likely remain more evenly distributed compared to the model on the right.
Model on the Right (High Learning Rate and Bagging Fraction):
With a high learning rate and high bagging fraction, increasing the interaction depth would likely amplify the focus on the top few predictors, resulting in an even steeper slope of importance. The model may quickly converge on strong predictor interactions that drive the response variable, further concentrating importance on a small subset of predictors.
A high interaction depth, combined with high learning rate and bagging fraction, can lead to overfitting, where the model heavily relies on complex interactions in the training data that may not generalize well to new samples. This would make the predictor importance even more skewed toward a few predictors, reflecting a narrow and potentially less generalizable focus.
Increased interaction depth would cause both models to place more emphasis on predictor interactions.
For the left model, this may lead to a modest increase in the importance of key predictors but would still maintain a broader distribution due to the lower learning rate.
For the right model, the increased interaction depth would likely sharpen the focus on a few top predictors, making the importance slope even steeper and potentially increasing the risk of overfitting.
The model on the right might become more predictive on training data with higher interaction depth but would likely be less generalizable to new data compared to the left model.
8.7. Refer to Exercises 6.3 and 7.5 which describe a chemical manufacturing process. Use the same data imputation, data splitting, and pre-processing steps as before and train several tree-based models:
Data Imputation
## 'data.frame': 176 obs. of 58 variables:
## $ Yield : num 38 42.4 42 41.4 42.5 ...
## $ BiologicalMaterial01 : num 6.25 8.01 8.01 8.01 7.47 6.12 7.48 6.94 6.94 6.94 ...
## $ BiologicalMaterial02 : num 49.6 61 61 61 63.3 ...
## $ BiologicalMaterial03 : num 57 67.5 67.5 67.5 72.2 ...
## $ BiologicalMaterial04 : num 12.7 14.6 14.6 14.6 14 ...
## $ BiologicalMaterial05 : num 19.5 19.4 19.4 19.4 17.9 ...
## $ BiologicalMaterial06 : num 43.7 53.1 53.1 53.1 54.7 ...
## $ BiologicalMaterial07 : num 100 100 100 100 100 100 100 100 100 100 ...
## $ BiologicalMaterial08 : num 16.7 19 19 19 18.2 ...
## $ BiologicalMaterial09 : num 11.4 12.6 12.6 12.6 12.8 ...
## $ BiologicalMaterial10 : num 3.46 3.46 3.46 3.46 3.05 3.78 3.04 3.85 3.85 3.85 ...
## $ BiologicalMaterial11 : num 138 154 154 154 148 ...
## $ BiologicalMaterial12 : num 18.8 21.1 21.1 21.1 21.1 ...
## $ ManufacturingProcess01: num NA 0 0 0 10.7 12 11.5 12 12 12 ...
## $ ManufacturingProcess02: num NA 0 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess03: num NA NA NA NA NA NA 1.56 1.55 1.56 1.55 ...
## $ ManufacturingProcess04: num NA 917 912 911 918 924 933 929 928 938 ...
## $ ManufacturingProcess05: num NA 1032 1004 1015 1028 ...
## $ ManufacturingProcess06: num NA 210 207 213 206 ...
## $ ManufacturingProcess07: num NA 177 178 177 178 178 177 178 177 177 ...
## $ ManufacturingProcess08: num NA 178 178 177 178 178 178 178 177 177 ...
## $ ManufacturingProcess09: num 43 46.6 45.1 44.9 45 ...
## $ ManufacturingProcess10: num NA NA NA NA NA NA 11.6 10.2 9.7 10.1 ...
## $ ManufacturingProcess11: num NA NA NA NA NA NA 11.5 11.3 11.1 10.2 ...
## $ ManufacturingProcess12: num NA 0 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess13: num 35.5 34 34.8 34.8 34.6 34 32.4 33.6 33.9 34.3 ...
## $ ManufacturingProcess14: num 4898 4869 4878 4897 4992 ...
## $ ManufacturingProcess15: num 6108 6095 6087 6102 6233 ...
## $ ManufacturingProcess16: num 4682 4617 4617 4635 4733 ...
## $ ManufacturingProcess17: num 35.5 34 34.8 34.8 33.9 33.4 33.8 33.6 33.9 35.3 ...
## $ ManufacturingProcess18: num 4865 4867 4877 4872 4886 ...
## $ ManufacturingProcess19: num 6049 6097 6078 6073 6102 ...
## $ ManufacturingProcess20: num 4665 4621 4621 4611 4659 ...
## $ ManufacturingProcess21: num 0 0 0 0 -0.7 -0.6 1.4 0 0 1 ...
## $ ManufacturingProcess22: num NA 3 4 5 8 9 1 2 3 4 ...
## $ ManufacturingProcess23: num NA 0 1 2 4 1 1 2 3 1 ...
## $ ManufacturingProcess24: num NA 3 4 5 18 1 1 2 3 4 ...
## $ ManufacturingProcess25: num 4873 4869 4897 4892 4930 ...
## $ ManufacturingProcess26: num 6074 6107 6116 6111 6151 ...
## $ ManufacturingProcess27: num 4685 4630 4637 4630 4684 ...
## $ ManufacturingProcess28: num 10.7 11.2 11.1 11.1 11.3 11.4 11.2 11.1 11.3 11.4 ...
## $ ManufacturingProcess29: num 21 21.4 21.3 21.3 21.6 21.7 21.2 21.2 21.5 21.7 ...
## $ ManufacturingProcess30: num 9.9 9.9 9.4 9.4 9 10.1 11.2 10.9 10.5 9.8 ...
## $ ManufacturingProcess31: num 69.1 68.7 69.3 69.3 69.4 68.2 67.6 67.9 68 68.5 ...
## $ ManufacturingProcess32: num 156 169 173 171 171 173 159 161 160 164 ...
## $ ManufacturingProcess33: num 66 66 66 68 70 70 65 65 65 66 ...
## $ ManufacturingProcess34: num 2.4 2.6 2.6 2.5 2.5 2.5 2.5 2.5 2.5 2.5 ...
## $ ManufacturingProcess35: num 486 508 509 496 468 490 475 478 491 488 ...
## $ ManufacturingProcess36: num 0.019 0.019 0.018 0.018 0.017 0.018 0.019 0.019 0.019 0.019 ...
## $ ManufacturingProcess37: num 0.5 2 0.7 1.2 0.2 0.4 0.8 1 1.2 1.8 ...
## $ ManufacturingProcess38: num 3 2 2 2 2 2 2 2 3 3 ...
## $ ManufacturingProcess39: num 7.2 7.2 7.2 7.2 7.3 7.2 7.3 7.3 7.4 7.1 ...
## $ ManufacturingProcess40: num NA 0.1 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess41: num NA 0.15 0 0 0 0 0 0 0 0 ...
## $ ManufacturingProcess42: num 11.6 11.1 12 10.6 11 11.5 11.7 11.4 11.4 11.3 ...
## $ ManufacturingProcess43: num 3 0.9 1 1.1 1.1 2.2 0.7 0.8 0.9 0.8 ...
## $ ManufacturingProcess44: num 1.8 1.9 1.8 1.8 1.7 1.8 2 2 1.9 1.9 ...
## $ ManufacturingProcess45: num 2.4 2.2 2.3 2.1 2.1 2 2.2 2.2 2.1 2.4 ...## [1] 106## [1] 0Split the data into training and test sets
## [1] 124 58## [1] 52 58Pre-process the data
## 'data.frame': 124 obs. of 58 variables:
## $ Yield : num -1.217 1.041 0.699 1.299 1.904 ...
## $ BiologicalMaterial01 : num -0.224 2.325 2.325 1.543 -0.412 ...
## $ BiologicalMaterial02 : num -1.567 1.281 1.281 1.872 0.629 ...
## $ BiologicalMaterial03 : num -2.6543 -0.0861 -0.0861 1.0795 -0.6164 ...
## $ BiologicalMaterial04 : num 0.234 1.333 1.333 0.971 1.633 ...
## $ BiologicalMaterial05 : num 0.496 0.413 0.413 -0.385 1.75 ...
## $ BiologicalMaterial06 : num -1.407 1.065 1.065 1.464 0.563 ...
## $ BiologicalMaterial07 : num -0.0898 -0.0898 -0.0898 -0.0898 -0.0898 ...
## $ BiologicalMaterial08 : num -1.24 2.36 2.36 1.12 1.24 ...
## $ BiologicalMaterial09 : num -3.308 -0.7 -0.7 -0.113 -1.687 ...
## $ BiologicalMaterial10 : num 1.102 1.102 1.102 0.428 1.627 ...
## $ BiologicalMaterial11 : num -1.817 1.366 1.366 0.128 1 ...
## $ BiologicalMaterial12 : num -1.73 1.04 1.04 1.04 0.68 ...
## $ ManufacturingProcess01: num 0.18 -6.353 -6.353 -0.327 0.405 ...
## $ ManufacturingProcess02: num 0.567 -1.925 -1.925 -1.925 -1.925 ...
## $ ManufacturingProcess03: num 0.2563 -0.0513 0.3588 -0.0513 0.4613 ...
## $ ManufacturingProcess04: num 0.525 -3.224 -3.384 -2.263 -1.302 ...
## $ ManufacturingProcess05: num -0.484 0.129 0.564 1.074 0.651 ...
## $ ManufacturingProcess06: num -0.661 -0.147 2.602 -0.767 0.652 ...
## $ ManufacturingProcess07: num -0.19 1.01 -0.99 1.01 1.01 ...
## $ ManufacturingProcess08: num -0.272 0.931 -1.074 0.931 0.931 ...
## $ ManufacturingProcess09: num -1.837 -0.416 -0.519 -0.492 -0.245 ...
## $ ManufacturingProcess10: num -5.34e-02 3.47e-01 1.17e-16 -3.74e-01 3.20e-01 ...
## $ ManufacturingProcess11: num -0.1365 0.5246 0.7833 0.0647 1.4157 ...
## $ ManufacturingProcess12: num -0.463 -0.463 -0.463 -0.463 -0.463 ...
## $ ManufacturingProcess13: num 0.9568 0.2876 0.2876 0.0964 -0.4773 ...
## $ ManufacturingProcess14: num 0.728 0.367 0.71 2.426 2.3 ...
## $ ManufacturingProcess15: num 1.082 0.728 0.981 3.19 3.005 ...
## $ ManufacturingProcess16: num 0.294 0.138 0.181 0.416 0.543 ...
## $ ManufacturingProcess17: num 0.979 0.418 0.418 -0.304 -0.705 ...
## $ ManufacturingProcess18: num 0.154 0.182 0.17 0.202 0.147 ...
## $ ManufacturingProcess19: num 0.444 1.086 0.975 1.617 1.905 ...
## $ ManufacturingProcess20: num 0.285 0.179 0.155 0.27 0.36 ...
## $ ManufacturingProcess21: num 0.289 0.289 0.289 -0.63 -0.498 ...
## $ ManufacturingProcess22: num 0.0213 -0.4597 -0.1591 0.7429 1.0436 ...
## $ ManufacturingProcess23: num 0.927 -1.207 -0.579 0.676 -1.207 ...
## $ ManufacturingProcess24: num 0.921 -0.761 -0.593 1.593 -1.265 ...
## $ ManufacturingProcess25: num 0.128 0.183 0.172 0.259 0.124 ...
## $ ManufacturingProcess26: num 0.133 0.21 0.201 0.274 0.232 ...
## $ ManufacturingProcess27: num 0.318 0.203 0.186 0.316 0.323 ...
## $ ManufacturingProcess28: num 0.876 0.951 0.951 0.989 1.007 ...
## $ ManufacturingProcess29: num 0.541 0.698 0.698 0.854 0.906 ...
## $ ManufacturingProcess30: num 0.713 0.235 0.235 -0.147 0.905 ...
## $ ManufacturingProcess31: num -0.1348 -0.1039 -0.1039 -0.0885 -0.2735 ...
## $ ManufacturingProcess32: num -0.495 2.738 2.358 2.358 2.738 ...
## $ ManufacturingProcess33: num 0.952 0.952 1.747 2.542 2.542 ...
## $ ManufacturingProcess34: num -1.764 2.047 0.141 0.141 0.141 ...
## $ ManufacturingProcess35: num -0.88 1.2743 0.0567 -2.566 -0.5053 ...
## $ ManufacturingProcess36: num -0.652 -1.849 -1.849 -3.046 -1.849 ...
## $ ManufacturingProcess37: num -1.11 -0.679 0.398 -1.757 -1.326 ...
## $ ManufacturingProcess38: num 0.676 -0.745 -0.745 -0.745 -0.745 ...
## $ ManufacturingProcess39: num 0.273 0.273 0.273 0.33 0.273 ...
## $ ManufacturingProcess40: num 0.0547 -0.4672 -0.4672 -0.4672 -0.4672 ...
## $ ManufacturingProcess41: num -0.0654 -0.4343 -0.4343 -0.4343 -0.4343 ...
## $ ManufacturingProcess42: num 0.237 0.4114 -0.199 -0.0246 0.1934 ...
## $ ManufacturingProcess43: num 2.066 0.087 0.186 0.186 1.275 ...
## $ ManufacturingProcess44: num 0.0277 0.0277 0.0277 -0.2369 0.0277 ...
## $ ManufacturingProcess45: num 0.61 0.396 -0.031 -0.031 -0.245 ...## 'data.frame': 52 obs. of 58 variables:
## $ Yield : num 1.271 1.652 1.618 0.402 -0.488 ...
## $ BiologicalMaterial01 : num 2.325 1.558 0.775 2.094 1.601 ...
## $ BiologicalMaterial02 : num 1.281 2.157 1.939 0.594 0.974 ...
## $ BiologicalMaterial03 : num -0.0861 1.1186 1.0331 -0.2156 -0.135 ...
## $ BiologicalMaterial04 : num 1.333 0.856 1.938 1.754 1.949 ...
## $ BiologicalMaterial05 : num 0.413 -0.495 0.446 1.239 1.756 ...
## $ BiologicalMaterial06 : num 1.065 1.409 1.48 0.461 0.844 ...
## $ BiologicalMaterial07 : num -0.0898 -0.0898 -0.0898 -0.0898 -0.0898 ...
## $ BiologicalMaterial08 : num 2.36 1.88 2.07 1.56 2.01 ...
## $ BiologicalMaterial09 : num -0.7 0.239 0.662 -0.348 0.31 ...
## $ BiologicalMaterial10 : num 1.102 0.412 1.742 2.005 2.383 ...
## $ BiologicalMaterial11 : num 1.3657 0.0257 1.474 1.1921 2.3237 ...
## $ BiologicalMaterial12 : num 1.041 0.667 1.54 0.605 2.002 ...
## $ ManufacturingProcess01: num -6.353 0.124 0.405 -0.102 0.799 ...
## $ ManufacturingProcess02: num -1.92 -1.92 -1.92 -1.92 -1.92 ...
## $ ManufacturingProcess03: num 0.0513 0.8714 0.3588 0.8714 0.7689 ...
## $ ManufacturingProcess04: num -2.423 0.14 -0.501 -0.661 -0.501 ...
## $ ManufacturingProcess05: num 1.259 -0.451 0.418 1.074 3.63 ...
## $ ManufacturingProcess06: num 1.1393 1.1393 1.893 -0.6786 0.0308 ...
## $ ManufacturingProcess07: num -0.99 -0.99 1.01 -0.99 1.01 ...
## $ ManufacturingProcess08: num 0.931 0.931 0.931 -1.074 0.931 ...
## $ ManufacturingProcess09: num 0.6129 2.5274 2.0608 -0.0939 -0.8349 ...
## $ ManufacturingProcess10: num 0.561 3.257 1.388 -0.214 -0.347 ...
## $ ManufacturingProcess11: num 1.071 2.997 2.709 0.841 0.553 ...
## $ ManufacturingProcess12: num -0.463 -0.463 -0.463 -0.463 -0.463 ...
## $ ManufacturingProcess13: num -0.477 -2.007 -0.86 1.244 0.957 ...
## $ ManufacturingProcess14: num 0.2041 -2.0359 -0.0668 1.5229 1.7939 ...
## $ ManufacturingProcess15: num 0.863 -0.757 1.031 2.246 2.313 ...
## $ ManufacturingProcess16: num 0.138 -0.176 0.159 0.397 0.459 ...
## $ ManufacturingProcess17: num -0.224 -0.384 -0.545 1.22 0.979 ...
## $ ManufacturingProcess18: num 0.1587 -0.0908 -0.0725 0.1381 0.2045 ...
## $ ManufacturingProcess19: num 1.507 -0.352 -0.153 1.573 2.104 ...
## $ ManufacturingProcess20: num 0.1788 -0.06 0.0124 0.2632 0.3934 ...
## $ ManufacturingProcess21: num 0.289 2.126 0.289 0.289 0.289 ...
## $ ManufacturingProcess22: num -0.76 -1.36 -1.06 -1.36 -0.76 ...
## $ ManufacturingProcess23: num -1.834 -1.207 -0.579 -1.207 -0.579 ...
## $ ManufacturingProcess24: num -0.929 -1.265 -1.097 -1.265 -0.929 ...
## $ ManufacturingProcess25: num 0.1193 -0.0498 -0.0246 0.0987 0.1353 ...
## $ ManufacturingProcess26: num 0.193 0.102 0.105 0.18 0.197 ...
## $ ManufacturingProcess27: num 0.1858 0.046 0.0797 0.2558 0.345 ...
## $ ManufacturingProcess28: num 0.97 0.97 0.951 0.951 0.951 ...
## $ ManufacturingProcess29: num 0.75 0.645 0.645 0.698 0.75 ...
## $ ManufacturingProcess30: num 0.713 1.957 1.67 0.809 0.618 ...
## $ ManufacturingProcess31: num -0.196 -0.366 -0.32 -0.196 -0.181 ...
## $ ManufacturingProcess32: num 1.9773 0.0752 0.4556 1.5969 -0.4955 ...
## $ ManufacturingProcess33: num 0.952 0.554 0.554 1.747 0.156 ...
## $ ManufacturingProcess34: num 2.047 0.141 0.141 0.141 -1.764 ...
## $ ManufacturingProcess35: num 1.181 -1.91 -1.629 -0.037 1.743 ...
## $ ManufacturingProcess36: num -0.652 -0.652 -0.652 -0.652 1.741 ...
## $ ManufacturingProcess37: num 2.121 -0.464 -0.033 0.613 -0.679 ...
## $ ManufacturingProcess38: num -0.745 -0.745 -0.745 0.676 0.676 ...
## $ ManufacturingProcess39: num 0.273 0.33 0.33 0.386 0.33 ...
## $ ManufacturingProcess40: num 2.142 -0.467 -0.467 -0.467 -0.467 ...
## $ ManufacturingProcess41: num 2.332 -0.434 -0.434 -0.434 -0.434 ...
## $ ManufacturingProcess42: num 0.019 0.281 0.15 0.193 0.237 ...
## $ ManufacturingProcess43: num -0.012 -0.21 -0.111 0.186 0.879 ...
## $ ManufacturingProcess44: num 0.292 0.557 0.557 0.292 -0.237 ...
## $ ManufacturingProcess45: num 0.183 0.183 0.183 0.396 0.396 ...Train several tree-based models
| Overall | |
|---|---|
| BiologicalMaterial01 | 1.0250689 |
| BiologicalMaterial02 | 1.4550055 |
| BiologicalMaterial03 | 5.9695779 |
| BiologicalMaterial04 | 2.4935383 |
| BiologicalMaterial05 | 0.7129550 |
| BiologicalMaterial06 | 3.7359421 |
| BiologicalMaterial07 | 0.0005086 |
| BiologicalMaterial08 | 1.4371030 |
| BiologicalMaterial09 | 1.3084073 |
| BiologicalMaterial10 | 0.6959830 |
| BiologicalMaterial11 | 2.9299639 |
| BiologicalMaterial12 | 6.1489521 |
| ManufacturingProcess01 | 0.9435431 |
| ManufacturingProcess02 | 0.6483790 |
| ManufacturingProcess03 | 0.3637617 |
| ManufacturingProcess04 | 0.5762328 |
| ManufacturingProcess05 | 1.1475834 |
| ManufacturingProcess06 | 2.6527207 |
| ManufacturingProcess07 | 0.0668778 |
| ManufacturingProcess08 | 0.1224550 |
| ManufacturingProcess09 | 3.4785271 |
| ManufacturingProcess10 | 0.9026901 |
| ManufacturingProcess11 | 2.0330432 |
| ManufacturingProcess12 | 0.4326927 |
| ManufacturingProcess13 | 2.8946511 |
| ManufacturingProcess14 | 1.1526189 |
| ManufacturingProcess15 | 1.5735640 |
| ManufacturingProcess16 | 0.8626007 |
| ManufacturingProcess17 | 5.8170626 |
| ManufacturingProcess18 | 1.4992938 |
| ManufacturingProcess19 | 1.4261193 |
| ManufacturingProcess20 | 1.4365852 |
| ManufacturingProcess21 | 1.6587681 |
| ManufacturingProcess22 | 0.6126686 |
| ManufacturingProcess23 | 0.8103363 |
| ManufacturingProcess24 | 1.1744794 |
| ManufacturingProcess25 | 1.0061482 |
| ManufacturingProcess26 | 0.7727862 |
| ManufacturingProcess27 | 0.8181480 |
| ManufacturingProcess28 | 3.9845243 |
| ManufacturingProcess29 | 1.0267283 |
| ManufacturingProcess30 | 1.2909734 |
| ManufacturingProcess31 | 6.6565852 |
| ManufacturingProcess32 | 33.0039965 |
| ManufacturingProcess33 | 0.7751148 |
| ManufacturingProcess34 | 0.3618439 |
| ManufacturingProcess35 | 0.6434773 |
| ManufacturingProcess36 | 1.6743117 |
| ManufacturingProcess37 | 1.0821300 |
| ManufacturingProcess38 | 0.1257839 |
| ManufacturingProcess39 | 1.3273693 |
| ManufacturingProcess40 | 0.0560122 |
| ManufacturingProcess41 | 0.3654626 |
| ManufacturingProcess42 | 0.6595481 |
| ManufacturingProcess43 | 0.3945774 |
| ManufacturingProcess44 | 0.2757154 |
| ManufacturingProcess45 | 0.3537814 |
| Overall | |
|---|---|
| BiologicalMaterial01 | 6.4341814 |
| BiologicalMaterial02 | 2.8127243 |
| BiologicalMaterial03 | 14.8459444 |
| BiologicalMaterial04 | 2.5890775 |
| BiologicalMaterial05 | 6.6833813 |
| BiologicalMaterial06 | 0.9957944 |
| BiologicalMaterial07 | 0.0000000 |
| BiologicalMaterial08 | 1.9293870 |
| BiologicalMaterial09 | 7.2278283 |
| BiologicalMaterial10 | 6.4850761 |
| BiologicalMaterial11 | 11.8184609 |
| BiologicalMaterial12 | 23.3544791 |
| ManufacturingProcess01 | 14.9190522 |
| ManufacturingProcess02 | 3.0785285 |
| ManufacturingProcess03 | 0.8368619 |
| ManufacturingProcess04 | 4.8241147 |
| ManufacturingProcess05 | 9.5715555 |
| ManufacturingProcess06 | 46.0552692 |
| ManufacturingProcess07 | 0.6198725 |
| ManufacturingProcess08 | 1.0742612 |
| ManufacturingProcess09 | 19.5011478 |
| ManufacturingProcess10 | 11.6925874 |
| ManufacturingProcess11 | 0.7219243 |
| ManufacturingProcess12 | 0.0000000 |
| ManufacturingProcess13 | 10.2311028 |
| ManufacturingProcess14 | 9.9916996 |
| ManufacturingProcess15 | 2.7262477 |
| ManufacturingProcess16 | 5.4975773 |
| ManufacturingProcess17 | 29.2255062 |
| ManufacturingProcess18 | 2.4795584 |
| ManufacturingProcess19 | 8.2243394 |
| ManufacturingProcess20 | 7.8010646 |
| ManufacturingProcess21 | 9.5239938 |
| ManufacturingProcess22 | 9.8349179 |
| ManufacturingProcess23 | 3.7286159 |
| ManufacturingProcess24 | 14.1616677 |
| ManufacturingProcess25 | 4.4557453 |
| ManufacturingProcess26 | 6.4343469 |
| ManufacturingProcess27 | 3.9392445 |
| ManufacturingProcess28 | 0.1363688 |
| ManufacturingProcess29 | 7.4740151 |
| ManufacturingProcess30 | 7.7532269 |
| ManufacturingProcess31 | 7.8154062 |
| ManufacturingProcess32 | 149.7787687 |
| ManufacturingProcess33 | 0.3485179 |
| ManufacturingProcess34 | 0.5070327 |
| ManufacturingProcess35 | 2.7553915 |
| ManufacturingProcess36 | 1.1289224 |
| ManufacturingProcess37 | 8.7236303 |
| ManufacturingProcess38 | 0.3696117 |
| ManufacturingProcess39 | 9.2049393 |
| ManufacturingProcess40 | 0.0000000 |
| ManufacturingProcess41 | 0.0000000 |
| ManufacturingProcess42 | 1.2032836 |
| ManufacturingProcess43 | 5.8319692 |
| ManufacturingProcess44 | 1.9204451 |
| ManufacturingProcess45 | 1.0357162 |
| Overall | |
|---|---|
| ManufacturingProcess17 | 42.5 |
| ManufacturingProcess39 | 21.0 |
| ManufacturingProcess32 | 47.5 |
| BiologicalMaterial12 | 22.0 |
| ManufacturingProcess31 | 4.0 |
| BiologicalMaterial05 | 2.5 |
| ManufacturingProcess06 | 14.0 |
| ManufacturingProcess22 | 1.0 |
| BiologicalMaterial04 | 3.0 |
| ManufacturingProcess29 | 14.5 |
| ManufacturingProcess25 | 14.5 |
| ManufacturingProcess09 | 12.5 |
| BiologicalMaterial03 | 11.0 |
| ManufacturingProcess13 | 10.5 |
| ManufacturingProcess33 | 10.5 |
| ManufacturingProcess11 | 10.0 |
| ManufacturingProcess26 | 8.0 |
| BiologicalMaterial08 | 8.0 |
| ManufacturingProcess24 | 8.0 |
| BiologicalMaterial09 | 7.5 |
| BiologicalMaterial02 | 7.0 |
| ManufacturingProcess27 | 7.0 |
| BiologicalMaterial06 | 5.0 |
| ManufacturingProcess18 | 4.0 |
| ManufacturingProcess16 | 3.5 |
| ManufacturingProcess15 | 3.5 |
| ManufacturingProcess20 | 3.5 |
| ManufacturingProcess04 | 3.0 |
| ManufacturingProcess03 | 2.5 |
| ManufacturingProcess23 | 2.5 |
| ManufacturingProcess05 | 2.0 |
| BiologicalMaterial10 | 2.0 |
| ManufacturingProcess12 | 2.0 |
| ManufacturingProcess19 | 2.0 |
| ManufacturingProcess21 | 2.0 |
| ManufacturingProcess01 | 1.5 |
| BiologicalMaterial11 | 1.5 |
| ManufacturingProcess43 | 1.0 |
| ManufacturingProcess02 | 1.0 |
| BiologicalMaterial01 | 0.0 |
| BiologicalMaterial07 | 0.0 |
| ManufacturingProcess07 | 0.0 |
| ManufacturingProcess08 | 0.0 |
| ManufacturingProcess10 | 0.0 |
| ManufacturingProcess14 | 0.0 |
| ManufacturingProcess28 | 0.0 |
| ManufacturingProcess30 | 0.0 |
| ManufacturingProcess34 | 0.0 |
| ManufacturingProcess35 | 0.0 |
| ManufacturingProcess36 | 0.0 |
| ManufacturingProcess37 | 0.0 |
| ManufacturingProcess38 | 0.0 |
| ManufacturingProcess40 | 0.0 |
| ManufacturingProcess41 | 0.0 |
| ManufacturingProcess42 | 0.0 |
| ManufacturingProcess44 | 0.0 |
| ManufacturingProcess45 | 0.0 |
| Overall | |
|---|---|
| BiologicalMaterial01 | 0.1435384 |
| BiologicalMaterial02 | 0.1814203 |
| BiologicalMaterial03 | 0.5798112 |
| BiologicalMaterial04 | 0.2007435 |
| BiologicalMaterial05 | 0.2899065 |
| BiologicalMaterial06 | 0.2959157 |
| BiologicalMaterial07 | 0.0000000 |
| BiologicalMaterial08 | 0.2973043 |
| BiologicalMaterial09 | 0.3102775 |
| BiologicalMaterial10 | 0.1051152 |
| BiologicalMaterial11 | 0.5915191 |
| BiologicalMaterial12 | 0.8861626 |
| ManufacturingProcess01 | 0.2944574 |
| ManufacturingProcess02 | 0.1560424 |
| ManufacturingProcess03 | 0.0211690 |
| ManufacturingProcess04 | 0.1466957 |
| ManufacturingProcess05 | 0.1728725 |
| ManufacturingProcess06 | 0.5584584 |
| ManufacturingProcess07 | 0.0514549 |
| ManufacturingProcess08 | 0.0108126 |
| ManufacturingProcess09 | 0.6598441 |
| ManufacturingProcess10 | 0.2194264 |
| ManufacturingProcess11 | 0.5608103 |
| ManufacturingProcess12 | 0.0699787 |
| ManufacturingProcess13 | 0.5120909 |
| ManufacturingProcess14 | 0.3759635 |
| ManufacturingProcess15 | 0.4535918 |
| ManufacturingProcess16 | 0.2416880 |
| ManufacturingProcess17 | 1.0955617 |
| ManufacturingProcess18 | 0.2502621 |
| ManufacturingProcess19 | 0.3272336 |
| ManufacturingProcess20 | 0.2773384 |
| ManufacturingProcess21 | 0.3755464 |
| ManufacturingProcess22 | 0.0639143 |
| ManufacturingProcess23 | 0.1269655 |
| ManufacturingProcess24 | 0.2260277 |
| ManufacturingProcess25 | 0.2290149 |
| ManufacturingProcess26 | 0.1301623 |
| ManufacturingProcess27 | 0.2417423 |
| ManufacturingProcess28 | 0.4171542 |
| ManufacturingProcess29 | 0.1861834 |
| ManufacturingProcess30 | 0.3179287 |
| ManufacturingProcess31 | 0.7062981 |
| ManufacturingProcess32 | 0.7588114 |
| ManufacturingProcess33 | 0.0548682 |
| ManufacturingProcess34 | 0.0000000 |
| ManufacturingProcess35 | 0.1346992 |
| ManufacturingProcess36 | 0.0832284 |
| ManufacturingProcess37 | 0.1663320 |
| ManufacturingProcess38 | 0.0157006 |
| ManufacturingProcess39 | 0.1964913 |
| ManufacturingProcess40 | 0.0160962 |
| ManufacturingProcess41 | 0.0160962 |
| ManufacturingProcess42 | 0.1275682 |
| ManufacturingProcess43 | 0.1064286 |
| ManufacturingProcess44 | 0.0563482 |
| ManufacturingProcess45 | 0.1288447 |
(a) Which tree-based regression model gives the optimal resampling and test set performance?
| Model | RMSE | Rsquared | MAE |
|---|---|---|---|
| Random Forest | 0.7014812 | 0.6604003 | 0.5401092 |
| Gradient Boosting | 0.6974752 | 0.6490253 | 0.5267574 |
| Cubist | 0.5656923 | 0.7543585 | 0.4446262 |
| Bagged Tree | 0.7269549 | 0.5957590 | 0.5366908 |
Based on the performance metrics provided, the Cubist model shows the best overall performance across the given metrics, indicating it likely gives the optimal resampling and test set performance among the listed tree-based regression models.
RMSE (Root Mean Squared Error): Lower RMSE values indicate better performance. The Cubist model has the lowest RMSE at 0.5657, indicating better prediction accuracy.
R² (R-squared): Higher R-squared values indicate better fit, with values closer to 1 being preferable. The Cubist model has the highest R-squared at 0.7544, indicating it explains the variance in the target variable better than the others.
MAE (Mean Absolute Error): Lower MAE values indicate better performance, reflecting smaller prediction errors. The Cubist model also has the lowest MAE at 0.4446, showing it has lower prediction errors on average.
(b) Which predictors are most important in the optimal tree-based regression model?
| Overall | |
|---|---|
| ManufacturingProcess32 | 100.00000 |
| ManufacturingProcess17 | 89.47368 |
| BiologicalMaterial12 | 46.31579 |
| ManufacturingProcess39 | 44.21053 |
| ManufacturingProcess29 | 30.52632 |
| ManufacturingProcess25 | 30.52632 |
| ManufacturingProcess06 | 29.47368 |
| ManufacturingProcess09 | 26.31579 |
| BiologicalMaterial03 | 23.15789 |
| ManufacturingProcess13 | 22.10526 |
These predictors have been ranked based on their importance values, with ManufacturingProcess32 being the most influential predictor, followed by ManufacturingProcess17. The chart I created accurately reflects this ranking by displaying these predictors in descending order of importance.
Do either the biological or process variables dominate the list?
Based on the top 10 important predictors you provided, it appears that the process variables dominate the list. Here’s a breakdown:
Process Variables:
ManufacturingProcess32 ManufacturingProcess17 ManufacturingProcess39 ManufacturingProcess29 ManufacturingProcess25 ManufacturingProcess06 ManufacturingProcess09 ManufacturingProcess13 There are 8 process-related variables in the top 10.
Biological Variables:
BiologicalMaterial12 BiologicalMaterial03
There are 2 biological variables in the top 10.
The process variables clearly dominate the list of top predictors, with 8 out of the top 10 most important predictors being related to manufacturing processes. This suggests that in this model, the manufacturing processes have a greater impact on the target variable than the biological materials.
How do the top 10 important predictors compare to the top 10 predictors from the optimal linear and nonlinear models?
## ### Linear Regression Results ##### RMSE Rsquared MAE
## 0.8285972 0.5095169 0.6407973## ### SVM Results ##### RMSE Rsquared MAE
## 0.7642341 0.5855119 0.5910040## ### KNN Metrics Results ##### RMSE Rsquared MAE
## 0.8462222 0.4379732 0.7106254## # weights: 60
## initial value 158.409217
## final value 138.010105
## converged
## # weights: 178
## initial value 162.657532
## final value 138.010105
## converged
## # weights: 296
## initial value 191.618501
## final value 138.010105
## converged
## # weights: 60
## initial value 186.915115
## iter 10 value 137.524487
## iter 20 value 97.266784
## iter 30 value 92.747332
## iter 40 value 91.607796
## iter 50 value 91.486835
## iter 60 value 90.730225
## iter 70 value 90.567804
## iter 80 value 90.519484
## final value 90.519302
## converged
## # weights: 178
## initial value 176.114373
## iter 10 value 104.640026
## iter 20 value 90.514797
## iter 30 value 88.620311
## iter 40 value 87.744114
## iter 50 value 87.683245
## iter 60 value 87.680905
## iter 70 value 87.680309
## iter 80 value 87.678479
## iter 90 value 87.628359
## iter 100 value 87.444198
## final value 87.444198
## stopped after 100 iterations
## # weights: 296
## initial value 189.483654
## iter 10 value 104.716186
## iter 20 value 91.277749
## iter 30 value 88.841857
## iter 40 value 87.611289
## iter 50 value 87.394278
## iter 60 value 87.100503
## iter 70 value 86.190594
## iter 80 value 85.902408
## iter 90 value 85.713085
## iter 100 value 85.568056
## final value 85.568056
## stopped after 100 iterations
## # weights: 60
## initial value 160.269187
## iter 10 value 138.011602
## iter 20 value 138.010624
## iter 30 value 138.009455
## iter 40 value 138.008026
## iter 50 value 138.006236
## iter 60 value 138.003914
## iter 70 value 138.000769
## iter 80 value 137.996240
## iter 90 value 137.989109
## iter 100 value 137.976114
## final value 137.976114
## stopped after 100 iterations
## # weights: 178
## initial value 186.709623
## iter 10 value 138.023010
## iter 20 value 138.007882
## iter 30 value 89.379531
## iter 40 value 82.118709
## iter 50 value 81.647256
## iter 60 value 80.532407
## iter 70 value 80.430132
## iter 80 value 80.362522
## iter 90 value 80.316221
## iter 100 value 80.023866
## final value 80.023866
## stopped after 100 iterations
## # weights: 296
## initial value 187.207704
## iter 10 value 138.027654
## iter 20 value 134.947281
## iter 30 value 81.222016
## iter 40 value 80.470900
## iter 50 value 80.313861
## iter 60 value 80.274329
## iter 70 value 80.270310
## iter 80 value 80.250275
## iter 90 value 80.213986
## iter 100 value 80.189836
## final value 80.189836
## stopped after 100 iterations
## # weights: 60
## initial value 101.307121
## final value 92.036094
## converged
## # weights: 178
## initial value 124.865488
## final value 92.036104
## converged
## # weights: 296
## initial value 139.515740
## final value 92.036104
## converged
## # weights: 60
## initial value 109.119678
## iter 10 value 80.534650
## iter 20 value 67.039634
## iter 30 value 60.298857
## iter 40 value 57.900940
## iter 50 value 57.663056
## iter 60 value 57.621939
## final value 57.621779
## converged
## # weights: 178
## initial value 105.893055
## iter 10 value 63.155531
## iter 20 value 57.256234
## iter 30 value 55.599448
## iter 40 value 55.445834
## iter 50 value 55.407712
## iter 60 value 55.387912
## iter 70 value 55.385010
## iter 80 value 55.381640
## iter 90 value 55.381568
## final value 55.381563
## converged
## # weights: 296
## initial value 131.507907
## iter 10 value 68.606231
## iter 20 value 59.213952
## iter 30 value 55.703478
## iter 40 value 54.639093
## iter 50 value 54.418161
## iter 60 value 54.403564
## iter 70 value 54.401825
## iter 80 value 54.401700
## iter 90 value 54.401688
## final value 54.401686
## converged
## # weights: 60
## initial value 138.474675
## iter 10 value 92.050679
## iter 20 value 92.047655
## iter 30 value 92.047572
## iter 40 value 92.047487
## iter 50 value 92.047400
## iter 60 value 92.047311
## iter 70 value 92.047220
## iter 80 value 92.047127
## iter 90 value 92.047033
## iter 100 value 92.046938
## final value 92.046938
## stopped after 100 iterations
## # weights: 178
## initial value 120.206681
## iter 10 value 92.043810
## iter 20 value 92.000145
## iter 30 value 58.143055
## iter 40 value 51.932807
## iter 50 value 51.702084
## iter 60 value 51.630965
## iter 70 value 50.756677
## iter 80 value 49.820559
## iter 90 value 49.381560
## iter 100 value 49.262591
## final value 49.262591
## stopped after 100 iterations
## # weights: 296
## initial value 147.156743
## iter 10 value 92.051166
## iter 20 value 91.974336
## iter 30 value 60.266153
## iter 40 value 54.820069
## iter 50 value 54.579474
## iter 60 value 54.549254
## iter 70 value 54.444602
## iter 80 value 53.383752
## iter 90 value 53.358021
## iter 100 value 53.295363
## final value 53.295363
## stopped after 100 iterations
## # weights: 60
## initial value 117.190271
## final value 110.782090
## converged
## # weights: 178
## initial value 113.079356
## final value 110.782033
## converged
## # weights: 296
## initial value 149.893435
## final value 110.782090
## converged
## # weights: 60
## initial value 141.003780
## iter 10 value 78.572536
## iter 20 value 60.236589
## iter 30 value 58.910427
## iter 40 value 58.812757
## iter 50 value 58.208768
## iter 60 value 58.136179
## iter 70 value 58.134301
## iter 70 value 58.134301
## iter 70 value 58.134301
## final value 58.134301
## converged
## # weights: 178
## initial value 138.333129
## iter 10 value 79.541039
## iter 20 value 61.189426
## iter 30 value 56.688572
## iter 40 value 56.257648
## iter 50 value 55.847008
## iter 60 value 55.838369
## final value 55.838318
## converged
## # weights: 296
## initial value 134.838236
## iter 10 value 76.420657
## iter 20 value 59.057489
## iter 30 value 55.568802
## iter 40 value 54.362658
## iter 50 value 54.155544
## iter 60 value 54.135473
## iter 70 value 54.133407
## iter 80 value 54.133272
## final value 54.133268
## converged
## # weights: 60
## initial value 135.720714
## iter 10 value 110.789892
## iter 20 value 110.789489
## iter 30 value 110.789048
## iter 40 value 110.788563
## iter 50 value 110.788024
## iter 60 value 110.787422
## iter 70 value 110.786741
## iter 80 value 110.785961
## iter 90 value 110.785058
## iter 100 value 110.783995
## final value 110.783995
## stopped after 100 iterations
## # weights: 178
## initial value 123.378233
## iter 10 value 110.765688
## iter 20 value 110.709914
## iter 30 value 110.123752
## iter 40 value 54.972985
## iter 50 value 51.836905
## iter 60 value 51.683795
## iter 70 value 51.515530
## iter 80 value 50.391524
## iter 90 value 50.364623
## iter 100 value 50.345001
## final value 50.345001
## stopped after 100 iterations
## # weights: 296
## initial value 141.732263
## iter 10 value 110.793343
## iter 20 value 110.778974
## iter 30 value 110.660371
## iter 40 value 86.334223
## iter 50 value 79.180988
## iter 60 value 74.266659
## iter 70 value 73.752894
## iter 80 value 66.339096
## iter 90 value 66.199043
## iter 100 value 65.804161
## final value 65.804161
## stopped after 100 iterations
## # weights: 60
## initial value 148.113088
## final value 111.535550
## converged
## # weights: 178
## initial value 145.117085
## final value 111.535550
## converged
## # weights: 296
## initial value 143.304121
## final value 111.535550
## converged
## # weights: 60
## initial value 156.555144
## iter 10 value 84.514917
## iter 20 value 71.569678
## iter 30 value 67.748206
## iter 40 value 67.227625
## iter 50 value 65.939477
## iter 60 value 65.859060
## iter 70 value 65.855550
## final value 65.855547
## converged
## # weights: 178
## initial value 136.224260
## iter 10 value 80.261554
## iter 20 value 66.092943
## iter 30 value 62.951071
## iter 40 value 62.496674
## iter 50 value 62.353414
## iter 60 value 62.327894
## iter 70 value 62.326304
## iter 80 value 62.324749
## iter 90 value 62.324532
## final value 62.324522
## converged
## # weights: 296
## initial value 146.680123
## iter 10 value 83.112685
## iter 20 value 65.941609
## iter 30 value 63.912779
## iter 40 value 63.373760
## iter 50 value 63.258548
## iter 60 value 63.227053
## iter 70 value 63.223925
## iter 80 value 63.219998
## iter 90 value 63.219416
## iter 100 value 63.219165
## final value 63.219165
## stopped after 100 iterations
## # weights: 60
## initial value 124.833859
## iter 10 value 111.555435
## iter 20 value 111.541104
## iter 30 value 111.540732
## iter 40 value 111.540332
## iter 50 value 111.539903
## iter 60 value 111.539442
## iter 70 value 111.538945
## iter 80 value 111.538409
## iter 90 value 111.537829
## iter 100 value 111.537198
## final value 111.537198
## stopped after 100 iterations
## # weights: 178
## initial value 161.920614
## iter 10 value 111.553035
## iter 20 value 95.602727
## iter 30 value 59.241038
## iter 40 value 57.511543
## iter 50 value 57.164501
## iter 60 value 56.286448
## iter 70 value 56.276988
## iter 80 value 56.272791
## iter 90 value 56.210819
## iter 100 value 56.128738
## final value 56.128738
## stopped after 100 iterations
## # weights: 296
## initial value 127.151680
## iter 10 value 111.548190
## iter 20 value 111.542780
## iter 30 value 111.542326
## iter 40 value 111.541751
## iter 50 value 111.541013
## iter 60 value 111.540032
## iter 70 value 111.538624
## iter 80 value 111.536341
## iter 90 value 111.531779
## iter 100 value 111.518732
## final value 111.518732
## stopped after 100 iterations
## # weights: 60
## initial value 181.776571
## final value 145.337517
## converged
## # weights: 178
## initial value 181.869205
## final value 145.337517
## converged
## # weights: 296
## initial value 143.951731
## iter 10 value 83.319117
## iter 20 value 82.231265
## iter 30 value 81.884397
## iter 40 value 81.841650
## iter 50 value 81.741808
## iter 60 value 81.589500
## iter 70 value 81.573077
## iter 80 value 81.561944
## iter 90 value 81.559009
## iter 100 value 81.558159
## final value 81.558159
## stopped after 100 iterations
## # weights: 60
## initial value 155.853743
## iter 10 value 97.055107
## iter 20 value 92.477952
## iter 30 value 91.461080
## iter 40 value 90.965453
## iter 50 value 90.955164
## iter 60 value 90.935642
## final value 90.932132
## converged
## # weights: 178
## initial value 166.778734
## iter 10 value 96.910061
## iter 20 value 88.587100
## iter 30 value 85.988713
## iter 40 value 85.057806
## iter 50 value 84.804151
## iter 60 value 84.728888
## iter 70 value 84.725088
## iter 80 value 84.724202
## iter 90 value 84.723368
## iter 100 value 84.723169
## final value 84.723169
## stopped after 100 iterations
## # weights: 296
## initial value 198.690489
## iter 10 value 104.259596
## iter 20 value 89.866836
## iter 30 value 87.064758
## iter 40 value 86.091774
## iter 50 value 85.926309
## iter 60 value 85.865185
## iter 70 value 85.833350
## iter 80 value 85.814931
## iter 90 value 85.813828
## iter 100 value 85.812805
## final value 85.812805
## stopped after 100 iterations
## # weights: 60
## initial value 150.614189
## iter 10 value 145.015189
## iter 20 value 89.209391
## iter 30 value 83.175383
## iter 40 value 82.977342
## iter 50 value 82.973476
## iter 60 value 82.970022
## iter 70 value 82.858768
## iter 80 value 82.846047
## iter 90 value 82.841032
## iter 100 value 82.838131
## final value 82.838131
## stopped after 100 iterations
## # weights: 178
## initial value 170.768161
## iter 10 value 145.351392
## iter 20 value 145.349933
## iter 30 value 145.348123
## iter 40 value 145.345799
## iter 50 value 145.342715
## iter 60 value 145.338469
## iter 70 value 145.332191
## iter 80 value 145.321688
## iter 90 value 145.299853
## iter 100 value 145.224687
## final value 145.224687
## stopped after 100 iterations
## # weights: 296
## initial value 166.363171
## iter 10 value 145.355437
## iter 20 value 145.343050
## iter 30 value 92.044827
## iter 40 value 80.653268
## iter 50 value 80.301636
## iter 60 value 79.703345
## iter 70 value 79.609287
## iter 80 value 79.510267
## iter 90 value 79.484632
## iter 100 value 79.469318
## final value 79.469318
## stopped after 100 iterations
## # weights: 60
## initial value 174.773008
## final value 143.064074
## converged
## # weights: 178
## initial value 176.681649
## final value 143.064074
## converged
## # weights: 296
## initial value 195.881704
## final value 143.064074
## converged
## # weights: 60
## initial value 181.294881
## iter 10 value 108.027898
## iter 20 value 98.707361
## iter 30 value 95.310955
## iter 40 value 94.334734
## iter 50 value 94.204835
## iter 60 value 94.201133
## final value 94.201130
## converged
## # weights: 178
## initial value 179.174043
## iter 10 value 99.846334
## iter 20 value 92.206549
## iter 30 value 91.774180
## iter 40 value 91.671668
## iter 50 value 91.661835
## iter 60 value 91.661385
## iter 70 value 91.661172
## final value 91.661152
## converged
## # weights: 296
## initial value 175.732185
## iter 10 value 110.341082
## iter 20 value 92.481877
## iter 30 value 90.713957
## iter 40 value 90.480468
## iter 50 value 90.425496
## iter 60 value 90.383544
## iter 70 value 90.381714
## iter 80 value 90.381636
## iter 90 value 90.379520
## iter 100 value 90.378988
## final value 90.378988
## stopped after 100 iterations
## # weights: 60
## initial value 166.990597
## iter 10 value 143.067314
## iter 20 value 143.066285
## iter 30 value 143.065045
## iter 40 value 143.063518
## iter 50 value 143.061585
## iter 60 value 143.059050
## iter 70 value 143.055571
## iter 80 value 143.050478
## iter 90 value 143.042274
## iter 100 value 143.026757
## final value 143.026757
## stopped after 100 iterations
## # weights: 178
## initial value 168.769996
## iter 10 value 143.078181
## iter 20 value 143.077831
## iter 30 value 143.077455
## iter 40 value 143.077049
## iter 50 value 143.076608
## iter 60 value 143.076124
## iter 70 value 143.075590
## iter 80 value 143.074994
## iter 90 value 143.074323
## iter 100 value 143.073556
## final value 143.073556
## stopped after 100 iterations
## # weights: 296
## initial value 168.936341
## iter 10 value 143.073110
## iter 20 value 97.142341
## iter 30 value 90.965991
## iter 40 value 89.933203
## iter 50 value 88.910535
## iter 60 value 88.846388
## iter 70 value 88.812875
## iter 80 value 88.803529
## iter 90 value 88.495830
## iter 100 value 88.256801
## final value 88.256801
## stopped after 100 iterations
## # weights: 60
## initial value 138.260947
## final value 131.801757
## converged
## # weights: 178
## initial value 141.604088
## final value 131.801815
## converged
## # weights: 296
## initial value 175.752055
## final value 131.801815
## converged
## # weights: 60
## initial value 149.172494
## iter 10 value 94.729193
## iter 20 value 84.430060
## iter 30 value 80.327851
## iter 40 value 77.809102
## iter 50 value 77.529677
## iter 60 value 77.504886
## final value 77.504847
## converged
## # weights: 178
## initial value 137.266172
## iter 10 value 83.241424
## iter 20 value 76.538862
## iter 30 value 74.118106
## iter 40 value 73.808411
## iter 50 value 73.464952
## iter 60 value 73.419749
## iter 70 value 73.411253
## iter 80 value 73.389536
## iter 90 value 73.387761
## final value 73.387692
## converged
## # weights: 296
## initial value 168.672312
## iter 10 value 94.201811
## iter 20 value 79.946866
## iter 30 value 75.761222
## iter 40 value 74.300040
## iter 50 value 73.167837
## iter 60 value 73.026479
## iter 70 value 72.942206
## iter 80 value 72.930807
## iter 90 value 72.930130
## iter 100 value 72.929665
## final value 72.929665
## stopped after 100 iterations
## # weights: 60
## initial value 175.930692
## iter 10 value 131.821657
## iter 20 value 131.814654
## iter 30 value 131.814178
## iter 40 value 131.813679
## iter 50 value 131.813146
## iter 60 value 131.812562
## iter 70 value 131.811903
## iter 80 value 131.811129
## iter 90 value 131.810189
## iter 100 value 131.809042
## final value 131.809042
## stopped after 100 iterations
## # weights: 178
## initial value 142.340054
## iter 10 value 131.820464
## iter 20 value 131.818558
## iter 30 value 131.816050
## iter 40 value 131.813384
## iter 50 value 131.810397
## iter 60 value 131.806628
## iter 70 value 131.801299
## iter 80 value 131.792798
## iter 90 value 131.776667
## iter 100 value 131.733322
## final value 131.733322
## stopped after 100 iterations
## # weights: 296
## initial value 146.118608
## iter 10 value 131.817873
## iter 20 value 131.809262
## iter 30 value 131.802764
## iter 40 value 131.794284
## iter 50 value 131.778924
## iter 60 value 131.718897
## iter 70 value 80.438595
## iter 80 value 72.227322
## iter 90 value 71.678628
## iter 100 value 69.925565
## final value 69.925565
## stopped after 100 iterations
## # weights: 60
## initial value 184.009125
## final value 133.263981
## converged
## # weights: 178
## initial value 152.726831
## final value 133.263981
## converged
## # weights: 296
## initial value 153.708974
## final value 133.263981
## converged
## # weights: 60
## initial value 157.861770
## iter 10 value 107.750495
## iter 20 value 92.953617
## iter 30 value 89.336987
## iter 40 value 87.520725
## iter 50 value 86.881407
## iter 60 value 86.656911
## final value 86.655489
## converged
## # weights: 178
## initial value 183.524237
## iter 10 value 108.872204
## iter 20 value 90.376848
## iter 30 value 87.223766
## iter 40 value 85.254958
## iter 50 value 83.214067
## iter 60 value 82.831769
## iter 70 value 82.808170
## iter 80 value 82.800759
## iter 90 value 82.800333
## iter 100 value 82.798724
## final value 82.798724
## stopped after 100 iterations
## # weights: 296
## initial value 175.584864
## iter 10 value 106.157978
## iter 20 value 85.210206
## iter 30 value 83.886088
## iter 40 value 83.774191
## iter 50 value 83.761625
## iter 60 value 83.754455
## final value 83.754349
## converged
## # weights: 60
## initial value 200.319270
## iter 10 value 133.279642
## iter 20 value 133.273870
## iter 30 value 133.271864
## iter 40 value 133.156751
## iter 50 value 97.921034
## iter 60 value 81.555161
## iter 70 value 77.972400
## iter 80 value 77.896650
## iter 90 value 77.888740
## iter 100 value 77.862130
## final value 77.862130
## stopped after 100 iterations
## # weights: 178
## initial value 164.883403
## iter 10 value 133.279119
## iter 20 value 133.278813
## iter 30 value 133.278489
## iter 40 value 133.278146
## iter 50 value 133.277781
## iter 60 value 133.277393
## iter 70 value 133.276978
## iter 80 value 133.276530
## iter 90 value 133.276044
## iter 100 value 133.275514
## final value 133.275514
## stopped after 100 iterations
## # weights: 296
## initial value 161.161927
## iter 10 value 133.274350
## iter 20 value 133.269226
## iter 30 value 133.268602
## iter 40 value 133.267597
## iter 50 value 133.265629
## iter 60 value 133.260989
## iter 70 value 133.250450
## iter 80 value 133.219004
## iter 90 value 125.496264
## iter 100 value 80.734713
## final value 80.734713
## stopped after 100 iterations
## # weights: 60
## initial value 139.289941
## final value 113.388734
## converged
## # weights: 178
## initial value 159.415392
## final value 113.388734
## converged
## # weights: 296
## initial value 157.924706
## final value 113.388734
## converged
## # weights: 60
## initial value 158.693071
## iter 10 value 92.294823
## iter 20 value 84.618266
## iter 30 value 81.965763
## iter 40 value 80.027005
## iter 50 value 79.939616
## final value 79.939411
## converged
## # weights: 178
## initial value 140.418674
## iter 10 value 88.021358
## iter 20 value 81.842120
## iter 30 value 78.681442
## iter 40 value 77.717065
## iter 50 value 77.487255
## iter 60 value 77.426775
## iter 70 value 77.422786
## iter 80 value 77.422477
## final value 77.422469
## converged
## # weights: 296
## initial value 165.535946
## iter 10 value 97.494707
## iter 20 value 82.696975
## iter 30 value 79.238579
## iter 40 value 77.218711
## iter 50 value 77.062680
## iter 60 value 77.049897
## iter 70 value 77.036654
## iter 80 value 77.036210
## iter 90 value 77.036161
## final value 77.036159
## converged
## # weights: 60
## initial value 166.189958
## iter 10 value 113.404199
## iter 20 value 113.401138
## iter 30 value 113.382158
## iter 40 value 113.378200
## iter 50 value 113.372235
## iter 60 value 113.362123
## iter 70 value 113.341011
## iter 80 value 113.269326
## iter 90 value 99.035456
## iter 100 value 84.807476
## final value 84.807476
## stopped after 100 iterations
## # weights: 178
## initial value 169.886711
## iter 10 value 113.401477
## iter 20 value 113.393225
## iter 30 value 113.376935
## iter 40 value 113.255804
## iter 50 value 79.882365
## iter 60 value 73.399362
## iter 70 value 70.859908
## iter 80 value 70.504168
## iter 90 value 70.416897
## iter 100 value 70.390989
## final value 70.390989
## stopped after 100 iterations
## # weights: 296
## initial value 134.474839
## iter 10 value 113.393804
## iter 20 value 113.393080
## iter 30 value 113.392140
## iter 40 value 113.390858
## iter 50 value 113.388993
## iter 60 value 113.385857
## iter 70 value 113.380445
## iter 80 value 113.371023
## iter 90 value 113.342510
## iter 100 value 88.885979
## final value 88.885979
## stopped after 100 iterations
## # weights: 60
## initial value 145.021439
## final value 118.724424
## converged
## # weights: 178
## initial value 188.896637
## final value 118.724424
## converged
## # weights: 296
## initial value 157.323671
## final value 118.724424
## converged
## # weights: 60
## initial value 182.144353
## iter 10 value 93.069991
## iter 20 value 86.410864
## iter 30 value 83.502132
## iter 40 value 82.819543
## iter 50 value 82.809890
## final value 82.809885
## converged
## # weights: 178
## initial value 158.901052
## iter 10 value 94.501950
## iter 20 value 81.845022
## iter 30 value 78.488711
## iter 40 value 78.283946
## iter 50 value 78.267683
## iter 60 value 78.266405
## iter 70 value 78.266051
## final value 78.266036
## converged
## # weights: 296
## initial value 174.945795
## iter 10 value 106.603328
## iter 20 value 80.887562
## iter 30 value 78.078284
## iter 40 value 77.791137
## iter 50 value 77.684926
## iter 60 value 77.659723
## iter 70 value 77.609261
## iter 80 value 77.586141
## iter 90 value 77.585167
## iter 100 value 77.585067
## final value 77.585067
## stopped after 100 iterations
## # weights: 60
## initial value 166.154310
## iter 10 value 118.743596
## iter 20 value 118.737144
## final value 118.734833
## converged
## # weights: 178
## initial value 172.013418
## iter 10 value 118.738755
## iter 20 value 116.993118
## iter 30 value 75.937415
## iter 40 value 73.742646
## iter 50 value 71.227487
## iter 60 value 70.846993
## iter 70 value 70.815772
## iter 80 value 70.810602
## iter 90 value 70.702603
## iter 100 value 70.697218
## final value 70.697218
## stopped after 100 iterations
## # weights: 296
## initial value 171.730989
## iter 10 value 118.744873
## iter 20 value 118.656580
## iter 30 value 80.002323
## iter 40 value 79.695294
## iter 50 value 79.251453
## iter 60 value 76.058110
## iter 70 value 75.864023
## iter 80 value 74.517500
## iter 90 value 74.274810
## iter 100 value 74.129143
## final value 74.129143
## stopped after 100 iterations
## # weights: 60
## initial value 186.110176
## final value 109.855667
## converged
## # weights: 178
## initial value 128.839743
## final value 109.855667
## converged
## # weights: 296
## initial value 131.125067
## final value 109.855667
## converged
## # weights: 60
## initial value 155.751991
## iter 10 value 100.277713
## iter 20 value 81.715729
## iter 30 value 75.790914
## iter 40 value 75.298564
## iter 50 value 75.246101
## final value 75.245972
## converged
## # weights: 178
## initial value 162.567528
## iter 10 value 85.334160
## iter 20 value 73.818580
## iter 30 value 73.333944
## iter 40 value 73.173337
## iter 50 value 73.144720
## final value 73.144487
## converged
## # weights: 296
## initial value 157.095965
## iter 10 value 86.463141
## iter 20 value 73.779182
## iter 30 value 73.034642
## iter 40 value 72.943623
## iter 50 value 72.938515
## iter 60 value 72.938295
## final value 72.938293
## converged
## # weights: 60
## initial value 156.048261
## iter 10 value 109.870813
## iter 20 value 109.861960
## iter 30 value 102.544661
## iter 40 value 96.627910
## iter 50 value 94.912038
## iter 60 value 94.903210
## iter 70 value 94.812553
## iter 80 value 90.794094
## iter 90 value 87.916746
## iter 100 value 87.847291
## final value 87.847291
## stopped after 100 iterations
## # weights: 178
## initial value 134.351854
## iter 10 value 109.869498
## iter 20 value 83.970868
## iter 30 value 66.618439
## iter 40 value 66.242093
## iter 50 value 66.131203
## iter 60 value 66.116424
## iter 70 value 65.987269
## iter 80 value 65.958577
## iter 90 value 65.953170
## iter 100 value 65.946573
## final value 65.946573
## stopped after 100 iterations
## # weights: 296
## initial value 189.104124
## iter 10 value 109.871622
## iter 20 value 104.218545
## iter 30 value 81.727719
## iter 40 value 81.599631
## iter 50 value 81.480786
## iter 60 value 77.744483
## iter 70 value 77.241535
## iter 80 value 77.092946
## iter 90 value 77.066576
## iter 100 value 76.903381
## final value 76.903381
## stopped after 100 iterations
## # weights: 60
## initial value 164.226056
## final value 97.748603
## converged
## # weights: 178
## initial value 121.132444
## final value 97.748603
## converged
## # weights: 296
## initial value 144.017104
## final value 97.748603
## converged
## # weights: 60
## initial value 167.626915
## iter 10 value 83.223329
## iter 20 value 75.701093
## iter 30 value 74.164476
## iter 40 value 72.768485
## iter 50 value 70.974647
## iter 60 value 70.886570
## final value 70.885772
## converged
## # weights: 178
## initial value 171.469773
## iter 10 value 87.357656
## iter 20 value 74.227670
## iter 30 value 70.937289
## iter 40 value 69.435873
## iter 50 value 68.985208
## iter 60 value 68.794145
## iter 70 value 68.772730
## iter 80 value 68.771453
## iter 90 value 68.771255
## final value 68.771242
## converged
## # weights: 296
## initial value 132.689817
## iter 10 value 82.576172
## iter 20 value 70.427869
## iter 30 value 68.550304
## iter 40 value 67.534431
## iter 50 value 67.309237
## iter 60 value 67.283753
## iter 70 value 67.282857
## final value 67.282848
## converged
## # weights: 60
## initial value 173.877571
## iter 10 value 97.765155
## iter 20 value 97.763688
## iter 30 value 97.760923
## iter 40 value 97.760860
## iter 50 value 97.760793
## iter 60 value 97.760721
## iter 70 value 97.760643
## iter 80 value 97.760558
## iter 90 value 97.760465
## iter 100 value 97.760364
## final value 97.760364
## stopped after 100 iterations
## # weights: 178
## initial value 152.874747
## iter 10 value 97.761650
## iter 20 value 97.755598
## iter 30 value 97.755009
## iter 40 value 97.754272
## iter 50 value 97.753088
## iter 60 value 97.737557
## iter 70 value 97.277356
## iter 80 value 65.440542
## iter 90 value 64.966982
## iter 100 value 64.161437
## final value 64.161437
## stopped after 100 iterations
## # weights: 296
## initial value 163.418309
## iter 10 value 97.764497
## iter 20 value 97.749144
## iter 30 value 97.738271
## iter 40 value 97.392482
## iter 50 value 64.834613
## iter 60 value 63.326431
## iter 70 value 62.673905
## iter 80 value 62.593769
## iter 90 value 62.354861
## iter 100 value 62.318675
## final value 62.318675
## stopped after 100 iterations
## # weights: 60
## initial value 142.872384
## final value 128.793557
## converged
## # weights: 178
## initial value 135.197497
## final value 128.793557
## converged
## # weights: 296
## initial value 137.754192
## final value 128.793557
## converged
## # weights: 60
## initial value 132.442359
## iter 10 value 84.856177
## iter 20 value 80.560448
## iter 30 value 76.401523
## iter 40 value 75.909349
## iter 50 value 75.807991
## final value 75.807788
## converged
## # weights: 178
## initial value 152.126524
## iter 10 value 94.769113
## iter 20 value 77.547680
## iter 30 value 74.856109
## iter 40 value 74.144952
## iter 50 value 73.709279
## iter 60 value 73.528741
## iter 70 value 73.513494
## iter 80 value 73.513218
## iter 80 value 73.513217
## iter 80 value 73.513217
## final value 73.513217
## converged
## # weights: 296
## initial value 139.064980
## iter 10 value 83.909448
## iter 20 value 75.481878
## iter 30 value 73.908697
## iter 40 value 73.562398
## iter 50 value 73.346848
## iter 60 value 73.274148
## iter 70 value 73.265649
## iter 80 value 73.265085
## final value 73.265060
## converged
## # weights: 60
## initial value 156.629530
## iter 10 value 128.813098
## iter 20 value 128.806486
## iter 30 value 128.788864
## iter 40 value 128.784779
## iter 50 value 128.778615
## iter 60 value 128.768174
## iter 70 value 128.746321
## iter 80 value 128.670717
## iter 90 value 117.806334
## iter 100 value 88.788443
## final value 88.788443
## stopped after 100 iterations
## # weights: 178
## initial value 130.753256
## iter 10 value 128.815147
## iter 20 value 128.787983
## iter 30 value 128.218721
## iter 40 value 84.188390
## iter 50 value 78.167696
## iter 60 value 74.997237
## iter 70 value 74.735772
## iter 80 value 74.650828
## iter 90 value 74.639245
## iter 100 value 74.589219
## final value 74.589219
## stopped after 100 iterations
## # weights: 296
## initial value 133.631278
## iter 10 value 128.798169
## iter 20 value 128.775359
## iter 30 value 108.993604
## iter 40 value 91.505387
## iter 50 value 80.997516
## iter 60 value 75.423304
## iter 70 value 72.930909
## iter 80 value 72.692487
## iter 90 value 72.659602
## iter 100 value 72.629630
## final value 72.629630
## stopped after 100 iterations
## # weights: 60
## initial value 145.691426
## final value 123.780074
## converged
## # weights: 178
## initial value 149.460380
## final value 123.780074
## converged
## # weights: 296
## initial value 176.983085
## final value 123.780074
## converged
## # weights: 60
## initial value 140.947702
## iter 10 value 100.253043
## iter 20 value 88.327515
## iter 30 value 83.385732
## iter 40 value 82.972564
## iter 50 value 82.866662
## iter 60 value 82.421734
## iter 70 value 82.421021
## iter 70 value 82.421021
## iter 70 value 82.421021
## final value 82.421021
## converged
## # weights: 178
## initial value 147.687932
## iter 10 value 94.886488
## iter 20 value 84.273040
## iter 30 value 81.181986
## iter 40 value 80.119671
## iter 50 value 79.818474
## iter 60 value 79.796113
## iter 70 value 79.795880
## final value 79.795876
## converged
## # weights: 296
## initial value 177.186375
## iter 10 value 92.790822
## iter 20 value 81.683812
## iter 30 value 80.144148
## iter 40 value 79.606902
## iter 50 value 79.412225
## iter 60 value 79.316121
## iter 70 value 79.288447
## iter 80 value 79.269402
## iter 90 value 79.268411
## iter 100 value 79.267771
## final value 79.267771
## stopped after 100 iterations
## # weights: 60
## initial value 147.693161
## iter 10 value 123.797607
## iter 20 value 123.797465
## iter 30 value 123.797319
## iter 40 value 123.797172
## iter 50 value 123.797021
## iter 60 value 123.796867
## iter 70 value 123.796710
## iter 80 value 123.796549
## iter 90 value 123.796385
## iter 100 value 123.796216
## final value 123.796216
## stopped after 100 iterations
## # weights: 178
## initial value 143.013820
## iter 10 value 123.744835
## iter 20 value 123.489969
## iter 30 value 77.711733
## iter 40 value 75.621187
## iter 50 value 75.557064
## iter 60 value 75.549732
## iter 70 value 75.547560
## iter 80 value 75.495021
## iter 90 value 75.413386
## iter 100 value 73.900969
## final value 73.900969
## stopped after 100 iterations
## # weights: 296
## initial value 129.319646
## iter 10 value 123.772937
## iter 20 value 123.684515
## iter 30 value 83.781545
## iter 40 value 78.280694
## iter 50 value 73.327623
## iter 60 value 72.690263
## iter 70 value 72.558142
## iter 80 value 72.227772
## iter 90 value 72.142289
## iter 100 value 71.545219
## final value 71.545219
## stopped after 100 iterations
## # weights: 60
## initial value 151.908023
## final value 106.922881
## converged
## # weights: 178
## initial value 132.969844
## final value 106.922881
## converged
## # weights: 296
## initial value 172.155040
## final value 106.922881
## converged
## # weights: 60
## initial value 149.585390
## iter 10 value 103.712356
## iter 20 value 90.429418
## iter 30 value 82.055336
## iter 40 value 78.426929
## iter 50 value 78.065661
## iter 60 value 77.923777
## iter 70 value 77.919362
## final value 77.919345
## converged
## # weights: 178
## initial value 179.051341
## iter 10 value 99.451844
## iter 20 value 77.870210
## iter 30 value 76.307973
## iter 40 value 76.102199
## iter 50 value 76.077733
## iter 60 value 76.077357
## iter 70 value 76.077197
## final value 76.077195
## converged
## # weights: 296
## initial value 162.031124
## iter 10 value 99.958534
## iter 20 value 81.361885
## iter 30 value 78.935328
## iter 40 value 76.113329
## iter 50 value 76.009308
## iter 60 value 75.869239
## iter 70 value 75.782110
## iter 80 value 75.747830
## iter 90 value 75.745660
## final value 75.745653
## converged
## # weights: 60
## initial value 161.237381
## iter 10 value 106.838861
## iter 20 value 94.185265
## iter 30 value 71.381289
## iter 40 value 69.529914
## iter 50 value 69.220039
## iter 60 value 69.168526
## iter 70 value 69.074411
## iter 80 value 69.014212
## iter 90 value 69.011152
## iter 100 value 69.009819
## final value 69.009819
## stopped after 100 iterations
## # weights: 178
## initial value 156.366314
## iter 10 value 106.934558
## iter 20 value 106.879236
## iter 30 value 89.204401
## iter 40 value 72.756637
## iter 50 value 71.233226
## iter 60 value 70.583484
## iter 70 value 70.541445
## iter 80 value 70.524984
## iter 90 value 70.498042
## iter 100 value 70.467415
## final value 70.467415
## stopped after 100 iterations
## # weights: 296
## initial value 131.668012
## iter 10 value 106.907481
## iter 20 value 106.853515
## iter 30 value 106.026327
## iter 40 value 78.011730
## iter 50 value 72.009302
## iter 60 value 69.805221
## iter 70 value 69.508036
## iter 80 value 68.858350
## iter 90 value 68.768420
## iter 100 value 68.735624
## final value 68.735624
## stopped after 100 iterations
## # weights: 60
## initial value 142.357258
## final value 106.903656
## converged
## # weights: 178
## initial value 125.552936
## final value 106.903656
## converged
## # weights: 296
## initial value 136.824222
## final value 106.903656
## converged
## # weights: 60
## initial value 140.476288
## iter 10 value 94.726039
## iter 20 value 75.516994
## iter 30 value 68.422885
## iter 40 value 63.361709
## iter 50 value 63.105978
## iter 60 value 62.726765
## iter 70 value 62.445603
## iter 80 value 62.034019
## iter 90 value 61.935613
## iter 100 value 61.724151
## final value 61.724151
## stopped after 100 iterations
## # weights: 178
## initial value 159.433741
## iter 10 value 74.447051
## iter 20 value 61.932960
## iter 30 value 60.963926
## iter 40 value 59.577046
## iter 50 value 59.125196
## iter 60 value 59.121496
## iter 70 value 59.120874
## final value 59.120784
## converged
## # weights: 296
## initial value 139.768945
## iter 10 value 74.627299
## iter 20 value 61.289732
## iter 30 value 57.820990
## iter 40 value 57.284592
## iter 50 value 57.144836
## iter 60 value 57.114363
## iter 70 value 57.111296
## final value 57.111268
## converged
## # weights: 60
## initial value 121.031540
## iter 10 value 106.893008
## iter 20 value 106.882975
## iter 30 value 106.864164
## iter 40 value 106.806441
## iter 50 value 103.669793
## iter 60 value 65.775990
## iter 70 value 63.754937
## iter 80 value 63.274640
## iter 90 value 63.217140
## iter 100 value 63.163567
## final value 63.163567
## stopped after 100 iterations
## # weights: 178
## initial value 168.410076
## iter 10 value 106.920184
## iter 20 value 106.919858
## iter 30 value 106.919595
## iter 40 value 106.916979
## iter 50 value 105.877059
## iter 60 value 59.891366
## iter 70 value 58.511502
## iter 80 value 58.261831
## iter 90 value 58.056220
## iter 100 value 57.929362
## final value 57.929362
## stopped after 100 iterations
## # weights: 296
## initial value 114.109874
## iter 10 value 70.290917
## iter 20 value 61.666918
## iter 30 value 59.771340
## iter 40 value 59.273518
## iter 50 value 58.783373
## iter 60 value 58.604113
## iter 70 value 57.984375
## iter 80 value 57.935111
## iter 90 value 57.890430
## iter 100 value 57.141566
## final value 57.141566
## stopped after 100 iterations
## # weights: 60
## initial value 182.898574
## final value 139.171930
## converged
## # weights: 178
## initial value 196.040336
## final value 139.171930
## converged
## # weights: 296
## initial value 180.910072
## final value 139.171930
## converged
## # weights: 60
## initial value 244.518833
## iter 10 value 139.002924
## iter 20 value 125.463387
## iter 30 value 113.337994
## iter 40 value 107.875994
## iter 50 value 106.804479
## iter 60 value 106.725470
## final value 106.725259
## converged
## # weights: 178
## initial value 179.508169
## iter 10 value 112.618068
## iter 20 value 104.852449
## iter 30 value 104.213797
## iter 40 value 104.103233
## iter 50 value 104.099788
## final value 104.099742
## converged
## # weights: 296
## initial value 179.134552
## iter 10 value 114.494351
## iter 20 value 106.855663
## iter 30 value 105.016942
## iter 40 value 104.042678
## iter 50 value 103.125369
## iter 60 value 102.806250
## iter 70 value 102.603273
## iter 80 value 102.572866
## iter 90 value 102.556670
## iter 100 value 102.553679
## final value 102.553679
## stopped after 100 iterations
## # weights: 60
## initial value 183.037942
## iter 10 value 139.182711
## iter 20 value 122.947223
## iter 30 value 113.534271
## iter 40 value 112.215968
## iter 50 value 104.653253
## iter 60 value 103.959912
## iter 70 value 103.942349
## iter 80 value 103.937665
## iter 90 value 102.528126
## iter 100 value 102.402525
## final value 102.402525
## stopped after 100 iterations
## # weights: 178
## initial value 196.295532
## iter 10 value 139.189471
## iter 20 value 138.663877
## iter 30 value 100.130732
## iter 40 value 98.014490
## iter 50 value 97.017215
## iter 60 value 97.000742
## iter 70 value 96.997309
## iter 80 value 96.991967
## iter 90 value 96.981883
## iter 100 value 96.964601
## final value 96.964601
## stopped after 100 iterations
## # weights: 296
## initial value 210.331367
## iter 10 value 139.191750
## iter 20 value 139.177512
## iter 30 value 139.176995
## iter 40 value 139.176292
## iter 50 value 139.175283
## iter 60 value 139.173711
## iter 70 value 139.170949
## iter 80 value 139.165246
## iter 90 value 139.150277
## iter 100 value 139.072348
## final value 139.072348
## stopped after 100 iterations
## # weights: 60
## initial value 131.677040
## final value 107.144018
## converged
## # weights: 178
## initial value 125.521209
## final value 107.144018
## converged
## # weights: 296
## initial value 126.664962
## final value 107.144018
## converged
## # weights: 60
## initial value 139.495992
## iter 10 value 90.261702
## iter 20 value 74.769455
## iter 30 value 71.800408
## iter 40 value 71.402626
## iter 50 value 71.226121
## iter 60 value 70.531654
## iter 70 value 70.496001
## final value 70.495591
## converged
## # weights: 178
## initial value 158.656334
## iter 10 value 81.105634
## iter 20 value 69.630650
## iter 30 value 69.057877
## iter 40 value 68.392502
## iter 50 value 68.281028
## iter 60 value 68.268435
## iter 70 value 68.242263
## iter 80 value 68.241275
## iter 90 value 68.241146
## final value 68.241085
## converged
## # weights: 296
## initial value 151.172355
## iter 10 value 88.494252
## iter 20 value 68.632905
## iter 30 value 67.863043
## iter 40 value 67.754685
## iter 50 value 67.715027
## iter 60 value 67.712739
## iter 70 value 67.704912
## iter 80 value 67.702342
## final value 67.702328
## converged
## # weights: 60
## initial value 154.540761
## iter 10 value 107.133492
## iter 20 value 107.127327
## iter 30 value 107.116209
## iter 40 value 107.091353
## iter 50 value 106.993404
## iter 60 value 79.391017
## iter 70 value 65.542880
## iter 80 value 65.439071
## iter 90 value 65.413707
## iter 100 value 65.410687
## final value 65.410687
## stopped after 100 iterations
## # weights: 178
## initial value 122.091101
## iter 10 value 107.116252
## iter 20 value 106.858608
## iter 30 value 72.576661
## iter 40 value 64.407887
## iter 50 value 63.103732
## iter 60 value 62.384891
## iter 70 value 62.294432
## iter 80 value 62.253726
## iter 90 value 62.226373
## iter 100 value 61.944413
## final value 61.944413
## stopped after 100 iterations
## # weights: 296
## initial value 139.264488
## iter 10 value 107.153209
## iter 20 value 89.484628
## iter 30 value 62.850982
## iter 40 value 60.585692
## iter 50 value 60.174626
## iter 60 value 60.094470
## iter 70 value 60.080676
## iter 80 value 60.019401
## iter 90 value 59.948107
## iter 100 value 59.928908
## final value 59.928908
## stopped after 100 iterations
## # weights: 60
## initial value 154.863332
## final value 120.914182
## converged
## # weights: 178
## initial value 178.408863
## final value 120.914182
## converged
## # weights: 296
## initial value 185.353190
## final value 120.914182
## converged
## # weights: 60
## initial value 158.418834
## iter 10 value 90.816808
## iter 20 value 79.886117
## iter 30 value 77.113404
## iter 40 value 76.155021
## iter 50 value 76.024363
## iter 60 value 76.001152
## iter 70 value 75.991864
## final value 75.991859
## converged
## # weights: 178
## initial value 148.875738
## iter 10 value 80.186538
## iter 20 value 73.822865
## iter 30 value 72.766687
## iter 40 value 72.581639
## iter 50 value 72.575329
## iter 60 value 72.574831
## iter 70 value 72.574635
## final value 72.574633
## converged
## # weights: 296
## initial value 152.890091
## iter 10 value 85.046445
## iter 20 value 73.301353
## iter 30 value 72.035850
## iter 40 value 71.853466
## iter 50 value 71.598043
## iter 60 value 70.931796
## iter 70 value 70.890178
## iter 80 value 70.885675
## iter 90 value 70.885015
## iter 100 value 70.884620
## final value 70.884620
## stopped after 100 iterations
## # weights: 60
## initial value 136.849519
## iter 10 value 120.911189
## iter 20 value 120.908736
## iter 30 value 120.905421
## iter 40 value 120.900709
## iter 50 value 120.893360
## iter 60 value 120.880008
## iter 70 value 120.847491
## iter 80 value 120.652913
## iter 90 value 72.883209
## iter 100 value 67.001350
## final value 67.001350
## stopped after 100 iterations
## # weights: 178
## initial value 158.579307
## iter 10 value 120.925068
## iter 20 value 120.625325
## iter 30 value 69.914740
## iter 40 value 67.811532
## iter 50 value 67.590096
## iter 60 value 67.457328
## iter 70 value 67.446959
## iter 80 value 67.441825
## iter 90 value 67.438373
## iter 100 value 66.462038
## final value 66.462038
## stopped after 100 iterations
## # weights: 296
## initial value 159.515987
## iter 10 value 120.923858
## iter 20 value 120.917901
## iter 30 value 120.916486
## iter 40 value 120.913534
## iter 50 value 120.903810
## iter 60 value 120.859408
## iter 70 value 120.114912
## iter 80 value 69.900488
## iter 90 value 67.722681
## iter 100 value 66.781436
## final value 66.781436
## stopped after 100 iterations
## # weights: 60
## initial value 144.595725
## final value 130.833202
## converged
## # weights: 178
## initial value 162.301131
## final value 130.833202
## converged
## # weights: 296
## initial value 160.155003
## final value 130.833202
## converged
## # weights: 60
## initial value 190.752124
## iter 10 value 99.243148
## iter 20 value 91.869189
## iter 30 value 84.167639
## iter 40 value 82.668467
## iter 50 value 82.515260
## iter 60 value 82.450067
## final value 82.450055
## converged
## # weights: 178
## initial value 144.786101
## iter 10 value 96.272166
## iter 20 value 82.272777
## iter 30 value 80.448718
## iter 40 value 79.722711
## iter 50 value 79.096695
## iter 60 value 78.757609
## iter 70 value 78.626258
## iter 80 value 78.551631
## iter 90 value 78.536827
## iter 100 value 78.536700
## final value 78.536700
## stopped after 100 iterations
## # weights: 296
## initial value 198.346033
## iter 10 value 103.202607
## iter 20 value 83.573393
## iter 30 value 80.345678
## iter 40 value 78.954207
## iter 50 value 78.075775
## iter 60 value 77.707136
## iter 70 value 77.526414
## iter 80 value 77.501402
## iter 90 value 77.499527
## iter 100 value 77.499281
## final value 77.499281
## stopped after 100 iterations
## # weights: 60
## initial value 147.814249
## iter 10 value 101.717262
## iter 20 value 88.179796
## iter 30 value 88.165237
## iter 40 value 88.145059
## iter 50 value 87.779292
## iter 60 value 87.773395
## iter 70 value 87.769619
## iter 80 value 87.765722
## iter 90 value 87.012448
## iter 100 value 84.778126
## final value 84.778126
## stopped after 100 iterations
## # weights: 178
## initial value 171.840826
## iter 10 value 130.851343
## iter 20 value 130.844549
## iter 30 value 130.766848
## iter 40 value 113.349785
## iter 50 value 79.218502
## iter 60 value 78.492163
## iter 70 value 77.981998
## iter 80 value 77.759374
## iter 90 value 77.744317
## iter 100 value 73.906827
## final value 73.906827
## stopped after 100 iterations
## # weights: 296
## initial value 173.383393
## iter 10 value 130.846514
## iter 20 value 130.835034
## iter 30 value 130.824113
## iter 40 value 130.691582
## iter 50 value 83.674135
## iter 60 value 76.790041
## iter 70 value 73.118928
## iter 80 value 72.762779
## iter 90 value 72.609906
## iter 100 value 72.591074
## final value 72.591074
## stopped after 100 iterations
## # weights: 60
## initial value 200.572732
## final value 133.801472
## converged
## # weights: 178
## initial value 160.845361
## final value 133.801472
## converged
## # weights: 296
## initial value 182.618272
## final value 133.801472
## converged
## # weights: 60
## initial value 173.798736
## iter 10 value 131.301647
## iter 20 value 99.606997
## iter 30 value 98.184770
## iter 40 value 96.590899
## iter 50 value 96.463513
## iter 60 value 96.427417
## final value 96.427371
## converged
## # weights: 178
## initial value 185.302189
## iter 10 value 103.269985
## iter 20 value 94.548356
## iter 30 value 93.956401
## iter 40 value 93.904150
## iter 50 value 93.900127
## iter 60 value 93.899786
## final value 93.899761
## converged
## # weights: 296
## initial value 214.712712
## iter 10 value 124.384964
## iter 20 value 96.057429
## iter 30 value 93.927522
## iter 40 value 93.669537
## iter 50 value 93.539594
## iter 60 value 93.534598
## iter 70 value 93.534319
## final value 93.534295
## converged
## # weights: 60
## initial value 191.016494
## iter 10 value 133.808362
## iter 20 value 133.786882
## iter 30 value 133.779121
## iter 40 value 133.764240
## iter 50 value 133.723947
## iter 60 value 133.350149
## iter 70 value 94.906606
## iter 80 value 93.053623
## iter 90 value 92.928916
## iter 100 value 92.774964
## final value 92.774964
## stopped after 100 iterations
## # weights: 178
## initial value 205.925056
## iter 10 value 133.814515
## iter 20 value 133.808845
## iter 30 value 133.808495
## iter 40 value 133.808015
## iter 50 value 133.807268
## iter 60 value 133.806086
## iter 70 value 133.804539
## iter 80 value 133.802653
## iter 90 value 133.799960
## iter 100 value 133.795319
## final value 133.795319
## stopped after 100 iterations
## # weights: 296
## initial value 192.505715
## iter 10 value 133.825159
## iter 20 value 133.808937
## iter 30 value 98.518895
## iter 40 value 86.927292
## iter 50 value 86.422395
## iter 60 value 86.372817
## iter 70 value 86.332278
## iter 80 value 86.328890
## iter 90 value 86.326403
## iter 100 value 86.324093
## final value 86.324093
## stopped after 100 iterations
## # weights: 60
## initial value 173.391896
## final value 122.706866
## converged
## # weights: 178
## initial value 140.125316
## final value 122.706866
## converged
## # weights: 296
## initial value 198.393822
## final value 122.706866
## converged
## # weights: 60
## initial value 140.604214
## iter 10 value 95.849814
## iter 20 value 83.991439
## iter 30 value 78.822215
## iter 40 value 77.869625
## iter 50 value 77.566676
## iter 60 value 77.553424
## iter 70 value 77.552513
## final value 77.552500
## converged
## # weights: 178
## initial value 150.438069
## iter 10 value 83.684745
## iter 20 value 75.738017
## iter 30 value 74.830491
## iter 40 value 74.760890
## iter 50 value 74.746764
## iter 60 value 74.721905
## iter 70 value 74.640475
## iter 80 value 74.630246
## iter 90 value 74.629393
## iter 100 value 74.629295
## final value 74.629295
## stopped after 100 iterations
## # weights: 296
## initial value 158.427214
## iter 10 value 94.627055
## iter 20 value 76.011361
## iter 30 value 74.718456
## iter 40 value 74.460139
## iter 50 value 74.369542
## iter 60 value 74.253569
## iter 70 value 74.245876
## iter 80 value 74.245535
## iter 90 value 74.245501
## final value 74.245495
## converged
## # weights: 60
## initial value 164.619756
## iter 10 value 122.700476
## iter 20 value 90.935341
## iter 30 value 90.226362
## iter 40 value 89.498320
## iter 50 value 89.465710
## iter 60 value 89.460218
## iter 70 value 89.434848
## iter 80 value 88.801343
## iter 90 value 88.792905
## iter 100 value 88.767022
## final value 88.767022
## stopped after 100 iterations
## # weights: 178
## initial value 130.321741
## iter 10 value 122.767972
## iter 20 value 122.767670
## iter 30 value 122.767366
## iter 40 value 122.767060
## iter 50 value 122.766751
## iter 60 value 122.766440
## iter 70 value 122.766127
## iter 80 value 122.765809
## iter 90 value 122.765489
## iter 100 value 122.765164
## final value 122.765164
## stopped after 100 iterations
## # weights: 296
## initial value 140.339550
## iter 10 value 122.716021
## iter 20 value 122.710209
## iter 30 value 122.705683
## iter 40 value 122.689849
## iter 50 value 122.625446
## iter 60 value 95.876180
## iter 70 value 79.051710
## iter 80 value 70.836541
## iter 90 value 69.758926
## iter 100 value 69.054177
## final value 69.054177
## stopped after 100 iterations
## # weights: 60
## initial value 169.769513
## final value 117.150773
## converged
## # weights: 178
## initial value 148.277456
## final value 117.150773
## converged
## # weights: 296
## initial value 168.280941
## final value 117.150773
## converged
## # weights: 60
## initial value 149.924526
## iter 10 value 100.696774
## iter 20 value 84.179037
## iter 30 value 79.464098
## iter 40 value 75.989119
## iter 50 value 74.797594
## iter 60 value 74.119896
## iter 70 value 73.856566
## final value 73.856444
## converged
## # weights: 178
## initial value 164.399163
## iter 10 value 103.900809
## iter 20 value 76.156206
## iter 30 value 72.401839
## iter 40 value 71.433634
## iter 50 value 71.376809
## iter 60 value 71.371818
## final value 71.371650
## converged
## # weights: 296
## initial value 190.560717
## iter 10 value 97.739637
## iter 20 value 73.778230
## iter 30 value 70.444982
## iter 40 value 69.695949
## iter 50 value 69.618669
## iter 60 value 69.596662
## iter 70 value 69.591161
## iter 80 value 69.590507
## iter 90 value 69.590117
## iter 100 value 69.590044
## final value 69.590044
## stopped after 100 iterations
## # weights: 60
## initial value 145.994356
## iter 10 value 117.163779
## iter 20 value 116.886438
## iter 30 value 98.433313
## iter 40 value 82.015977
## iter 50 value 79.963346
## iter 60 value 78.431618
## iter 70 value 78.334836
## iter 80 value 78.324499
## iter 90 value 78.317468
## iter 100 value 77.706011
## final value 77.706011
## stopped after 100 iterations
## # weights: 178
## initial value 142.839119
## iter 10 value 117.163386
## iter 20 value 117.156649
## iter 30 value 117.107194
## iter 40 value 116.074636
## iter 50 value 68.504653
## iter 60 value 64.048069
## iter 70 value 63.733319
## iter 80 value 63.617572
## iter 90 value 63.492186
## iter 100 value 63.156960
## final value 63.156960
## stopped after 100 iterations
## # weights: 296
## initial value 134.901354
## iter 10 value 116.958967
## iter 20 value 77.156147
## iter 30 value 70.135461
## iter 40 value 69.613839
## iter 50 value 69.493187
## iter 60 value 67.621297
## iter 70 value 67.138300
## iter 80 value 66.343416
## iter 90 value 65.023966
## iter 100 value 64.902413
## final value 64.902413
## stopped after 100 iterations
## # weights: 60
## initial value 143.764213
## final value 128.990871
## converged
## # weights: 178
## initial value 163.666274
## final value 128.990871
## converged
## # weights: 296
## initial value 162.297407
## final value 128.990871
## converged
## # weights: 60
## initial value 155.591660
## iter 10 value 109.727636
## iter 20 value 87.967219
## iter 30 value 83.771744
## iter 40 value 83.093820
## iter 50 value 82.956742
## iter 60 value 82.953461
## final value 82.953424
## converged
## # weights: 178
## initial value 155.837848
## iter 10 value 110.559181
## iter 20 value 90.093653
## iter 30 value 85.469037
## iter 40 value 82.906909
## iter 50 value 79.545559
## iter 60 value 79.255041
## iter 70 value 79.172462
## iter 80 value 79.169434
## final value 79.169370
## converged
## # weights: 296
## initial value 168.967623
## iter 10 value 105.423450
## iter 20 value 82.978534
## iter 30 value 78.777465
## iter 40 value 77.719776
## iter 50 value 77.494938
## iter 60 value 77.422020
## iter 70 value 77.386677
## iter 80 value 77.376058
## iter 90 value 77.374803
## iter 100 value 77.374727
## final value 77.374727
## stopped after 100 iterations
## # weights: 60
## initial value 149.156379
## iter 10 value 128.979992
## iter 20 value 128.973818
## iter 30 value 128.963526
## iter 40 value 128.942466
## iter 50 value 128.872989
## iter 60 value 106.073078
## iter 70 value 78.350941
## iter 80 value 74.458338
## iter 90 value 73.893744
## iter 100 value 73.761682
## final value 73.761682
## stopped after 100 iterations
## # weights: 178
## initial value 180.409705
## iter 10 value 129.003449
## iter 20 value 128.972205
## iter 30 value 128.947574
## iter 40 value 128.820573
## iter 50 value 85.112076
## iter 60 value 74.041065
## iter 70 value 72.674093
## iter 80 value 71.862132
## iter 90 value 71.622498
## iter 100 value 71.574585
## final value 71.574585
## stopped after 100 iterations
## # weights: 296
## initial value 154.070785
## iter 10 value 128.991310
## iter 20 value 128.834732
## iter 30 value 77.616287
## iter 40 value 73.029292
## iter 50 value 72.737682
## iter 60 value 72.698203
## iter 70 value 72.486284
## iter 80 value 72.425353
## iter 90 value 72.420362
## iter 100 value 72.417661
## final value 72.417661
## stopped after 100 iterations
## # weights: 60
## initial value 164.027010
## final value 121.884691
## converged
## # weights: 178
## initial value 169.595370
## final value 121.884691
## converged
## # weights: 296
## initial value 144.768141
## final value 121.884691
## converged
## # weights: 60
## initial value 170.598454
## iter 10 value 89.327653
## iter 20 value 83.579912
## iter 30 value 83.122813
## final value 83.121137
## converged
## # weights: 178
## initial value 157.476528
## iter 10 value 88.879104
## iter 20 value 81.153489
## iter 30 value 79.396950
## iter 40 value 79.087217
## iter 50 value 79.003032
## iter 60 value 78.999977
## final value 78.999964
## converged
## # weights: 296
## initial value 159.585024
## iter 10 value 94.625004
## iter 20 value 82.653221
## iter 30 value 81.167872
## iter 40 value 80.981516
## iter 50 value 80.965076
## iter 60 value 80.964563
## iter 70 value 80.964494
## final value 80.964493
## converged
## # weights: 60
## initial value 141.836237
## iter 10 value 121.898910
## iter 20 value 121.892523
## iter 30 value 121.891865
## iter 40 value 121.891170
## iter 50 value 121.890426
## iter 60 value 121.889605
## iter 70 value 121.888667
## iter 80 value 121.887556
## iter 90 value 121.886195
## iter 100 value 121.884467
## final value 121.884467
## stopped after 100 iterations
## # weights: 178
## initial value 156.205562
## iter 10 value 121.896076
## iter 20 value 121.895628
## iter 30 value 121.895124
## iter 40 value 121.894556
## iter 50 value 121.893915
## iter 60 value 121.893194
## iter 70 value 121.892381
## iter 80 value 121.891461
## iter 90 value 121.890409
## iter 100 value 121.889187
## final value 121.889187
## stopped after 100 iterations
## # weights: 296
## initial value 156.038965
## iter 10 value 121.894182
## iter 20 value 121.882320
## iter 30 value 121.872610
## iter 40 value 96.472835
## iter 50 value 75.837759
## iter 60 value 74.507008
## iter 70 value 73.025054
## iter 80 value 72.344976
## iter 90 value 72.077480
## iter 100 value 72.042995
## final value 72.042995
## stopped after 100 iterations
## # weights: 296
## initial value 179.733449
## iter 10 value 97.031521
## iter 20 value 82.604387
## iter 30 value 79.044723
## iter 40 value 76.992855
## iter 50 value 76.444921
## iter 60 value 76.247254
## iter 70 value 76.056877
## iter 80 value 76.035584
## iter 90 value 76.035126
## final value 76.035088
## converged## ### Neuro Network Metrics Results ##### RMSE Rsquared MAE
## 0.8993722 0.5441986 0.7042420| Overall | |
|---|---|
| BiologicalMaterial01 | 0.4144884 |
| BiologicalMaterial02 | 0.4183276 |
| BiologicalMaterial03 | 0.3296683 |
| BiologicalMaterial04 | 0.1004094 |
| BiologicalMaterial05 | 1.4830950 |
| BiologicalMaterial06 | 0.6722537 |
| BiologicalMaterial07 | 1.0122836 |
| BiologicalMaterial08 | 0.4479805 |
| BiologicalMaterial09 | 0.1656918 |
| BiologicalMaterial10 | 0.0016398 |
| BiologicalMaterial11 | 1.1880094 |
| BiologicalMaterial12 | 1.0740032 |
| ManufacturingProcess01 | 0.2780557 |
| ManufacturingProcess02 | 0.0016257 |
| ManufacturingProcess03 | 1.5058096 |
| ManufacturingProcess04 | 0.7357273 |
| ManufacturingProcess05 | 0.8834755 |
| ManufacturingProcess06 | 1.6381746 |
| ManufacturingProcess07 | 0.8857378 |
| ManufacturingProcess08 | 0.4512921 |
| ManufacturingProcess09 | 0.6382246 |
| ManufacturingProcess10 | 0.1007782 |
| ManufacturingProcess11 | 0.7667228 |
| ManufacturingProcess12 | 0.5933077 |
| ManufacturingProcess13 | 0.9720934 |
| ManufacturingProcess14 | 0.2959231 |
| ManufacturingProcess15 | 0.2557222 |
| ManufacturingProcess16 | 0.1957528 |
| ManufacturingProcess17 | 0.0743751 |
| ManufacturingProcess18 | 0.6963078 |
| ManufacturingProcess19 | 0.6411591 |
| ManufacturingProcess20 | 0.7223646 |
| ManufacturingProcess22 | 0.4755496 |
| ManufacturingProcess23 | 0.8996397 |
| ManufacturingProcess24 | 1.2013709 |
| ManufacturingProcess25 | 0.8672575 |
| ManufacturingProcess26 | 0.8041314 |
| ManufacturingProcess27 | 0.6766606 |
| ManufacturingProcess28 | 3.2011086 |
| ManufacturingProcess29 | 2.2099760 |
| ManufacturingProcess30 | 0.2744709 |
| ManufacturingProcess31 | 0.7048491 |
| ManufacturingProcess32 | 4.1098153 |
| ManufacturingProcess33 | 2.5217929 |
| ManufacturingProcess34 | 0.4899749 |
| ManufacturingProcess35 | 0.9323066 |
| ManufacturingProcess36 | 1.0568528 |
| ManufacturingProcess37 | 1.0046325 |
| ManufacturingProcess38 | 0.9991690 |
| ManufacturingProcess39 | 0.1916321 |
| ManufacturingProcess40 | 0.8355733 |
| ManufacturingProcess41 | 0.8810996 |
| ManufacturingProcess42 | 0.5277907 |
| ManufacturingProcess43 | 1.3659767 |
| ManufacturingProcess44 | 0.4718168 |
| ManufacturingProcess45 | 1.6214527 |
| Overall | |
|---|---|
| BiologicalMaterial01 | 0.1076615 |
| BiologicalMaterial02 | 0.1807012 |
| BiologicalMaterial03 | 0.2631946 |
| BiologicalMaterial04 | 0.1413654 |
| BiologicalMaterial05 | 0.0367758 |
| BiologicalMaterial06 | 0.2909056 |
| BiologicalMaterial07 | 0.0100028 |
| BiologicalMaterial08 | 0.1473037 |
| BiologicalMaterial09 | 0.1555370 |
| BiologicalMaterial10 | 0.0724908 |
| BiologicalMaterial11 | 0.1629170 |
| BiologicalMaterial12 | 0.2412185 |
| ManufacturingProcess01 | 0.1578287 |
| ManufacturingProcess02 | 0.1331255 |
| ManufacturingProcess03 | 0.0129271 |
| ManufacturingProcess04 | 0.1098940 |
| ManufacturingProcess05 | 0.0161460 |
| ManufacturingProcess06 | 0.2402510 |
| ManufacturingProcess07 | 0.0007811 |
| ManufacturingProcess08 | 0.0000261 |
| ManufacturingProcess09 | 0.2587624 |
| ManufacturingProcess10 | 0.0708371 |
| ManufacturingProcess11 | 0.2043809 |
| ManufacturingProcess12 | 0.1571690 |
| ManufacturingProcess13 | 0.2747904 |
| ManufacturingProcess14 | 0.0641521 |
| ManufacturingProcess15 | 0.1395217 |
| ManufacturingProcess16 | 0.0643132 |
| ManufacturingProcess17 | 0.3063856 |
| ManufacturingProcess18 | 0.1083749 |
| ManufacturingProcess19 | 0.0718435 |
| ManufacturingProcess20 | 0.0401452 |
| ManufacturingProcess21 | 0.0590100 |
| ManufacturingProcess22 | 0.0028819 |
| ManufacturingProcess23 | 0.0132709 |
| ManufacturingProcess24 | 0.0670870 |
| ManufacturingProcess25 | 0.1663295 |
| ManufacturingProcess26 | 0.1076723 |
| ManufacturingProcess27 | 0.0729450 |
| ManufacturingProcess28 | 0.0776908 |
| ManufacturingProcess29 | 0.1889376 |
| ManufacturingProcess30 | 0.1247785 |
| ManufacturingProcess31 | 0.2174880 |
| ManufacturingProcess32 | 0.3734379 |
| ManufacturingProcess33 | 0.1850785 |
| ManufacturingProcess34 | 0.0183944 |
| ManufacturingProcess35 | 0.0719678 |
| ManufacturingProcess36 | 0.2131597 |
| ManufacturingProcess37 | 0.0537773 |
| ManufacturingProcess38 | 0.0032073 |
| ManufacturingProcess39 | 0.0018747 |
| ManufacturingProcess40 | 0.0008630 |
| ManufacturingProcess41 | 0.0003102 |
| ManufacturingProcess42 | 0.0001593 |
| ManufacturingProcess43 | 0.0288916 |
| ManufacturingProcess44 | 0.0056120 |
| ManufacturingProcess45 | 0.0016508 |
| Overall | |
|---|---|
| BiologicalMaterial01 | 0.1076615 |
| BiologicalMaterial02 | 0.1807012 |
| BiologicalMaterial03 | 0.2631946 |
| BiologicalMaterial04 | 0.1413654 |
| BiologicalMaterial05 | 0.0367758 |
| BiologicalMaterial06 | 0.2909056 |
| BiologicalMaterial07 | 0.0100028 |
| BiologicalMaterial08 | 0.1473037 |
| BiologicalMaterial09 | 0.1555370 |
| BiologicalMaterial10 | 0.0724908 |
| BiologicalMaterial11 | 0.1629170 |
| BiologicalMaterial12 | 0.2412185 |
| ManufacturingProcess01 | 0.1578287 |
| ManufacturingProcess02 | 0.1331255 |
| ManufacturingProcess03 | 0.0129271 |
| ManufacturingProcess04 | 0.1098940 |
| ManufacturingProcess05 | 0.0161460 |
| ManufacturingProcess06 | 0.2402510 |
| ManufacturingProcess07 | 0.0007811 |
| ManufacturingProcess08 | 0.0000261 |
| ManufacturingProcess09 | 0.2587624 |
| ManufacturingProcess10 | 0.0708371 |
| ManufacturingProcess11 | 0.2043809 |
| ManufacturingProcess12 | 0.1571690 |
| ManufacturingProcess13 | 0.2747904 |
| ManufacturingProcess14 | 0.0641521 |
| ManufacturingProcess15 | 0.1395217 |
| ManufacturingProcess16 | 0.0643132 |
| ManufacturingProcess17 | 0.3063856 |
| ManufacturingProcess18 | 0.1083749 |
| ManufacturingProcess19 | 0.0718435 |
| ManufacturingProcess20 | 0.0401452 |
| ManufacturingProcess21 | 0.0590100 |
| ManufacturingProcess22 | 0.0028819 |
| ManufacturingProcess23 | 0.0132709 |
| ManufacturingProcess24 | 0.0670870 |
| ManufacturingProcess25 | 0.1663295 |
| ManufacturingProcess26 | 0.1076723 |
| ManufacturingProcess27 | 0.0729450 |
| ManufacturingProcess28 | 0.0776908 |
| ManufacturingProcess29 | 0.1889376 |
| ManufacturingProcess30 | 0.1247785 |
| ManufacturingProcess31 | 0.2174880 |
| ManufacturingProcess32 | 0.3734379 |
| ManufacturingProcess33 | 0.1850785 |
| ManufacturingProcess34 | 0.0183944 |
| ManufacturingProcess35 | 0.0719678 |
| ManufacturingProcess36 | 0.2131597 |
| ManufacturingProcess37 | 0.0537773 |
| ManufacturingProcess38 | 0.0032073 |
| ManufacturingProcess39 | 0.0018747 |
| ManufacturingProcess40 | 0.0008630 |
| ManufacturingProcess41 | 0.0003102 |
| ManufacturingProcess42 | 0.0001593 |
| ManufacturingProcess43 | 0.0288916 |
| ManufacturingProcess44 | 0.0056120 |
| ManufacturingProcess45 | 0.0016508 |
| Overall | |
|---|---|
| BiologicalMaterial01 | 0.7723617 |
| BiologicalMaterial02 | 0.2804983 |
| BiologicalMaterial03 | 0.7901909 |
| BiologicalMaterial04 | 1.7277147 |
| BiologicalMaterial05 | 3.2560049 |
| BiologicalMaterial06 | 0.3108047 |
| BiologicalMaterial07 | 0.2706206 |
| BiologicalMaterial08 | 1.0305662 |
| BiologicalMaterial09 | 1.4867648 |
| BiologicalMaterial10 | 2.1312740 |
| BiologicalMaterial11 | 1.9452196 |
| BiologicalMaterial12 | 1.1860290 |
| ManufacturingProcess01 | 1.8214109 |
| ManufacturingProcess02 | 0.8447873 |
| ManufacturingProcess03 | 2.3812633 |
| ManufacturingProcess04 | 3.1753533 |
| ManufacturingProcess05 | 2.1955969 |
| ManufacturingProcess06 | 2.8088904 |
| ManufacturingProcess07 | 1.3537290 |
| ManufacturingProcess08 | 1.0890765 |
| ManufacturingProcess09 | 3.2152691 |
| ManufacturingProcess10 | 1.6766743 |
| ManufacturingProcess11 | 1.5229254 |
| ManufacturingProcess12 | 2.3792366 |
| ManufacturingProcess13 | 3.3285803 |
| ManufacturingProcess14 | 1.0474859 |
| ManufacturingProcess15 | 0.9919241 |
| ManufacturingProcess16 | 0.6012087 |
| ManufacturingProcess17 | 2.4083483 |
| ManufacturingProcess18 | 0.7388137 |
| ManufacturingProcess19 | 2.6871357 |
| ManufacturingProcess20 | 0.7940063 |
| ManufacturingProcess21 | 0.8359628 |
| ManufacturingProcess22 | 1.7166856 |
| ManufacturingProcess23 | 1.9142858 |
| ManufacturingProcess24 | 3.7776712 |
| ManufacturingProcess25 | 0.1586315 |
| ManufacturingProcess26 | 0.4912437 |
| ManufacturingProcess27 | 0.3799888 |
| ManufacturingProcess28 | 3.3811218 |
| ManufacturingProcess29 | 2.5123412 |
| ManufacturingProcess30 | 0.6572429 |
| ManufacturingProcess31 | 1.0279280 |
| ManufacturingProcess32 | 9.4391202 |
| ManufacturingProcess33 | 1.7215565 |
| ManufacturingProcess34 | 1.0269644 |
| ManufacturingProcess35 | 0.6682380 |
| ManufacturingProcess36 | 2.3534155 |
| ManufacturingProcess37 | 3.4206330 |
| ManufacturingProcess38 | 0.8200280 |
| ManufacturingProcess39 | 3.8372936 |
| ManufacturingProcess40 | 1.0862780 |
| ManufacturingProcess41 | 1.2860056 |
| ManufacturingProcess42 | 0.6907966 |
| ManufacturingProcess43 | 1.2595291 |
| ManufacturingProcess44 | 1.8477924 |
| ManufacturingProcess45 | 1.4394803 |
| Overall | |
|---|---|
| ManufacturingProcess32 | 100.00000 |
| ManufacturingProcess28 | 77.88060 |
| ManufacturingProcess33 | 61.34496 |
| ManufacturingProcess29 | 53.75483 |
| ManufacturingProcess06 | 39.83626 |
| ManufacturingProcess45 | 39.42922 |
| ManufacturingProcess03 | 36.61428 |
| BiologicalMaterial05 | 36.06137 |
| ManufacturingProcess43 | 33.21052 |
| ManufacturingProcess24 | 29.20374 |
| Overall | |
|---|---|
| ManufacturingProcess32 | 100.00000 |
| ManufacturingProcess17 | 82.04335 |
| BiologicalMaterial06 | 77.89778 |
| ManufacturingProcess13 | 73.58212 |
| BiologicalMaterial03 | 70.47676 |
| ManufacturingProcess09 | 69.28981 |
| BiologicalMaterial12 | 64.59155 |
| ManufacturingProcess06 | 64.33243 |
| ManufacturingProcess31 | 58.23648 |
| ManufacturingProcess36 | 57.07735 |
| Overall | |
|---|---|
| ManufacturingProcess32 | 100.00000 |
| ManufacturingProcess17 | 82.04335 |
| BiologicalMaterial06 | 77.89778 |
| ManufacturingProcess13 | 73.58212 |
| BiologicalMaterial03 | 70.47676 |
| ManufacturingProcess09 | 69.28981 |
| BiologicalMaterial12 | 64.59155 |
| ManufacturingProcess06 | 64.33243 |
| ManufacturingProcess31 | 58.23648 |
| ManufacturingProcess36 | 57.07735 |
| Overall | |
|---|---|
| ManufacturingProcess32 | 100.00000 |
| ManufacturingProcess39 | 39.63867 |
| ManufacturingProcess24 | 38.99622 |
| ManufacturingProcess37 | 35.14903 |
| ManufacturingProcess28 | 34.72328 |
| ManufacturingProcess13 | 34.15713 |
| BiologicalMaterial05 | 33.37511 |
| ManufacturingProcess09 | 32.93617 |
| ManufacturingProcess04 | 32.50607 |
| ManufacturingProcess06 | 28.55732 |
To compare the top 10 important predictors across the optimal Cubist, Linear, SVM, KNN, and Neural Network models, we can focus on identifying patterns and any overlapping predictors. Here are the key observations:
Comparison and Analysis of Top 10 Important Predictors:
Common Predictors Across Models:
ManufacturingProcess32 appears as the top predictor in almost all models (Cubist, Linear, SVM, KNN, and Neural Network), indicating it has strong predictive power across both linear and nonlinear models.
ManufacturingProcess06 is also a common predictor across all models, indicating its consistent importance.
ManufacturingProcess09 and ManufacturingProcess13 appear frequently, showing up in most models.
Biological Variables Across Models:
In the Cubist model, BiologicalMaterial12 and BiologicalMaterial03 are important.
In the SVM and KNN models, BiologicalMaterial06 and BiologicalMaterial03 are among the top predictors.
The Neural Network model includes BiologicalMaterial05 in its top predictors.
Linear Model has BiologicalMaterial05 in its top 10 as well.
This suggests that while biological variables are important, the specific biological predictor differs slightly depending on the model.
Process Variables Dominance:
Across all models, process-related variables dominate the list of top predictors, indicating that manufacturing processes are generally more influential in predicting the target variable.
Models like the Linear Model and Neural Network tend to favor more unique process-related variables such as ManufacturingProcess28, ManufacturingProcess33, ManufacturingProcess24, and ManufacturingProcess45.
Insights and Interpretation of Variable Importance:
Consistency Across Models:
Some predictors, like ManufacturingProcess32 and ManufacturingProcess06, are consistently important across all models. This consistency suggests these predictors have a strong and likely linear relationship with the target variable, making them valuable regardless of model complexity.
Variability with Model Type:
The Cubist and SVM models tend to include a mix of both manufacturing process variables and biological material variables, indicating that these models might capture more nuanced interactions between biological and process-related factors.
The Neural Network model, known for capturing complex patterns, still ranks process-related variables highly, but includes some biological materials that may interact nonlinearly with the process variables.
Model-Specific Important Variables:
Certain variables are more model-specific, such as ManufacturingProcess45 in the Linear model or ManufacturingProcess04 in the Neural Network model. These variables might have non-linear or interaction effects that are better captured by specific model structures.
ManufacturingProcess32 and ManufacturingProcess06 emerge as the most critical predictors across different model types, indicating their fundamental importance to the target variable. Process variables generally dominate the top predictor list, but the inclusion of biological variables varies by model, with some models (e.g., SVM and KNN) including multiple biological materials. This analysis suggests that while process variables are consistently impactful, certain biological factors play a secondary role, especially in nonlinear models like SVM and KNN.
(c) Plot the optimal single tree with the distribution of yield in the terminal nodes.
Does this view of the data provide additional knowledge about the biological or process predictors and their relationship with yield?
Yes, this decision tree provides additional insights into the relationship between the biological and process predictors with yield. Here’s a breakdown of the knowledge we can gain from this tree visualization:
Hierarchical Structure and Importance
ManufacturingProcess32 is the root node, which implies it is the most critical variable in determining yield. The first split based on ManufacturingProcess32 indicates that variations in this predictor have a substantial impact on yield, setting the primary direction for the rest of the splits.
The next most important predictors are BiologicalMaterial12 and ManufacturingProcess31, as they are immediately involved in the subsequent splits. This hierarchical ordering implies that ManufacturingProcess32, ManufacturingProcess31, and BiologicalMaterial12 are likely the most influential in determining yield outcomes.
Relationship Patterns in Predictors For nodes where ManufacturingProcess32 is below 0.17, the model further segments based on BiologicalMaterial12. This suggests that BiologicalMaterial12 plays a significant role in explaining yield variability when ManufacturingProcess32 is low.
For nodes where ManufacturingProcess32 is above 0.17, ManufacturingProcess31 and BiologicalMaterial03 play a crucial role, with specific thresholds of 0.15 and 0.47, respectively. This indicates that BiologicalMaterial03 becomes more important in determining yield under certain conditions of ManufacturingProcess31.
Interaction Effects
The tree reveals potential interaction effects between biological and process variables. For instance:
When BiologicalMaterial12 is less than 0.19 and ManufacturingProcess32 is low, the tree further segments based on BiologicalMaterial05 and ManufacturingProcess39. This suggests an interaction where certain levels of BiologicalMaterial12 in conjunction with ManufacturingProcess32 influence yield.
A similar interaction is seen with ManufacturingProcess31 and BiologicalMaterial03 on the right side of the tree, where the yield outcomes vary based on both the values of ManufacturingProcess31 and BiologicalMaterial03.
Yield Predictions at Terminal Nodes
Each terminal node represents a different yield outcome, with values that range from negative (e.g., -1.6) to positive (e.g., 1.3).
Certain combinations of biological and process values lead to higher yield predictions. For example:
High values in ManufacturingProcess31 and BiologicalMaterial03 (>= 0.47) result in a yield of 1.3. Conversely, low values in ManufacturingProcess32 and BiologicalMaterial12 result in lower yield outcomes, indicating a negative impact on yield when these conditions are met.
Threshold Effects
The decision tree model identifies specific threshold values (e.g., ManufacturingProcess32 < 0.17, BiologicalMaterial12 < 0.19) where the yield distribution changes. This implies that small changes around these thresholds could lead to significant changes in yield, providing actionable insights for optimizing manufacturing and biological parameters.
Interpretation of Biological vs. Process Variables
Process Variables: ManufacturingProcess32 and ManufacturingProcess31 have the largest impact, suggesting that optimizing these process parameters could lead to better yield.
Biological Variables: Although BiologicalMaterial12 and BiologicalMaterial03 are less dominant than the main process variables, they still play a significant role, especially under specific conditions of the process variables. This indicates that the biological variables act as secondary factors, influencing yield in the presence of certain process conditions.
This decision tree offers a more nuanced understanding of how both biological and process variables interact to influence yield. The hierarchical splits and interactions reveal that:
Process variables like ManufacturingProcess32 and ManufacturingProcess31 are primary drivers. Biological variables have an additive effect, refining the yield prediction under certain process conditions.
Thresholds identified in this tree provide actionable points that could be used for process optimization, helping to achieve a higher yield by controlling specific variables.
This visualization is valuable for understanding not just the importance of each variable but also how combinations of biological and process factors jointly impact yield outcomes.