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I
MATHEMATICAL MODEL ON THE CELLULASE
AS A FUNCTION OF PRODUCTION SENZYME
VISCOSITY
FAHIMEH ABDEYAZDAN
DISSERTATION SUBMITTED IN FULFILLMENT OF
THE REQUIREMENT FOR THE DEGREE OF MASTER
OF SCIENCE
INSTITUTE OF BIOLOGICAL SCIENCE
FACULTY OF SCIENCE
UNIVERSITY OF MALAYA
KUALA LUMPUR
2011
III
Declaration
Name of Candidate: FAHIMEH ABDEYAZDAN (I.C/Passport No: L13473857)
Registration/Matric No: SGR080115 Name of Degree: MASTER OF SCIENCE
Title of Project Paper/Research Report/Dissertation/Thesis (―this Work‖):
MATHEMATICAL MODEL ON THE CELLULASE ENZYME PRODUCTION AS A
FUNCTION OF VISCOSITY
Field of Study: Biotechnology
I do solemnly and sincerely declare that:
I am the sole author/writer of this Work;
(1) This Work is original;
(2) Any use of any work in which copyright exists was done by way of fair dealing and
for permitted purposes and any excerpt or extract from, or reference to or
reproduction of any copyright work has been disclosed expressly and sufficiently
and the title of the Work and its authorship have been acknowledged in this Work;
(3) I do not have any actual knowledge nor do I ought reasonably to know that the
making of this work constitutes an infringement of any copyright work;
(4) I hereby assign all and every rights in the copyright to this Work to the University of
Malaya (―UM‖), who henceforth shall be owner of the copyright in this Work and
that any reproduction or use in any form or by any means whatsoever is prohibited
without the written consent of UM having been first had and obtained;
(5) I am fully aware that if in the course of making this Work I have infringed any
copyright whether intentionally or otherwise, I may be subject to legal action or any
other action as may be determined by UM.
Candidate’s Signature Date
Subscribed and solemnly declared before,
Witness’s Signature Date
Name:
Designation:
IV
Abstract
As cellulosic material is the most abundant and renewable source of organic
matter, ethanol can be produced cheaply from cellulosic waste. The cellulose must be
hydrolyzed to glucose before it can be fermented to ethanol. The enzymatic hydrolysis
of cellulose using cellulase enzymes is considered an environmental- friendly and less
energy intensive alternative.
White-rot fungi belong to the wood-destroying basidiomycetes and are well
known as the only micro-organisms responsible for the enzyme hydrolysis of all major
wood polymers, including lignin, cellulose and hemicelluloses.
On the other hand, the production cost of cellulase enzymes is a limitation in
ethanol fermentation. Therefore, the goal is to produce the enzymes economically by
means of high-yield cellulase fermentation.
Different type of bacteria and fungi can be used to achieve to this goal. In the
present study, the ability of Pycnoporus sanguineus, a white rot fungus to produce
cellulase was investigated since there are no reports of its cellulase production
available. Different types of basal media were tested and enzyme activity was measured
in the presence of cellulose powder, carboxymethylcellulose (CMC), Tween 80 and
yeast extract. The cost of each medium is an important consideration. The highest
amount of reducing sugar production was observed when CMC and Tween 80 were
V
used as the components of the medium. This formulation is the most cost effective
among the medium formulation.
The study also presents the development of a mathematical model for cellulase
production in submerged fermentation as a function of medium’s viscosity. To achieve
this, the fungus was grown in two different media on agar plates. Then, the inoculation
was carried out from these plates to a medium formulation in the shake flasks using
variable concentration of CMC for determination of CMCase activity. Enzyme activity
and viscosities of media were measured simultaneously. Mathematical function was
explored for each media and then a unique model was reported for each media.
VI
Abstrak
Memandangkan sebatian selulos merupakan bahan organik yang banyak dan
sumber yang boleh diperbaharui secara semula jadi, etanol dapat dihasilkan dengan
kos yang rendah daripada sisa-sisa selulos. Selulos harus di hydrolisiskan kepada
glukos sebelum proses penapaian etanol dapat dilakukan. Pencernaan (hidrolisis)
selulose dengan menggunakan enzim selulase merupakan satu kaedah yang tidak
mencemarkan alam sekitar dan tidak membebankan.
Sebaliknya, kulat putih reput kepunyaan basidiomycetes memusnahkan kayu
dan dikenali sebagai mikroorganisma sahaja bertanggungiawab untuk pemineralan
semnua polimer kayu yang utama, termasuk lignin, selulosa dan hemicelluloses.
Penggunaan enzim selulose dalam proses penapaian etanol memerlukan kos
penghasilan yang tinggi. Oleh itu, tujuan utama kajian ini adalah untuk
menghasilkan enzim ini dalam kuantiti yang banyak tanpa mengeluarkan kos yang
tinggi.
Berbagai jenis bacteria dan kulat boleh digunakan untuk mencapai matlamat
ini. Dalam kajian ini, kemampuan Pycnoporus sanguineus iaitu cendawan pelapuk
putih yang dapat menghasilkan selulase telah dikaji dan diselidik kerana tiada
laporan kajian mengenai pengahasilan enzim ini daripada spesies tersebut. Berbagai
jenis media dasar diuji dan aktiviti enzim diukur dengan adanya serbuk selulosa
carboxymethyl cellulose (CMC), Tween 80 and ekstrak yis.
VII
Kemudian, kos setiap media akan menjadi pelaburan. Jumlah tertinggi
mengurangkan pengeluaran gula apabila CMC dan Tween 80 telah digunakan
sebagai media. Mujurlah media ini adalah media termurah antara yang lain yang
telah disiasat.
Disertasi ini juga menerangkan pembangunan model matematik untuk
penghasilan selulase dalam fermentasi terendam sebagai fungsi dari viskositi
medium. Untuk mencapai matlamat ini, kulat ditumbuhkan dalam dua media yang
berbeza pada plat agar . kemudian, inokulasi dilakukan daripada plat agar ke dalam
flask yang mengandungi medium yang telah diformulasikan dimana kepekatan
CMC telah dimanipulasikan untuk penentuan aktiviti CMCase. Aktiviti enzim dan
viskositi media diukur serentak. Fungsi matematik yang menyeluruh telah dijalankan
dan model yang unik telah dipersembahkan untuk setiap media.
VIII
Acknowledgements
I am indebted to my helpful supervisor, Assoc. Prof. M Suffian M Annuar,
whose encouragement, guidance and support from the initial to the final level
enabled me to develop an understanding of the subject. The supervision and support
that he gave truly help not only my thesis even my life.
I’m heartily thankful to Dr. Ahmad Neyamadpour, for his help during
accomplish my project and his guide to understanding of mathematical modelling
aspect of thesis step by step. Also, Great deals appreciated go to Dr. Ahmad Faris
Mohd Adnan, my co- supervisor for his advices.
To Professors Amru Nasrulhaq and Rosli Hashim, heads of Institute of
Biological Science, I am grateful for the trust deposited in my work and for the
motivation demonstrated.
I offer my regards and blessings to my knowledgeable friend Masoud
Razavian and my lab mate Muhamad Alimin; they supported me in any respect
during the completion of the project.
Lastly, I would also to express my appreciation to my liberal parents and my
brother and sister, Mohammad Ali and Farideh; their love gave me forces to make
this work.
Fahimeh Abdeyazdan
December, 2011
IX
Table of contents
MATHEMATICAL MODEL ON THE CELLULASE ENZYMES
PRODUCTION AS A FUNCTION OF VISCOSITY ............................................. I
Declaration ............................................................................................................... III
Abstract .................................................................................................................... IV
Abstrak ..................................................................................................................... VI
Acknowledgements ............................................................................................... VIII
Table of contents ..................................................................................................... IX
List of Tables ........................................................................................................ XIII
List of Figures ....................................................................................................... XIX
Publication ........................................................................................................... XXII
Abbreviations .................................................................................................... XXIII
Chapter 1 .................................................................................................................... 1
Introduction ................................................................................................................ 1
1.1. Background and scope of research .................................................................... 1
1.1. Objectives of thesis ........................................................................................... 2
1.2. Outline of the thesis .......................................................................................... 3
X
Chapter 2 .................................................................................................................... 4
Literature review ........................................................................................................ 4
2.1. Biological part ................................................................................................... 4
2.1.1. White-rot Fungi .............................................................................................. 4
2.1.2. Cellulose structure ........................................................................................ 10
2.1.3. Cellulase enzyme system ............................................................................. 13
2.1.4. Endogluconases activity using viscometric method .................................... 21
2.2. Mathematical modeling ................................................................................... 23
2.2.1. General Regression Theory .......................................................................... 24
2.2.2. Derivatives and Nonlinear Regression ......................................................... 29
2.2.3. Understanding and Interpreting Regression Results .................................... 30
Residuals ................................................................................................................ 30
Sum of Residuals ................................................................................................... 31
Average Residual ................................................................................................... 31
Residual Sum of Squares ....................................................................................... 32
Error Variance ........................................................................................................ 33
Standard Error of the Estimate ............................................................................... 33
R2, or Coefficient of Multiple Determination ........................................................ 33
2.2.4. Regression Variable (parameter) Results ..................................................... 34
XI
2.2.5. Confidence Intervals .................................................................................... 35
2.2.6. Variance Inflation Factors (VIF) .................................................................. 36
2.2.7. Determining the goodness of fit ................................................................... 37
Chapter 3 .................................................................................................................. 41
Materials and Methods ............................................................................................ 41
3.1. Microorganism ................................................................................................ 41
3.2. Media preparation ........................................................................................... 41
3.3. Inoculation and incubation .............................................................................. 43
3.4. Enzyme production ......................................................................................... 43
3.4.1. Glucose standard calibration ........................................................................ 45
3.4.2. CMCase activity using spectrometer ........................................................... 47
3.4.3. FPase activity using spectrometer ................................................................ 48
3.5. Enzyme activity using commercial cellulase from Aspergilleus niger ........... 48
3.6. Viscometric method for cellulase assay .......................................................... 49
3.6.1. Media composition ....................................................................................... 51
3.6.2. CMCase activity measurement .................................................................... 52
3.6.3. Viscosity measurement ................................................................................ 52
3.6.4. Vibro viscometer system .............................................................................. 53
Chapter 4 .................................................................................................................. 56
XII
Results and discussion ............................................................................................. 56
4.1. Fungal cellulase production in modified media .............................................. 56
4.2. Commercial enzyme production ..................................................................... 66
4.3. Comparison of costs of selected media ........................................................... 67
4.4. Mathematical modelling part .......................................................................... 68
Chapter 5 .................................................................................................................. 83
Conclusions ............................................................................................................... 83
References ................................................................................................................. 86
Appendix A ............................................................................................................... 99
XIII
List of Tables
Table 2.1. Distribution of cellulase in fungi. ............................................................... 7
Table 3.1. Composition of potato dextrose broth. ...................................................... 41
Table 3.2. Basal medium composition. ...................................................................... 43
Table 3.3. Media compositions for fungal cellulase production in shake flasks. ...... 44
Table 3.4. Composition of GYMP Agar. ................................................................... 51
Table 4.1. The viscosity and enzyme activities when inocula were prepared in
GYMP (pH= 5.5 at 25oC). ......................................................................... 69
Table 4.2. The viscosity and enzyme activities when inocula were prepared in PDA
media (pH= 5.5 at 25oC). ........................................................................... 70
Table 4.3. Summary of regression results for the best fit modelling study for media
with GYMP inocula. .................................................................................. 72
Table 4.4. 99% Confidence Intervals, GYMP inocula, 5 g L-1
CMC concentration. 74
Table 4.5. 99% Confidence Intervals, GYMP inocula, 10 g L-1
CMC concentration.
.................................................................................................................................... 74
Table 4.6. 99% Confidence Intervals, GYMP inocula, 15 g L-1
CMC concentration.
.................................................................................................................................... 75
Table 4.7. 99% Confidence Intervals, GYMP inocula, 20 g L-1
CMC concentration.
.................................................................................................................................... 75
Table 4.8. 99% Confidence Intervals, GYMP inocula, 20 g L-1
CMC concentration.
.................................................................................................................................... 76
XIV
Table 4.9. Summary of regression results for the best fit modelling study for media
with PDA inocula. ..................................................................................... 77
Table 4.10. 99% Confidence Intervals, PDA inocula, 5 g L-1
CMC concentration. .. 79
Table 4.11. 99% Confidence Intervals, PDA inocula, 10 g L-1
CMC concentration. 79
Table 4.12. 99% Confidence Intervals, PDA inocula, 15 g L-1
CMC concentration. 80
Table 4.13. 99% Confidence Intervals, PDA inocula, 20 g L-1
CMC concentration. 80
Table 4.14. 99% Confidence Intervals, PDA inocula, 25 g L-1
CMC concentration. 81
Table A.1. Regression Variable Results, media= GYMP, 5 g L
-1 CMC concentration.
.................................................................................................................................... 99
Table A.2. 68% Confidence Intervals, media= GYMP, 5 g L-1
CMC concentration.
.................................................................................................................................... 99
Table A.3. 90% Confidence Intervals, media= GYMP, 5 g L-1
CMC concentration.
.................................................................................................................................. 100
Table A.4. 95% Confidence Intervals, media= GYMP, 5 g L-1
CMC concentration.
.................................................................................................................................. 100
Table A.5. 99% Confidence Intervals, media= GYMP, 5 g L-1
CMC concentration.
.................................................................................................................................. 100
Table A.6. Variance Analysis, media= GYMP, 5 g L-1
CMC concentration. ......... 101
Table A.7. Regression Variable Results, media= GYMP, 10 g L-1
CMC
concentration. ........................................................................................ 101
Table A.8. 68% Confidence Intervals, media= GYMP, 10 g L-1
CMC concentration.
.................................................................................................................................. 101
Table A.9. 90% Confidence Intervals, media= GYMP, 10 g L-1
CMC concentration.
.................................................................................................................................. 102
XV
Table A. 10. 95% Confidence Intervals, media= GYMP, 10 g L-1
CMC
concentration. ............................................................................................. 102
Table A. 11. 99% Confidence Intervals, media= GYMP, 10 g L-1
CMC
concentration. ............................................................................................. 103
Table A.12. Variance Analysis, media= GYMP, 5 g L-1
CMC concentration. ....... 103
Table A.13. Regression Variable Results, media= GYMP, 15 g L-1
CMC
concentration. ........................................................................................ 103
Table A.14. 68% Confidence Intervals, media= GYMP, 15 g L-1
CMC
concentration. ........................................................................................ 104
Table A.15. 90% Confidence Intervals, media= GYMP, 15 g L-1
CMC
concentration. ........................................................................................ 104
Table A.16. 95 % Confidence Intervals, media= GYMP, 15 g L-1
CMC
concentration. ........................................................................................ 104
Table A.17. 99 % Confidence Intervals, media= GYMP, 15 g L-1
CMC
concentration. ........................................................................................ 105
Table A.18. Variance Analysis, media= GYMP, 15 g L-1
CMC concentration. ..... 105
Table A.19. Regression Variable Results, media= GYMP, 20 g L-1
CMC
concentration. ........................................................................................ 105
Table A.20. 68% Confidence Intervals, media= GYMP, 20 g L-1
CMC
concentration. ........................................................................................ 106
Table A.21. 90% Confidence Intervals, media= GYMP, 20 g L-1
CMC
concentration. ........................................................................................ 106
Table A. 22. 95% Confidence Intervals, media= GYMP, 20 g L-1
CMC
concentration. ........................................................................................ 107
XVI
Table A. 23. 99% Confidence Intervals, media= GYMP, 20 g L-1
CMC
concentration. ........................................................................................ 107
Table A.24. Variance Analysis, media= GYMP, 20 g L-1
CMC concentration. ..... 107
Table A. 25. Regression Variable Results, media= GYMP, 25 g L-1
CMC
concentration. ........................................................................................ 108
Table A.26. 68% Confidence Intervals, media= GYMP, 20 g L-1
CMC
concentration. ........................................................................................ 108
Table A.27. 90% Confidence Intervals, media= GYMP, 25 g L-1
CMC
concentration. ........................................................................................ 108
Table A. 28. 95% Confidence Intervals, media= GYMP, 25 g L-1
CMC
concentration. ........................................................................................ 109
Table A.29. 99% Confidence Intervals, media= GYMP, 25 g L-1
CMC
concentration. ........................................................................................ 109
Table A.30. Variance Analysis, media= GYMP, 20 g L-1
CMC concentration. ..... 110
Table A.31. Regression Variable Results, media= PDA, 5 g L-1
CMC concentration.
.................................................................................................................................. 110
Table A. 32. 68% Confidence Intervals, media= PDA, 5 g L-1
CMC concentration.
.................................................................................................................................. 110
Table A. 33. 90% Confidence Intervals, media= PDA, 5 g L-1
CMC concentration.
.................................................................................................................................. 111
Table A. 34. 95% Confidence Intervals, media= PDA, 5 g L-1
CMC concentration.
.................................................................................................................................. 111
Table A.35. 99% Confidence Intervals, media= PDA, 5 g L-1
CMC concentration.
.................................................................................................................................. 111
XVII
Table A.36. Variance Analysis, media= PDA, 5 g L-1
CMC concentration. ........... 112
Table A.37. Regression Variable Results, media= PDA, 10 g L-1
CMC
concentration. ........................................................................................ 112
Table A.38. 68% Confidence Intervals, media= PDA, 10 g L-1
CMC concentration.
.................................................................................................................................. 112
Table A.39. 90% Confidence Intervals, media= PDA, 10 g L-1
CMC concentration.
.................................................................................................................................. 113
Table A.40. 95% Confidence Intervals, media= PDA, 10 g L-1
CMC concentration.
.................................................................................................................................. 113
Table A.41. 99% Confidence Intervals, media= PDA, 10 g L-1
CMC concentration.
.................................................................................................................................. 113
Table A.42. Variance Analysis, media= PDA, 10 g L-1
CMC concentration. ......... 114
Table A.43. Regression Variable Results, media= PDA, 15 g L-1
CMC
concentration. ...................................................................................... 114
Table A.44. 68% Confidence Intervals, media= PDA, 15 g L-1
CMC concentration.
.................................................................................................................................. 114
Table A.45. 90% Confidence Intervals, media= PDA, 15 g L-1
CMC concentration.
.................................................................................................................................. 115
Table A.46. 95% Confidence Intervals, media= PDA, 15 g L-1
CMC concentration.
.................................................................................................................................. 115
Table A. 47. 99% Confidence Intervals, media= PDA, 15 g L-1
CMC concentration.
.................................................................................................................................. 116
Table A.48. Variance Analysis, media= PDA, 15 g L-1
CMC concentration. ......... 116
XVIII
Table A.49. Regression Variable Results, media= PDA, 20 g L-1
CMC
concentration. ...................................................................................... 116
Table A.50. 68% Confidence Intervals, media= PDA, 20 g L-1
CMC concentration.
.................................................................................................................................. 116
Table A.51. 90% Confidence Intervals, media= PDA, 20 g L-1
CMC concentration.
.................................................................................................................................. 117
Table A.52. 95% Confidence Intervals, media= PDA, 20 g L-1
CMC concentration.
.................................................................................................................................. 117
Table A.53. 99% Confidence Intervals, media= PDA, 20 g L-1
CMC concentration.
.................................................................................................................................. 118
Table A.54. Variance Analysis, media= PDA, 20 g L-1
CMC concentration. ......... 118
Table A.55. Regression Variable Results, media= PDA, 25 g L-1
CMC
concentration. ...................................................................................... 118
Table A.56. 68% Confidence Intervals, media= PDA, 25 g L-1
CMC concentration.
.................................................................................................................................. 119
Table A.57. 90% Confidence Intervals, media= PDA, 25 g L-1
CMC concentration.
.................................................................................................................................. 119
Table A.58. 95% Confidence Intervals, media= PDA, 25 g L-1
CMC concentration.
.................................................................................................................................. 119
Table A.59. 99% Confidence Intervals, media= PDA, 25 g L-1
CMC concentration.
.................................................................................................................................. 120
Table A.60. Variance Analysis, media= PDA, 25 g L-1
CMC concentration. ......... 120
XIX
List of Figures
Figure 2.1. Diagram of the structural formula for the β-1,4-glucan polymer chain
(cellulose). The repeating unit, cellobiose is indicated in brackets (Brown
et al., 1996).............................................................................................. 11
Figure 2.2. A simplified model to illustrate the cross-linking of cellulose microfibrils
and hemicellulose in the lignocellulosic biomass. .................................. 12
Figure 2.3. Enzymatic hydrolysis of cellulose to glucose. ......................................... 13
Figure 2.4. Typical cellulase structure. (a): Exogluconase, (b): Endogluconase. ...... 15
Figure 2.5. Hypothesis for the role of oligomers during microbially and
enzymatically mediated cellulose hydrolysis .......................................... 16
Figure 2.6. Schematic representation of the hydrolysis of amorphous and
microcrystalline cellulose by non-complexed (a) and complexed (b)
cellulase systems. not shown to scale...................................................... 17
Figure 3.1. Schematic diagram for enzyme activity measurement……………….....43
Figure 3.2. Glucose standard calibration.................................................................... 46
Figure 3.3. Spectrophotometric system (V-630 Jusco). ............................................. 47
Figure 3.4. Schematic diagram for mathematical modeling methodology………....51
Figure 3.5. Glass fibre for sample filtration. .............................................................. 53
Figure 3.6. Vibro viscometer system. ........................................................................ 53
Figure 3.7. Vibro viscometer (detection system). ...................................................... 54
Figure 4.1. Reducing sugars production and enzyme activities from CMCase and
FPase when 20 g L-1
cellulose powder was used as the major source of carbon. ...... 57
XX
Figure 4.2. Reducing sugars production and enzyme activities from CMCase and
FPase when 20 g L-1
cellulose was as the major source of carbon and Tween
80 was included in the basal media. ............................................................... 58
Figure 4.3. Reducing sugars production and enzyme activities from CMCase and
FPase when 10 g L-1
cellulose was as the major source of carbon and 10
g L-1
yeast extract supplementation. ..................................................... 59
Figure 4.4. Reducing sugar production and enzyme activities from CMCase and
FPase when 10 g L-1
cellulose, 10 g L-1
yeast extract and Tween 80 was
included in the medium. .......................................................................... 59
Figure 4.5. The reducing sugars production in different media composition with
cellulose as a major carbon source. T: Tween 80, Y: yeast extract. ....... 60
Figure 4.6. Reducing sugars production and enzyme activities from CMCase and
FPase when 20 g L-1
CMC was the major source of carbon in the media.
................................................................................................................. 61
Figure 4.7. Reducing sugars production and enzyme activities from CMCase and
Fpase when 20 g L-1
CMC was the major source of carbon and Tween
80 was included in the basal media. ........................................................ 62
Figure 4.8. Reducing sugar production and enzyme activities from CMCase and
FPase when 10 g L-1
CMC, 10 g L-1
yeast extract was included in the
medium. ................................................................................................... 63
Figure 4.9. Reducing sugars production and enzyme activities from CMCase and
Fpase when 10 g L-1
CMC, 10 g L-1
yeast extract and Tween 80 were
included in the medium. .......................................................................... 64
XXI
Figure 4.10. The reducing sugars production in different media composition in the
presence of CMC as a major carbon source. ........................................... 65
Figure 4.11. Reducing sugars production using commercial cellulase. ..................... 67
Figure 4.12. Costs in Malaysian Ringgit to produce 1 L of production media and
reducing sugars production after 144 hours. ........................................... 68
Figure 4.13. Agreement between the proposed model outputs and experimental data
(GYMP inocula, a) 5 g L-1
, b) 10 g L-1
, c) 15 g L-1
, d) 20 g L-1
, d)25 gL-1
CMC concentration). ............................................................................... 73
Figure 4.14. Agreement between the proposed model outputs and experimental data
PDA inocula, a) 5 g L-1
, b) 10 g L-1
, c) 15 g L-1
, d) 20 g L-1
, d) 25 g L-1
CMC concentration. ................................................................................ 78
Figure 5.1. Enzyme assay using viscometric and spectrophotometric methods in (a)
GYMP media and (b) PDA media........................................................85
XXII
Publication
The following paper has been published from this thesis:
Conference:
Media strategies to increase cellulase production from Pycnoporus sanguineus.
15th
Biological Graduate Congress, University of Malaya, Kuala Lumpur, Malaysia.
XXIII
Abbreviations
AR Average Residual
Avicelase Avicel hydrolysis activity
BG β-glycosidase
CBH Cellobiohydrolase
CMC Carboxymethylcellulose
CMCase Carboxymcthyl cellulase
Ea Enzyme activity
EG Endoglucanase
Fp Filter paper
FPase Filter paper hydrolyse
mol. wt. molecular weight
Glu Glucose
R2 Coefficient of Multiple Determination
Ra2 Adjusted Coefficient of Multiple Determinations
RSS Residual Sum of Squares
SEE Standard Error of the Estimate
SR Sum of Residuals
T Time
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