# Quantitative Quality Evaluation of Software Products by Considering Summary and Comments Entropy of a Reported Bug

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

## 1. Introduction

- Case 1:
- Prediction of latent bugs based on calendar time (month).
- Case 2:
- Prediction of latent bugs based on summary_entropy.
- Case 3:
- Prediction of latent bugs based on comment_entropy.

Case 1 | Time vs. bugs | In this case, the software reliability growth models in [7,8,9,12,14,15] have been used to predict the potential bugs lying dormant in the software. |

Case 2 | Summary_entropyvs. bugs | In this case, summary_entropy based bug prediction models have been proposed. |

Case 3 | Comment_entropyvs. bugs | In this case, comment_entropy based bug prediction models have been proposed. |

^{2}, bias, variation, mean squared error (MSE) and root mean squared prediction error (RMSPE).

## 2. Data Collection, Preprocessing and Model Building for Bug Prediction

#### 2.1. Data Collection

#### 2.2. Extraction ofthe Terms and Its Weight Using Summary Attributes

#### 2.3. Entropy

_{1}, a

_{2}, a

_{3},…, a

_{n}} and its probability distribution is P = {p

_{1}, p

_{2}, p

_{3},…, p

_{n}}, the random uncertainty is measured by Shannon’sentropy, Sn is defined as:

#### 2.4. Software Reliability Growth Modeling

#### 2.4.1. Software Reliability Growth Models (Time vs. Bugs, i.e.,Case 1 in Introduction Section)

**Model 1. G-O model [14]:**

**Model 2. Yamada-delayed S-shaped model [9]:**

**Model 3. Kapur-3-stage model [15]:**

**Model 4. K-G model [7]:**

_{1}and y

_{2}are the number of independent and dependent bugs respectively.

_{1}(t) and x

_{2}(t) denote the mean value functions of independent and dependent bugs fixed in a time interval. The fixing of independent bugs follows exponential growth curves as these bugs are simple in nature and removed immediately. The following differential equation has thus been written as follows in [14]:

**Model 5. Error Dependency Model [8]:**

_{1}(t) from Equation (11) in Equation (12) and by taking θ(t) = 0, we get the following:

**Model 6. Huang et al. Model 1 [12]:**

**Model 7. Huang et al. Model 2 [12]:**

#### 2.4.2. Entropy-Based Software Reliability Growth Models (Entropy Vs bugs, i.e.,Case 2 and Case 3 in the Introduction Section)

**Model 8:**

**Model 9:**

**Model 10:**

**Model 11:**

_{1}and p

_{2}be the proportion of independent and dependent software bugs lying dormant in the software. The following equation where p is the sum of both independent and dependent bugs, can be written:

_{1}(H(t)) and x

_{2}(H(t)) denote the mean value functions of independent and dependent bugs fixed in time interval [0,t].

**Model 12:**

_{1}(H(t)) from Equation (29) and by taking $\phi \left(H\left(0\right)\right)=0$ in Equation (30), the following ensues:

**Model 13:**

**Model 14:**

## 3. Results and Analysis

^{2}, MSE, Bias, Variance and RMSPE of all the models have been tabulated in Table 10, Table 11, Table 12, Table 13, Table 14, Table 15, Table 16 and Table 17. In the performance table, the bold value indicates the maximum value of R

^{2}across all the cases for all the products.

## 4. Related Work

#### 4.1. Bug Triaging

#### 4.2. Prediction Modeling Based on Bug Summary Metric

#### 4.3. Bug Comments

#### 4.4. NHPP-Based Software Reliability Growth Modeling

#### 4.5. Entropy-Based Prediction Modeling

^{2}was found to be more than 0.95. In another study [5], the authors proposed an approach that predicted the potential number of bugs by considering: (i) traditional SRGM, (ii) entropy-based models and (iii) potential bugs based on entropy. In thestudy, it was observed that the potential complexity of code change(entropy)-based approach wasbetter. Instudy [59], the authors proposed entropy-based software reliability analysis. The experimental result was validated on five products of the Apache open source projects, namely Avro, Pig, Hive, jUDDI and Whirr. In [58] the authors proposed an entropy optimized Latent Dirichlet Allocation (LDA) approach for bug assignment. The experimental results were validated on the Eclipse JDT and Mozilla Firefox projects and recallsofup to 84% and 58% were achieved, and precisionsof ofup to 28% and 41%, respectively. Recently, the authors developed entropy-based regression models to predict the bad smells [6].

## 5. Conclusions

^{2}, variation and RMSPE. Summary entropy metric-based proposed modelswere observed to have performed better in 78.57%of the cases in comparison with time-based models. Comment entropy metric-based proposed models performed better in 85.71% cases in comparison withtime-based models.We also observed that in the cases, where case 1, i.e., t vs. bugs performs better, it overestimated the value of the potential number of bugs. From this premise, the authors concluded that the proposed models performed significantly better in comparison with t vs. bugs models (model 1 to 7). It also provided an optimal value of potential bugs. In the future, further work could be done in the area of the summary_entropy and comment_entropymetric-based models using other project data to make it general.

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

Acronyms | |

OSS | Open Source Software |

NHPP | Non Homogenous Poisson Process |

SPSS | Statistical Package for Social Sciences |

SRGM | Software Reliability Growth Model |

Notations | |

t | Time |

y/p | Potential number of bugs lying dormant in the software that can be fixed over a long run |

y_{1}/p_{1} | Number of independent bugs |

y_{2}/p_{2} | Number of dependent bugs |

x(t) | Mean value function of bug detection/fixed up to time t |

x_{1}(t) | Mean value function of the expected number of independent bugs |

x_{2}(t) | Mean value function of the expected number of dependent bugs |

g/k | Rate of bug detection/fixed |

r/l | Rate of bug detection/fixed of independent bugs |

c/d | Rate of bug detection/fixed of dependent bugs |

θ(t)/θ(H(t)) | Delay–effect factor i.e., debugging time lag |

ψ | Inflection factor |

q | Proportion of the independent bugs |

β | Constant and >0 |

H(t) or H(t) | The value of summary/comment entropy at time t be consistent writing H or H |

x(H(t)) | Bugs removed by cumulative entropy value H(t) |

δ | Constant and >0 |

## References

- Godbole, N.S. Software Quality Assurance: Principles and Practice; Alpha Science Intl Ltd.: Oxford, UK, 2004. [Google Scholar]
- Hassan, A.E. Predicting bugs using the complexity of code changes. In Proceedings of the 31st International Conference on Software Engineering, Washington, DC, USA, 16–24 May 2009; pp. 78–88. [Google Scholar]
- Shannon, C.E. A Mathematical Theory of Communication. Bell Syst. Tech. J.
**1948**, 27, 379–423. [Google Scholar] [CrossRef] - Chaturvedi, K.K.; Kapur, P.K.; Anand, S.; Singh, V.B. Predicting the complexity of code changes using entropy based measures. Int. J. Syst. Assur. Eng. Manag.
**2014**, 5, 155–164. [Google Scholar] [CrossRef] - Singh, V.B.; Chaturvedi, K.K.; Khatri, S.K.; Kumar, V. Bug prediction modeling using complexity of code changes. Int. J. Syst. Assur. Eng. Manag.
**2015**, 6, 44–60. [Google Scholar] [CrossRef] - Gupta, A.; Suri, B.; Kumar, V.; Misra, S.; Blažauskas, T.; Damaševičius, R. Software Code Smell Prediction Model Using Shannon, Rényi and Tsallis Entropies. Entropy
**2018**, 20, 372. [Google Scholar] [CrossRef] - Kapur, P.K.; Garg, R.B. A software reliability growth model for an error-removal phenomenon. Softw. Eng. J.
**1992**, 7, 291–294. [Google Scholar] [CrossRef] - Kapur, P.K.; Younes, S. Software reliability growth model with error dependency. Microelectron. Reliab.
**1995**, 35, 273–278. [Google Scholar] [CrossRef] - Yamada, S.; Ohba, M.; Osaki, S. S-shaped reliability growth modeling for software error detection. IEEE Trans. Reliab.
**1983**, 32, 475–484. [Google Scholar] [CrossRef] - Kapur, P.K.; Singh, V.B.; Anand, S.; Yadavalli, V.S.S. Software reliability growth model with change-point and effort control using a power function of the testing time. Int. J. Prod. Res.
**2008**, 46, 771–787. [Google Scholar] [CrossRef] - Kapur, P.K.; Gupta, A.; Yadavalli, V.S.S. Software reliability growth modeling using power function of testing time. Int. J. Oper. Quant. Manag.
**2006**, 12, 127–140. [Google Scholar] - Huang, C.Y.; Lin, C.T. Software reliability analysis by considering fault dependency and debugging time lag. IEEE Trans. Reliab.
**2006**, 55, 436–450. [Google Scholar] [CrossRef] - Singh, V.B.; Yadav, K.; Kapur, R.; Yadavalli, V.S.S. Considering the fault dependency concept with debugging time lag in software reliability growth modeling using a power function of testing time. Int. J. Autom. Comput.
**2007**, 4, 359–368. [Google Scholar] [CrossRef] - Goel, A.L.; Okumoto, K. Time-dependent error-detection rate model for software reliability and other performance measures. IEEE Trans. Reliab.
**1979**, 28, 206–211. [Google Scholar] [CrossRef] - Kapur, P.K.; Younes, S.; Agarwala, S. Generalized Erlang software reliability growth model. Asor Bull.
**1995**, 14, 5–11. [Google Scholar] - Huang, C.Y.; Kuo, S.Y.; Chen, Y. Analysis of a software reliability growth model with logistic testing-effort function. In Proceedings of the Eighth International Symposium on Software Reliability Engineering, Albuquerque, NM, USA, 2–5 November 1997; pp. 378–388. [Google Scholar]
- Yamada, S.; Ohtera, H.; Narihisa, H. Software reliability growth models with testing-effort. IEEE Trans. Reliab.
**1986**, 35, 19–23. [Google Scholar] [CrossRef] - Huang, C.Y. Performance analysis of software reliability growth models with testing-effort and change-point. J. Syst. Softw.
**2005**, 76, 181–194. [Google Scholar] [CrossRef] - Huang, C.Y.; Kuo, S.Y. Analysis of incorporating logistic testing-effort function into software reliability modeling. IEEE Trans. Reliab.
**2002**, 51, 261–270. [Google Scholar] [CrossRef] [Green Version] - Malaiya, Y.K.; Li, M.N.; Bieman, J.M.; Karcich, R. Software reliability growth with test coverage. Ieee Trans. Reliab.
**2002**, 51, 420–426. [Google Scholar] [CrossRef] - Wang, X.; He, Y. Learning from uncertainty for big data: Future analytical challenges and strategies. IEEE Syst. ManCybern. Mag.
**2016**, 2, 26–31. [Google Scholar] [CrossRef] - Available online: http://bugs.eclipse.org/bugs/ (accessed on 28 June 2018).
- Porter, M.F. An algorithm for suffix stripping. Program
**1980**, 14, 130–137. [Google Scholar] [CrossRef] - Murphy, G.; Cubranic, D. Automatic bug triage using text categorization. In Proceedings of the Sixteenth International Conference on Software Engineering & Knowledge Engineering, Banff, AB, Canada, 20–24 June 2004; pp. 1–6. [Google Scholar]
- Anvik, J.; Hiew, L.; Murphy, G.C. Who should fix this bug? In Proceedings of the 28th international Conference on Software Engineering, Shanghai, China, 20–28 May 2006; pp. 361–370. [Google Scholar]
- Moin, A.; Neumann, G. Assisting bug triage in large open source projects using approximate string matching. In Proceedings of the 7th nternational Conference on Software Engineering Advances (ICSEA 2012), Lissabon, Portugal, 18–23 November 2012; pp. 1–6. [Google Scholar]
- Bhattacharya, P.; Neamtiu, I.; Shelton, C.R. Automated, highly-accurate, bug assignment using machine learning and tossing graphs. J. Syst. Softw.
**2012**, 85, 2275–2292. [Google Scholar] [CrossRef] - Tamrawi, A.; Nguyen, T.T.; Al-Kofahi, J.M.; Nguyen, T.N. Fuzzy set and cache-based approach for bug triaging. In Proceedings of the 19th ACM SIGSOFT Symposium and the 13th European Conference on Foundations of Software Engineering, Szeged, Hungary, 5–9 September 2011; pp. 365–375. [Google Scholar]
- Bhattacharya, P.; Neamtiu, I. Fine-grained incremental learning and multi-feature tossing graphs to improve bug triaging. In Proceedings of the 2010 IEEE International Conference Software Maintenance (ICSM), Timisoara, Romania, 12–18 September 2010; pp. 1–10. [Google Scholar]
- Alenezi, M.; Magel, K.; Banitaan, S. Efficient Bug Triaging Using Text Mining. JSW
**2013**, 8, 2185–2190. [Google Scholar] [CrossRef] - Jeong, G.; Kim, S.; Zimmermann, T. Improving bug triage with bug tossing graphs. In Proceedings of the the 7th Joint Meeting of the European Software Engineering Conference and the ACM SIGSOFT Symposium on The Foundations of Software Engineering, Amsterdam, The Netherlands, 24–28 August 2009; pp. 111–120. [Google Scholar]
- Xuan, J.; Jiang, H.; Ren, Z.; Yan, J.; Luo, Z. Automatic bug triage using semi-supervised text classification. arXiv, 2017; arXiv:1704.04769. [Google Scholar]
- Govindasamy, V.; Akila, V.; Anjanadevi, G.; Deepika, H.; Sivasankari, G. Data reduction for bug triage using effective prediction of reduction order techniques. In Proceedings of the 2016 International Conference on Computation of Power, Energy Information and Commuincation (ICCPEIC), Chennai, India, 20–21 April 2016; pp. 85–90. [Google Scholar]
- Xuan, J.; Jiang, H.; Hu, Y.; Ren, Z.; Zou, W.; Luo, Z.; Wu, X. Towards effective bug triage with software data reduction techniques. IEEE Trans. Knowl. Data Eng.
**2014**, 27, 264–280. [Google Scholar] [CrossRef] - Tian, Y.; Wijedasa, D.; Lo, D.; Le Goues, C. Learning to rank for bug report assignee recommendation. In Proceedings of the 2016 IEEE 24th International Conference on Program Comprehension (ICPC), Austin, TX, USA, 16–17 May 2016; pp. 1–10. [Google Scholar]
- Anvik, J.; Murphy, G.C. Reducing the effort of bug report triage: Recommenders for development-oriented decisions. ACM Trans. Softw. Eng. Methodol. (TOSEM)
**2011**, 20, 10. [Google Scholar] [CrossRef] - Shokripour, R.; Anvik, J.; Kasirun, Z.M.; Zamani, S. Why so complicated? simple term filtering and weighting for location-based bug report assignment recommendation. In Proceedings of the 2013 10th IEEE Working Conference on Mining Software Repositories (MSR), San Francisco, CA, USA, 18–19 May 2013; pp. 2–11. [Google Scholar]
- Goyal, A.; Sardana, N. Efficient bug triage in issue tracking systems. In Proceedings of the Doctoral Consortium at the 13th International Conference on Open Source Systems, Buenos Aires, Argentina, 22 May 2017; pp. 15–24. [Google Scholar]
- Jin, K.; Dashbalbar, A.; Yang, G.; Lee, B. Improving Predictions about Bug Severity by Utilizing Bugs Classified as Normal. Contemp. Eng. Sci.
**2016**, 9, 933–942. [Google Scholar] [CrossRef] - Zhang, T.; Yang, G.; Lee, B.; Chan, A.T. Predicting severity of bug report by mining bug repository with concept profile. In Proceedings of the 30th Annual ACM Symposium on Applied Computing, Salamanca, Spain, 13–17 April 2015; pp. 1553–1558. [Google Scholar]
- Roy, N.K.S.; Rossi, B. Towards an improvement of bug severity classification. In Proceedings of the 2014 40th EUROMICRO Conference on Software Engineering and Advanced Applications (SEAA), Verona, Italy, 27–29 August 2014; pp. 269–276. [Google Scholar]
- Chaturvedi, K.K.; Singh, V.B. An empirical comparison of machine learning techniques in predicting the bug severity of open and closed source projects. Int. J. Open Source Softw. Process. (IJOSSP)
**2012**, 4, 32–59. [Google Scholar] [CrossRef] - Tian, Y.; Lo, D.; Sun, C. Information retrieval based nearest neighbor classification for fine-grained bug severity prediction. In Proceedings of the 2012 19th Working Conference on Reverse Engineering, Kingston, ON, Canada, 15–18 October 2012; pp. 215–224. [Google Scholar]
- Yang, C.Z.; Hou, C.C.; Kao, W.C.; Chen, X. An Empirical Study on Improving Severity Prediction of Defect Reports using Feature Selection. In Proceedings of the 19th Asia-Pacific Software Engineering Conference, Hong Kong, China, 4–7 December 2012; pp. 240–249. [Google Scholar]
- Chaturvedi, K.K.; Singh, V.B. Determining Bug Severity Using Machine Learning Techniques. In Proceedings of the 2012 CSI Sixth International Conference on Software Engineering, Indore, India, 5–7 September 2012; pp. 1–6. [Google Scholar]
- Lamkanfi, A.; Demeyer, S.; Giger, E.; Goethals, B. Predicting the Severity of a Reported Bug. In Proceedings of the 2010 7th IEEE Working Conference on Mining Software Repositories, Cape Town, South Africa, 2–3 May 2010; pp. 1–10. [Google Scholar]
- Lamkanfi, A.; Demeyer, S.; Soetens, Q.D.; Verdonck, T. Comparing Mining Algorithms for Predicting the Severity of a Reported Bug. In Proceedings of the 2011 15th European Conference on Software Maintenance and Reengineering, Oldenburg, Germany, 1–4 March 2011; pp. 249–258. [Google Scholar]
- Menzies, T.; Marcus, A. Automated Severity Assessment of Software Defect Reports. In Proceedings of the 2008 IEEE International Conference Software Maintenance, Beijing, China, 28 September–4 October 2008; pp. 346–355. [Google Scholar]
- Alenezi, M.; Banitaan, S. Bug Reports Prioritization: Which Features and Classifier to Use? In Proceedings of the 2013 12th International Conference on Machine Learning and Applications, Miami, FL, USA, 4–7 December 2013; pp. 112–116. [Google Scholar]
- Kanwal, J.; Maqbool, O. Managing open bug repositories through bug report prioritization using SVMs. In Proceedings of the International Conference on Open-Source Systems and Technologies, Lahore, Pakistan, 22–24 December 2010. [Google Scholar]
- Kanwal, J.; Maqbool, O. Bug prioritization to facilitate bug report triage. J. Comput. Sci. Technol.
**2012**, 27, 397–412. [Google Scholar] [CrossRef] - Sharma, M.; Bedi, P.; Chaturvedi, K.K.; Singh, V.B. Predicting the priority of a reported bug using machine learning techniques and cross project validation. In Proceedings of the 2012 12th International Conference on Intelligent Systems Design and Applications (ISDA), Kochi, India, 27–29 November 2012; pp. 539–545. [Google Scholar]
- Dit, B.; Poshyvanyk, D.; Marcus, A. Measuring the semantic similarity of comments in bug reports. Proc. 1st Stsm
**2008**, 8, 64. [Google Scholar] - Xuan, J.; Jiang, H.; Zhang, H.; Ren, Z. Developer recommendation on bug commenting: A ranking approach for the developer crowd. Sci. China Inf. Sci.
**2017**, 60, 072105. [Google Scholar] [CrossRef] - Pham, H.; Zhang, X. NHPP software reliability and cost models with testing coverage. Eur. J. Oper. Res.
**2003**, 145, 443–454. [Google Scholar] [CrossRef] - Inoue, S.; Yamada, S. Two-dimensional software reliability measurement technologies. In Proceedings of the 2009 IEEE International Conference on Industrial Engineering and Engineering Management, Hong Kong, China, 8–11 December 2009; pp. 223–227. [Google Scholar]
- Kapur, P.K.; Garg, R.B.; Aggarwal, A.G.; Tandon, A. Two dimensional flexible software reliability growth model and related release policy. In Proceedings of the 4th National Conference, INDIACom-2010, New Delhi, India, 25–26 February 2010. [Google Scholar]
- Zhang, W.; Cui, Y.; Yoshida, T. En-LDA: An novel approach to automatic bug report assignment with entropy optimized latent dirichletallocation. Entropy
**2017**, 19, 173. [Google Scholar] [CrossRef] - Singh, V.B.; Sharma, M.; Pham, H. Entropy Based Software Reliability Analysis of Multi-Version Open Source Software. IEEE Trans. Softw. Eng.
**2018**, 44, 1207–1223. [Google Scholar] [CrossRef] - Wu, H.; Li, Y.; Bi, X.; Zhang, L.; Bie, R.; Wang, Y. Joint entropy based learning model for image retrieval. J. Vis. Commun. Image Represent.
**2018**, 55, 415–423. [Google Scholar] [CrossRef]

**Figure 1.**A part of the bug report for bug id 139050 of BIRT products of Eclipse projects with its three comments and summary.

Product | Number of Bugs | Observation Period |
---|---|---|

BIRT | 15,914 | January2005–May 2018 |

CDT | 12,438 | January 2002–June 2018 |

Community | 14,881 | March 2002–June 2018 |

EclipseLink | 9447 | March 2002–June 2018 |

EMF | 5413 | September 2002–June 2018 |

Equinox | 8066 | October 2001–June 2018 |

Orion | 7425 | December 2010–June 2018 |

Platform | 39,434 | October 2001–June 2018 |

Models | Prediction Classes | Actual Bugs | Parameter Estimates | ||||||
---|---|---|---|---|---|---|---|---|---|

y | g | c | q | r | ψ | β | |||

Model 1 | Case 1 | 15,914 | 17,831 | 0.019 | - | - | - | - | - |

Model 8 | Case 2 | 26,390 | 0.001 | - | - | - | - | - | |

Model 8 | Case 3 | 27,393 | 0.060 | - | - | - | - | - | |

Model 2 | Case 1 | 16,302 | 0.047 | - | - | - | - | - | |

Model 9 | Case 2 | 20,305 | 0.002 | - | - | - | - | - | |

Model 9 | Case 3 | 20,398 | 0.205 | - | - | - | - | - | |

Model 3 | Case 1 | 15,923 | 0.074 | - | - | - | - | - | |

Model 10 | Case 2 | 17,427 | 0.004 | - | - | - | - | - | |

Model 10 | Case 3 | 17,489 | 0.381 | - | - | - | - | - | |

Model 4 | Case 1 | 16,018 | 0.056 | - | - | - | - | 5.473 | |

Model 11 | Case 2 | 26,364 | 0.001 | - | - | - | - | 1.966 | |

Model 11 | Case 3 | 24,895 | 0.136 | - | - | - | - | 2.166 | |

Model 5 | Case 1 | 16,230 | - | 0.373 | 0.168 | 0.021 | - | - | |

Model 12 | Case 2 | 26,581 | - | 0.028 | 0.024 | 0.020 | - | - | |

Model 12 | Case 3 | 22,901 | - | 0.561 | 0.202 | 0.183 | - | - | |

Model 6 | Case 1 | 16,125 | - | 0.074 | 0.677 | 0.053 | - | - | |

Model 13 | Case 2 | 28,425 | - | 0.011 | 0.062 | 0.009 | - | - | |

Model 13 | Case 3 | 18,254 | - | 0.439 | 0.418 | 0.334 | - | - | |

Model 7 | Case 1 | 16,143 | - | 0.180 | 0.321 | 0.035 | 1.000 | - | |

Model 14 | Case 2 | 28,485 | - | 0.020 | 0.032 | 0.009 | 0.992 | - | |

Model 14 | Case 3 | 28,131 | - | 0.617 | 0.117 | 0.244 | 0.000 | - |

Models | Prediction Classes | Actual Bugs | Parameter Estimates | ||||||
---|---|---|---|---|---|---|---|---|---|

y | g | c | q | r | ψ | β | |||

Model 1 | Case 1 | 12,438 | 20,039 | 0.005 | - | - | - | - | - |

Model 8 | Case 2 | 29,190 | 0.001 | - | - | - | - | - | |

Model 8 | Case 3 | 22,449 | 0.061 | - | - | - | - | - | |

Model 2 | Case 1 | 16,437 | 0.015 | - | - | - | - | - | |

Model 9 | Case 2 | 14,343 | 0.003 | - | - | - | - | - | |

Model 9 | Case 3 | 12,697 | 0.318 | - | - | - | - | - | |

Model 3 | Case 1 | 13,601 | 0.028 | - | - | - | - | - | |

Model 10 | Case 2 | 12,365 | 0.006 | - | - | - | - | - | |

Model 10 | Case 3 | 11,629 | 0.549 | - | - | - | - | - | |

Model 4 | Case 1 | 12,591 | 0.031 | - | - | - | - | 15.207 | |

Model 11 | Case 2 | 18,114 | 0.002 | - | - | - | - | 2.024 | |

Model 11 | Case 3 | 22,114 | 0.063 | - | - | - | - | 0.016 | |

Model 5 | Case 1 | 13,907 | - | 0.580 | 0.058 | 0.005 | - | - | |

Model 12 | Case 2 | 26,113 | - | 0.011 | 0.057 | 0.015 | - | - | |

Model 12 | Case 3 | 24,188 | - | 0.094 | 0.476 | 0.120 | - | - | |

Model 6 | Case 1 | 13,717 | - | 0.160 | 0.114 | 0.027 | - | - | |

Model 13 | Case 2 | 25,343 | - | 0.026 | 0.026 | 0.024 | - | - | |

Model 13 | Case 3 | 26,486 | - | 0.376 | 0.119 | 1.000 | - | - | |

Model 7 | Case 1 | 20,952 | - | 0.206 | 0.030 | 0.035 | 1.00 | - | |

Model 14 | Case 2 | 29,598 | - | 0.004 | 0.996 | 0.001 | 0.98 | - | |

Model 14 | Case 3 | 22,034 | - | 0.069 | 0.918 | 0.067 | 0.00 | - |

Models | Prediction Classes | Actual Bugs | Parameter Estimates | ||||||
---|---|---|---|---|---|---|---|---|---|

y | g | c | q | r | ψ | β | |||

Model 1 | Case 1 | 14,880 | 18,764 | 0.006 | - | - | - | - | - |

Model 8 | Case 2 | 21,459 | 0.001 | - | - | - | - | - | |

Model 8 | Case 3 | 25,765 | 0.057 | - | - | - | - | - | |

Model 2 | Case 1 | 36,742 | 0.008 | - | - | - | - | - | |

Model 9 | Case 2 | 15,904 | 0.003 | - | - | - | - | - | |

Model 9 | Case 3 | 16,347 | 0.250 | - | - | - | - | - | |

Model 3 | Case 1 | 20,035 | 0.022 | - | - | - | - | - | |

Model 10 | Case 2 | 13,751 | 0.006 | - | - | - | - | - | |

Model 10 | Case 3 | 13,945 | 0.468 | - | - | - | - | - | |

Model 4 | Case 1 | 25,352 | 0.017 | - | - | - | - | 15.207 | |

Model 11 | Case 2 | 22,653 | 0.002 | - | - | - | - | 1.440 | |

Model 11 | Case 3 | 31,681 | 0.079 | - | - | - | - | 1.169 | |

Model 5 | Case 1 | 21,790 | - | 0.174 | 0.046 | 0.017 | - | - | |

Model 12 | Case 2 | 21,125 | - | 0.009 | 0.129 | 0.004 | - | - | |

Model 12 | Case 3 | 27,363 | - | 0.193 | 0.445 | 0.094 | - | - | |

Model 6 | Case 1 | 25,043 | - | 0.273 | 0.032 | 0.028 | - | - | |

Model 13 | Case 2 | 24,922 | - | 0.024 | 0.035 | 0.022 | - | - | |

Model 13 | Case 3 | 26,304 | - | 0.237 | 0.233 | 0.472 | - | - | |

Model 7 | Case 1 | 20,385 | - | 0.105 | 0.068 | 0.029 | 0.971 | - | |

Model 14 | Case 2 | 19,304 | - | 0.003 | 0.755 | 0.002 | 1.000 | - | |

Model 14 | Case 3 | 28,628 | - | 0.089 | 0.750 | 0.104 | 0.993 | - |

Models | Prediction Classes | Actual Bugs | Parameter Estimates | ||||||
---|---|---|---|---|---|---|---|---|---|

y | g | c | q | r | ψ | β | |||

Model1 | Case 1 | 9447 | 9308 | 0.011 | - | - | - | - | - |

Model 8 | Case 2 | 15,517 | 0.001 | - | - | - | - | - | |

Model 8 | Case 3 | 15,552 | 0.062 | - | - | - | - | - | |

Model 2 | Case 1 | 11,259 | 0.021 | - | - | - | - | - | |

Model 9 | Case 2 | 13,609 | 0.980 | - | - | - | - | - | |

Model 9 | Case 3 | 10,221 | 0.270 | - | - | - | - | - | |

Model 3 | Case 1 | 8791 | 0.042 | - | - | - | - | - | |

Model 10 | Case 2 | 10,175 | 0.006 | - | - | - | - | - | |

Model 10 | Case 3 | 8814 | 0.498 | - | - | - | - | - | |

Model 4 | Case 1 | 28,848 | 0.008 | - | - | - | - | 2.952 | |

Model 11 | Case 2 | 19,976 | 0.002 | - | - | - | - | 3.756 | |

Model 11 | Case 3 | 19,678 | 0.077 | - | - | - | - | 0.866 | |

Model 5 | Case 1 | 9469 | - | 0.147 | 0.107 | 0.030 | - | - | |

Model 12 | Case 2 | 14,495 | - | 0.064 | 0.016 | 0.000 | - | - | |

Model 12 | Case 3 | 10,343 | - | 0.746 | 0.254 | 0.210 | - | - | |

Model 6 | Case 1 | 16,686 | - | 0.080 | 0.071 | 0.099 | - | - | |

Model 13 | Case 2 | 12,320 | - | 0.048 | 0.030 | 0.021 | - | - | |

Model 13 | Case 3 | 18,645 | - | 0.249 | 0.197 | 0.534 | - | - | |

Model 7 | Case 1 | 9574 | - | 0.064 | 0.512 | 0.016 | 0.723 | - | |

Model 14 | Case 2 | 11,849 | - | 0.012 | 0.896 | 0.002 | 1.000 | - | |

Model 14 | Case 3 | 11,609 | - | 0.207 | 0.681 | 0.187 | 0.955 | - |

Models | Prediction Classes | Actual Bugs | Parameter Estimates | ||||||
---|---|---|---|---|---|---|---|---|---|

y | g | c | q | r | ψ | β | |||

Model1 | Case 1 | 5413 | 8327 | 0.005 | - | - | - | - | - |

Model 8 | Case 2 | 10,924 | 0.001 | - | - | - | - | - | |

Model 8 | Case 3 | 13,177 | 0.042 | - | - | - | - | - | |

Model 2 | Case 1 | 7767 | 0.015 | - | - | - | - | - | |

Model 9 | Case 2 | 7415 | 0.999 | - | - | - | - | - | |

Model 9 | Case 3 | 5913 | 0.288 | - | - | - | - | - | |

Model 3 | Case 1 | 6228 | 0.029 | - | - | - | - | - | |

Model 10 | Case 2 | 6045 | 0.010 | - | - | - | - | - | |

Model 10 | Case 3 | 5249 | 0.518 | - | - | - | - | - | |

Model 4 | Case 1 | 5173 | 0.053 | - | - | - | - | 69.853 | |

Model 11 | Case 2 | 4045 | 0.196 | - | - | - | - | 266.921 | |

Model 11 | Case 3 | 10,766 | 0.065 | - | - | - | - | 0.259 | |

Model 5 | Case 1 | 5332 | 0.006 | 0.640 | 0.067 | - | - | - | |

Model 12 | Case 2 | 10,082 | 0.306 | 0.071 | 0.020 | - | - | - | |

Model 12 | Case 3 | 12,337 | 0.061 | 0.060 | 0.746 | - | - | - | |

Model 6 | Case 1 | 7457 | - | 0.552 | 0.021 | 0.038 | - | - | |

Model 13 | Case 2 | 8304 | - | 0.006 | 0.432 | 0.008 | - | - | |

Model 13 | Case 3 | 12,752 | - | 0.345 | 0.120 | 0.822 | - | - | |

Model 7 | Case 1 | 4942 | - | 0.725 | 0.044 | 0.018 | 1.00 | - | |

Model 14 | Case 2 | 11,233 | - | 0.009 | 0.201 | 0.004 | 0.00 | - | |

Model 14 | Case 3 | 12,653 | - | 0.093 | 0.430 | 0.104 | 0.00 | - |

Models | Prediction Classes | Actual Bugs | Parameter Estimates | ||||||
---|---|---|---|---|---|---|---|---|---|

y | g | c | q | r | ψ | β | |||

Model 1 | Case 1 | 8066 | 11,515 | 0.009 | - | - | - | - | - |

Model 8 | Case 2 | 9567 | 0.002 | - | - | - | - | - | |

Model 8 | Case 3 | 12,531 | 0.076 | - | - | - | - | - | |

Model 2 | Case 1 | 8121 | 0.038 | - | - | - | - | - | |

Model 9 | Case 2 | 10,015 | 0.005 | - | - | - | - | - | |

Model 9 | Case 3 | 9360 | 0.259 | - | - | - | - | - | |

Model 3 | Case 1 | 7749 | 0.062 | - | - | - | - | - | |

Model 10 | Case 2 | 8588 | 0.009 | - | - | - | - | - | |

Model 10 | Case 3 | 8271 | 0.459 | - | - | - | - | - | |

Model 4 | Case 1 | 7782 | 0.048 | - | - | - | - | 6.259 | |

Model 11 | Case 2 | 14,583 | 0.002 | - | - | - | - | 1.743 | |

Model 11 | Case 3 | 15,143 | 0.094 | - | - | - | - | 0.961 | |

Model 5 | Case 1 | 7931 | - | 0.435 | 0.107 | 0.019 | - | - | |

Model 12 | Case 2 | 17,575 | - | 0.649 | 0.002 | 0.000 | - | - | |

Model 12 | Case 3 | 20,563 | - | 0.190 | 0.218 | 0.164 | - | - | |

Model 6 | Case 1 | 8207 | - | 0.232 | 0.677 | 0.031 | - | - | |

Model 13 | Case 2 | 17,900 | - | 0.041 | 0.025 | 0.040 | - | - | |

Model 13 | Case 3 | 19,612 | - | 0.370 | 0.108 | 0.809 | - | - | |

Model 7 | Case 1 | 7633 | - | 0.731 | 0.060 | 0.037 | 0.991 | - | |

Model 14 | Case 2 | 26,896 | - | 0.031 | 0.020 | 0.018 | 0.003 | - | |

Model 14 | Case 3 | 17,406 | - | 0.144 | 0.415 | 0.103 | 0.007 | - |

Models | Prediction Classes | Actual Bugs | Parameter Estimates | ||||||
---|---|---|---|---|---|---|---|---|---|

y | g | c | q | r | ψ | β | |||

Model 1 | Case 1 | 7425 | 10,502 | 0.016 | - | - | - | - | - |

Model 8 | Case 2 | 50,546 | 0.000 | - | - | - | - | - | |

Model 8 | Case 3 | 70,489 | 0.009 | - | - | - | - | - | |

Model 2 | Case 1 | 7573 | 0.058 | - | - | - | - | - | |

Model 9 | Case 2 | 9382 | 0.991 | - | - | - | - | - | |

Model 9 | Case 3 | 9382 | 0.006 | - | - | - | - | - | |

Model 3 | Case 1 | 7082 | 0.096 | - | - | - | - | - | |

Model 10 | Case 2 | 7813 | 0.011 | - | - | - | - | - | |

Model 10 | Case 3 | 8382 | 0.377 | - | - | - | - | - | |

Model 4 | Case 1 | 10,502 | 0.016 | - | - | - | - | 0.000 | |

Model 11 | Case 2 | 6043 | 0.037 | - | - | - | - | 1936.012 | |

Model 11 | Case 3 | 14,352 | 0.134 | - | - | - | - | 3.100 | |

Model 5 | Case 1 | 11,633 | - | 0.251 | 0.050 | 0.515 | - | - | |

Model 12 | Case 2 | 29,024 | - | 0.036 | 0.017 | 0.019 | - | - | |

Model 12 | Case 3 | 17,483 | - | 0.253 | 0.388 | 0.068 | - | - | |

Model 6 | Case 1 | 12,138 | - | 0.170 | 0.068 | 0.667 | - | - | |

Model 13 | Case 2 | 29,752 | - | 0.023 | 0.026 | 0.030 | - | - | |

Model 13 | Case 3 | 19,846 | - | 0.210 | 0.181 | 0.363 | - | - | |

Model 7 | Case 1 | 10,181 | - | 0.022 | 0.687 | 0.023 | 0.00 | - | |

Model 14 | Case 2 | 25,198 | - | 0.040 | 0.018 | 0.019 | 0.01 | - | |

Model 14 | Case 3 | 21,858 | - | 0.201 | 0.233 | 0.123 | 0.38 | - |

Models | Prediction Classes | Actual Bugs | Parameter Estimates | ||||||
---|---|---|---|---|---|---|---|---|---|

y | g | c | q | r | ψ | β | |||

Model 1 | Case 1 | 39,671 | 38,839 | 0.014 | - | - | - | - | - |

Model 8 | Case 2 | 77,829 | 0.000 | - | - | - | - | - | |

Model 8 | Case 3 | 52,937 | 0.083 | - | - | - | - | - | |

Model 2 | Case 1 | 34,392 | 0.037 | - | - | - | - | - | |

Model 9 | Case 2 | 49,091 | 0.001 | - | - | - | - | - | |

Model 9 | Case 3 | 40,539 | 0.277 | - | - | - | - | - | |

Model 3 | Case 1 | 33,245 | 0.061 | - | - | - | - | - | |

Model 10 | Case 2 | 40,691 | 0.002 | - | - | - | - | - | |

Model 10 | Case 3 | 36,771 | 0.475 | - | - | - | - | - | |

Model 4 | Case 1 | 38,839 | 0.014 | - | - | - | - | 0.000 | |

Model 11 | Case 2 | 65,121 | 0.001 | - | - | - | - | 2.239 | |

Model 11 | Case 3 | 66,742 | 0.064 | - | - | - | - | 0.076 | |

Model 5 | Case 1 | 38,193 | - | 0.474 | 0.031 | 0.233 | - | - | |

Model 12 | Case 2 | 145,329 | - | 0.024 | 0.005 | 0.007 | - | - | |

Model 12 | Case 3 | 66,742 | - | 0.076 | 0.164 | 0.064 | - | - | |

Model 6 | Case 1 | 38,381 | - | 0.135 | 0.106 | 0.219 | - | - | |

Model 13 | Case 2 | 118,171 | - | 0.012 | 0.012 | 0.009 | - | - | |

Model 13 | Case 3 | 89,932 | - | 0.358 | 0.104 | 1.000 | - | - | |

Model 7 | Case 1 | 37,297 | - | 0.268 | 0.760 | 0.017 | 0.88 | - | |

Model 14 | Case 2 | 98,807 | - | 0.008 | 0.024 | 0.003 | 0.00 | - | |

Model 14 | Case 3 | 70,590 | - | 0.087 | 0.549 | 0.104 | 0.00 | - |

Models | Prediction Classes | Performance Measures | ||||
---|---|---|---|---|---|---|

R^{2} | Bias | MSE | Variation | RMSPE | ||

Model 1 | Case 1 | 0.954 | −163.495 | 1,194,892.241 | 1084.230 | 1096.488 |

Model 8 | Case 2 | 0.982 | −17.696 | 453,766.553 | 675.517 | 675.749 |

Model 8 | Case 3 | 0.985 | −98.599 | 394,474.665 | 622.244 | 630.008 |

Model 2 | Case 1 | 0.982 | −7.395 | 453,323.773 | 675.380 | 675.420 |

Model 9 | Case 2 | 0.994 | 69.679 | 146,078.571 | 376.984 | 383.370 |

Model 9 | Case 3 | 0.994 | 74.541 | 150,867.384 | 382.401 | 389.599 |

Model 3 | Case 1 | 0.941 | 99.646 | 541,276.388 | 731.239 | 737.997 |

Model 10 | Case 2 | 0.985 | 122.257 | 375,407.367 | 602.281 | 614.564 |

Model 10 | Case 3 | 0.985 | 127.544 | 381,748.506 | 606.460 | 619.727 |

Model 4 | Case 1 | 0.986 | 1.244 | 351,146.125 | 594.447 | 594.448 |

Model 11 | Case 2 | 1.000 | 23.738 | 38,455.058 | 195.273 | 196.710 |

Model 11 | Case 3 | 0.999 | 42.930 | 12,988.803 | 105.907 | 114.277 |

Model 5 | Case 1 | 0.984 | 12.355 | 405,231.593 | 638.469 | 638.589 |

Model 12 | Case 2 | 0.985 | 4.661 | 390,022.091 | 626.473 | 626.491 |

Model 12 | Case 3 | 0.998 | 12.001 | 57,487.729 | 240.222 | 240.522 |

Model 6 | Case 1 | 0.984 | 23.937 | 415,426.803 | 646.127 | 646.570 |

Model 13 | Case 2 | 0.997 | 96.403 | 83,831.124 | 273.878 | 290.350 |

Model 13 | Case 3 | 0.990 | 246.435 | 266,484.564 | 455.035 | 517.481 |

Model 7 | Case 1 | 0.985 | 2.000 | 390,062.997 | 626.520 | 626.524 |

Model 14 | Case 2 | 0.996 | −163.103 | 105,145.596 | 281.141 | 325.027 |

Model 14 | Case 3 | 0.999 | 51.892 | 33,526.995 | 176.151 | 183.636 |

Models | Prediction Classes | Performance Measures | ||||
---|---|---|---|---|---|---|

R^{2} | Bias | MSE | Variation | RMSPE | ||

Model 1 | Case 1 | 0.936 | −307.488 | 1,164,072.526 | 1034.178 | 1078.922 |

Model 8 | Case 2 | 0.996 | 0.905 | 65,518.687 | 255.965 | 255.966 |

Model 8 | Case 3 | 1.000 | 6.020 | 6334.770 | 79.363 | 79.591 |

Model 2 | Case 1 | 0.990 | −52.882 | 189,299.515 | 431.860 | 435.086 |

Model 9 | Case 2 | 0.990 | 131.072 | 175,543.721 | 397.950 | 418.979 |

Model 9 | Case 3 | 0.985 | 169.365 | 278,993.022 | 500.309 | 528.198 |

Model 3 | Case 1 | 0.993 | 30.106 | 134,173.962 | 365.058 | 366.298 |

Model 10 | Case 2 | 0.974 | 229.204 | 478,157.939 | 652.398 | 691.490 |

Model 10 | Case 3 | 0.963 | 282.772 | 674,920.035 | 771.336 | 821.535 |

Model 4 | Case 1 | 0.994 | −18.394 | 117,906.308 | 342.882 | 343.375 |

Model 11 | Case 2 | 1.000 | 46.601 | 8678.597 | 80.665 | 93.159 |

Model 11 | Case 3 | 1.000 | 7.838 | 6412.712 | 79.695 | 80.079 |

Model 5 | Case 1 | 0.993 | −23.043 | 136,263.595 | 368.419 | 369.139 |

Model 12 | Case 2 | 0.999 | 40.189 | 22,924.823 | 145.978 | 151.409 |

Model 12 | Case 3 | 1.000 | 4.323 | 6046.042 | 77.636 | 77.756 |

Model 6 | Case 1 | 0.993 | 25.781 | 127,341.016 | 355.916 | 356.849 |

Model 13 | Case 2 | 0.999 | 26.686 | 30,079.843 | 171.370 | 173.435 |

Model 13 | Case 3 | 0.999 | 63.130 | 24,504.164 | 143.244 | 156.538 |

Model 7 | Case 1 | 0.988 | −46.152 | 218,158.724 | 464.789 | 467.075 |

Model 14 | Case 2 | 1.000 | −0.397 | 1040.268 | 32.251 | 32.253 |

Model 14 | Case 3 | 1.000 | 5.465 | 6319.237 | 79.306 | 79.494 |

Models | Prediction Classes | Performance Measures | ||||
---|---|---|---|---|---|---|

R^{2} | Bias | MSE | Variation | RMSPE | ||

Model 1 | Case 1 | 0.870 | −377.826 | 2,651,431.333 | 1583.881 | 1628.322 |

Model 8 | Case 2 | 0.985 | 38.621 | 280,844.882 | 528.539 | 529.948 |

Model 8 | Case 3 | 0.990 | −110.623 | 212,211.498 | 447.185 | 460.664 |

Model 2 | Case 1 | 0.997 | 46.663 | 53,829.332 | 227.270 | 232.011 |

Model 9 | Case 2 | 0.988 | 176.111 | 248,543.613 | 466.399 | 498.541 |

Model 9 | Case 3 | 0.986 | 189.262 | 282,806.236 | 496.977 | 531.795 |

Model 3 | Case 1 | 0.990 | 141.903 | 213,061.200 | 439.232 | 461.586 |

Model 10 | Case 2 | 0.968 | 287.249 | 645,863.042 | 750.567 | 803.656 |

Model 10 | Case 3 | 0.967 | 141.903 | 213,061.200 | 439.232 | 461.586 |

Model 4 | Case 1 | 0.998 | −39.074 | 36,042.701 | 185.785 | 189.849 |

Model 11 | Case 2 | 1.000 | 24.461 | 5645.190 | 71.041 | 75.134 |

Model 11 | Case 3 | 1.000 | 24.311 | 7576.764 | 83.581 | 87.045 |

Model 5 | Case 1 | 0.979 | −49.445 | 426,340.972 | 651.073 | 652.948 |

Model 12 | Case 2 | 0.998 | 58.820 | 40,477.491 | 192.400 | 201.190 |

Model 12 | Case 3 | 0.999 | 12.254 | 11,536.524 | 106.707 | 107.408 |

Model 6 | Case 1 | 0.990 | 22.104 | 194,491.013 | 440.457 | 441.011 |

Model 13 | Case 2 | 0.997 | 43.838 | 63,797.015 | 248.747 | 252.581 |

Model 13 | Case 3 | 0.992 | 164.222 | 164,655.758 | 371.062 | 405.778 |

Model 7 | Case 1 | 0.959 | 260.299 | 838,248.268 | 877.777 | 915.559 |

Model 14 | Case 2 | 0.999 | 23.633 | 15,895.979 | 123.845 | 126.079 |

Model 14 | Case 3 | 0.999 | 24.528 | 10,470.253 | 99.341 | 102.324 |

Models | Prediction Classes | Performance Measures | ||||
---|---|---|---|---|---|---|

R^{2} | Bias | MSE | Variation | RMSPE | ||

Model 1 | Case 1 | 0.890 | −68.855 | 678,238.979 | 820.669 | 823.553 |

Model 8 | Case 2 | 0.948 | −21.774 | 323,428.341 | 568.291 | 568.708 |

Model 8 | Case 3 | 0.987 | 10.891 | 79,180.202 | 281.179 | 281.390 |

Model 2 | Case 1 | 0.934 | 137.527 | 407,579.417 | 623.431 | 638.419 |

Model 9 | Case 2 | 0.988 | 108.322 | 123,830.963 | 334.809 | 351.896 |

Model 9 | Case 3 | 0.985 | 94.631 | 95,383.522 | 293.987 | 308.842 |

Model 3 | Case 1 | 0.898 | 205.498 | 634,357.651 | 769.499 | 796.466 |

Model 10 | Case 2 | 0.958 | 165.170 | 259,656.410 | 482.053 | 509.565 |

Model 10 | Case 3 | 0.961 | 153.624 | 238,577.579 | 463.656 | 488.444 |

Model 4 | Case 1 | 0.969 | 54.919 | 192,514.466 | 435.314 | 438.765 |

Model 11 | Case 2 | 0.997 | 27.387 | 20,699.431 | 141.242 | 143.873 |

Model 11 | Case 3 | 1.000 | 8.512 | 2201.280 | 46.139 | 46.918 |

Model 5 | Case 1 | 0.929 | 152.657 | 441,328.862 | 646.548 | 664.326 |

Model 12 | Case 2 | 0.943 | −95.121 | 353,611.586 | 586.995 | 594.652 |

Model 12 | Case 3 | 0.992 | 54.938 | 49,197.141 | 214.893 | 221.804 |

Model 6 | Case 1 | 0.950 | 1.184 | 307,477.827 | 554.506 | 554.507 |

Model 13 | Case 2 | 0.955 | 165.150 | 280,454.177 | 503.170 | 529.579 |

Model 13 | Case 3 | 0.993 | 77.748 | 44,252.107 | 195.467 | 210.362 |

Model 7 | Case 1 | 0.940 | 91.341 | 373,154.792 | 603.996 | 610.864 |

Model 14 | Case 2 | 0.957 | 155.151 | 263,713.386 | 489.532 | 513.530 |

Model 14 | Case 3 | 0.996 | 20.478 | 23,867.677 | 153.128 | 154.492 |

Models | Prediction Classes | Performance Measures | ||||
---|---|---|---|---|---|---|

R^{2} | Bias | MSE | Variation | RMSPE | ||

Model 1 | Case 1 | 0.867 | −194.454 | 566,339.067 | 726.998 | 752.555 |

Model 8 | Case 2 | 0.992 | −5.880 | 34,692.570 | 186.167 | 186.259 |

Model 8 | Case 3 | 0.998 | 9.949 | 9583.560 | 97.389 | 97.896 |

Model 2 | Case 1 | 0.953 | −95.060 | 199,671.668 | 436.618 | 446.846 |

Model 9 | Case 2 | 0.999 | 25.565 | 4533.714 | 62.291 | 67.333 |

Model 9 | Case 3 | 0.990 | 38.686 | 41,304.357 | 199.519 | 203.235 |

Model 3 | Case 1 | 0.971 | −69.054 | 124,805.672 | 346.464 | 353.278 |

Model 10 | Case 2 | 0.997 | 32.121 | 13,362.272 | 111.043 | 115.595 |

Model 10 | Case 3 | 0.982 | 47.216 | 74,767.394 | 269.329 | 273.436 |

Model 4 | Case 1 | 0.980 | −35.506 | 86,137.501 | 291.336 | 293.492 |

Model 11 | Case 2 | 0.790 | 5.153 | 895,970.753 | 946.543 | 946.557 |

Model 11 | Case 3 | 0.998 | 14.328 | 10,192.590 | 99.936 | 100.958 |

Model 5 | Case 1 | 0.945 | −36.387 | 234,715.476 | 483.106 | 484.474 |

Model 12 | Case 2 | 0.987 | −57.478 | 55,974.800 | 229.502 | 236.590 |

Model 12 | Case 3 | 0.998 | 12.348 | 9539.927 | 96.889 | 97.673 |

Model 6 | Case 1 | 0.966 | −63.531 | 143,888.622 | 373.968 | 379.327 |

Model 13 | Case 2 | 0.999 | 27.787 | 4036.419 | 57.134 | 63.533 |

Model 13 | Case 3 | 0.997 | 26.620 | 13,777.412 | 114.319 | 117.377 |

Model 7 | Case 1 | 0.931 | −3.437 | 292,928.848 | 541.218 | 541.229 |

Model 14 | Case 2 | 1.000 | 6.864 | 316.260 | 16.406 | 17.784 |

Model 14 | Case 3 | 0.998 | 11.915 | 9511.022 | 96.794 | 97.524 |

Models | Prediction Classes | Performance Measures | ||||
---|---|---|---|---|---|---|

R^{2} | Bias | MSE | Variation | RMSPE | ||

Model 1 | Case 1 | 0.962 | −40.095 | 242,895.945 | 491.211 | 492.845 |

Model 8 | Case 2 | 0.956 | −56.757 | 278,566.818 | 524.734 | 527.794 |

Model 8 | Case 3 | 0.989 | −6.788 | 68,392.382 | 261.431 | 261.519 |

Model 2 | Case 1 | 0.992 | 13.917 | 51,576.341 | 226.677 | 227.104 |

Model 9 | Case 2 | 0.989 | 87.786 | 72,045.729 | 253.652 | 268.413 |

Model 9 | Case 3 | 0.987 | 91.327 | 81,140.316 | 269.814 | 284.851 |

Model 3 | Case 1 | 0.991 | 63.199 | 59,405.042 | 235.395 | 243.731 |

Model 10 | Case 2 | 0.973 | 145.920 | 171,480.372 | 387.541 | 414.102 |

Model 10 | Case 3 | 0.970 | 152.727 | 193,297.437 | 412.277 | 439.656 |

Model 4 | Case 1 | 0.993 | 9.389 | 45,949.640 | 214.153 | 214.359 |

Model 11 | Case 2 | 1.000 | 14.159 | 1736.049 | 39.186 | 41.666 |

Model 11 | Case 3 | 1.000 | 6.741 | 1489.955 | 38.007 | 38.600 |

Model 5 | Case 1 | 0.993 | 22.176 | 43,161.357 | 206.566 | 207.753 |

Model 12 | Case 2 | 0.993 | −68.241 | 42,137.573 | 193.599 | 205.274 |

Model 12 | Case 3 | 1.000 | 4.367 | 1152.694 | 33.669 | 33.951 |

Model 6 | Case 1 | 0.994 | 44.660 | 37,420.240 | 188.217 | 193.443 |

Model 13 | Case 2 | 0.997 | 11.406 | 18,191.483 | 134.393 | 134.876 |

Model 13 | Case 3 | 0.997 | 45.049 | 17,913.479 | 126.032 | 133.841 |

Model 7 | Case 1 | 0.991 | 82.876 | 56,042.397 | 221.752 | 236.733 |

Model 14 | Case 2 | 1.000 | 12.361 | 4062.648 | 62.529 | 63.739 |

Model 14 | Case 3 | 1.000 | 3.191 | 1167.919 | 34.025 | 34.175 |

Models | Prediction Classes | Performance Measures | ||||
---|---|---|---|---|---|---|

R^{2} | Bias | MSE | Variation | RMSPE | ||

Model 1 | Case 1 | 0.995 | 18.588 | 23,679.888 | 152.756 | 153.883 |

Model 8 | Case 2 | 0.998 | −22.362 | 7555.096 | 83.994 | 86.920 |

Model 8 | Case 3 | 0.993 | −37.593 | 32,104.300 | 175.189 | 179.177 |

Model 2 | Case 1 | 0.996 | 116.875 | 151,851.918 | 371.742 | 389.682 |

Model 9 | Case 2 | 0.991 | 41.627 | 39,464.244 | 194.246 | 198.656 |

Model 9 | Case 3 | 0.991 | 44.431 | 35,004.897 | 181.744 | 187.096 |

Model 3 | Case 1 | 0.932 | 181.410 | 309,045.757 | 525.487 | 555.919 |

Model 10 | Case 2 | 0.973 | 81.913 | 121,771.764 | 339.208 | 348.958 |

Model 10 | Case 3 | 0.977 | 83.590 | 102,003.389 | 308.247 | 319.380 |

Model 4 | Case 1 | 0.995 | 181.410 | 309,045.757 | 525.487 | 555.919 |

Model 11 | Case 2 | 0.769 | 300.134 | 1,042,674.949 | 976.009 | 1021.115 |

Model 11 | Case 3 | 1.000 | 4.173 | 2098.407 | 45.618 | 45.808 |

Model 5 | Case 1 | 0.984 | −2.093 | 17,985.360 | 134.093 | 134.110 |

Model 12 | Case 2 | 1.000 | −0.863 | 1212.484 | 34.810 | 34.821 |

Model 12 | Case 3 | 0.999 | 6.399 | 2300.080 | 47.530 | 47.959 |

Model 6 | Case 1 | 0.996 | 2.455 | 17,943.138 | 133.929 | 133.952 |

Model 13 | Case 2 | 1.000 | 8.771 | 1822.765 | 41.783 | 42.694 |

Model 13 | Case 3 | 0.995 | 36.389 | 22,420.814 | 145.247 | 149.736 |

Model 7 | Case 1 | 0.995 | 19.784 | 23,315.361 | 151.407 | 152.694 |

Model 14 | Case 2 | 1.000 | 8.032 | 1946.990 | 43.387 | 44.125 |

Model 14 | Case 3 | 0.999 | 6.208 | 2396.167 | 48.555 | 48.951 |

Models | Prediction Classes | Performance Measures | ||||
---|---|---|---|---|---|---|

R^{2} | Bias | MSE | Variation | RMSPE | ||

Model1 | Case 1 | 0.988 | −60.812 | 1,253,249.581 | 1117.833 | 1119.486 |

Model 8 | Case 2 | 0.986 | −225.334 | 1,406,893.822 | 1164.525 | 1186.126 |

Model 8 | Case 3 | 0.992 | 390.633 | 760,803.806 | 779.878 | 872.241 |

Model 2 | Case 1 | 0.968 | 269.670 | 3,202,764.241 | 1769.193 | 1789.627 |

Model 9 | Case 2 | 0.988 | 251.961 | 1,238,555.994 | 1084.007 | 1112.904 |

Model 9 | Case 3 | 0.981 | 349.006 | 1,960,595.755 | 1356.020 | 1400.213 |

Model 3 | Case 1 | 0.941 | 454.483 | 6,030,048.031 | 2413.192 | 2455.616 |

Model 10 | Case 2 | 0.968 | 439.203 | 3,195,122.116 | 1732.692 | 1787.490 |

Model 10 | Case 3 | 0.954 | 574.790 | 4,688,401.115 | 2087.587 | 2165.272 |

Model 4 | Case 1 | 0.988 | −60.812 | 1,253,249.581 | 1117.833 | 1119.486 |

Model 11 | Case 2 | 0.999 | 61.744 | 68,204.084 | 253.755 | 261.159 |

Model 11 | Case 3 | 1.000 | 41.716 | 17,430.761 | 125.262 | 132.026 |

Model 5 | Case 1 | 0.988 | −8.745 | 1,195,080.065 | 1093.162 | 1093.197 |

Model 12 | Case 2 | 0.995 | −14.352 | 124,215.189 | 352.149 | 352.442 |

Model 12 | Case 3 | 0.998 | −454.100 | 465,100.649 | 508.816 | 681.983 |

Model 6 | Case 1 | 0.988 | 5.076 | 1,188,051.280 | 1089.966 | 1089.978 |

Model 13 | Case 2 | 0.998 | 108.426 | 210,247.736 | 445.524 | 458.528 |

Model 13 | Case 3 | 0.999 | 80.470 | 137,436.012 | 361.885 | 370.724 |

Model 7 | Case 1 | 0.989 | 114.197 | 1,134,247.913 | 1058.871 | 1065.011 |

Model 14 | Case 2 | 0.998 | 51.394 | 216,738.414 | 462.706 | 465.552 |

Model 14 | Case 3 | 1.000 | 20.934 | 13,982.125 | 116.378 | 118.246 |

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## Share and Cite

**MDPI and ACS Style**

Kumari, M.; Misra, A.; Misra, S.; Fernandez Sanz, L.; Damasevicius, R.; Singh, V.B.
Quantitative Quality Evaluation of Software Products by Considering Summary and Comments Entropy of a Reported Bug. *Entropy* **2019**, *21*, 91.
https://doi.org/10.3390/e21010091

**AMA Style**

Kumari M, Misra A, Misra S, Fernandez Sanz L, Damasevicius R, Singh VB.
Quantitative Quality Evaluation of Software Products by Considering Summary and Comments Entropy of a Reported Bug. *Entropy*. 2019; 21(1):91.
https://doi.org/10.3390/e21010091

**Chicago/Turabian Style**

Kumari, Madhu, Ananya Misra, Sanjay Misra, Luis Fernandez Sanz, Robertas Damasevicius, and V.B. Singh.
2019. "Quantitative Quality Evaluation of Software Products by Considering Summary and Comments Entropy of a Reported Bug" *Entropy* 21, no. 1: 91.
https://doi.org/10.3390/e21010091