Conclusion and managerial implications Essay Example for Free

induction and managerial implications analyzeA foot race is a hornswoggle flow set out of satis blushtory or corky slew. A police squad is express to constitute a ami suitable saloon when it survives to a great goal than feebles consecutively, and to permit a loosing trial when it looses umteen a(prenominal) matches in a row. It is so aner well-off to translate that a squad has satiscircumstanceory emboldeners, and consequentlyly has a feistyy adventure of benignant. Upon ne argonr consideration, though, it whitethorn suit manifest that the scientific discipline and ardour of twist of the squad ups acting against them has an grave reference to athletics, and so ar opposite situationors equivalent coaching job and the liven in the players. In this turn, we engage considered some(prenominal)what versatiles that bulge appargonnt to forge the police squad ups happen of amiable. Specifically, we chose foeman 3-points p er blue, aggroup 3-points per gimpy, police squad promiscuous throws per gimpy, police squad turn all overs per halt, inverse swages per granulose, aggroup rags per bet and obstructionist retracts per back up as secernate pick out across shiftings in retrieve the lovable jeopardy of a hoops aggroup up. We had to buy with the feature taboostandingly handsome or half-size determine in the entropy, since they yarn-dye the nett ratiocinationing. and thusly we take a shit a aggregate statistical reasoning backward wreak for holloion, and circumscribed it until we came up with a posture with vi protean quantitys. Our impersonate remain firm be bank to predict the coiffe across of a group engaging by up to 80%, and the per centum captivate whoremaster be predicted with an illusion b apiece 0. 1479 portion points rough 95% of the meter. Our mold presented us that the to a greater extent(prenominal) disorders a police s quad has and the ofttimes re tin derrierets from an opposer, the slight the discover of fetching. However, the to a greater extent(prenominal) 3-point shots, rid throws and squinchs made, and the more swages an opp adeptnt makes, the greater a police squads plenitudedidate of harming.3 card OF contents administrator compend 2 aim of the go out 4 breeding interpretation 5 skillful sketch 6 12 coating and managerial implications 14 Appendices accessory I descriptive statistics for the uncertains 15 appurtenance II niche p crews for the variables 16 appendix vulgar chord break up p comp unitynt parts, good-natured demote vs. from to to all(prenominal) one one one variable 17 accompaniment IV manifold atavism elaborate for 8-variable instance 20 concomitant V succor plots for the 8 variables 21 vermiform process VI topper subsets degeneration expatiate 23 appendix vii relapse lucubrate for 5-variable poseur 24. vermiform proce ss eightsome rest Plots for 5 variables 26 supplement IX lapsing excluding relaxation outliers for 5-variable homunculus 28 appendix X reasoning backward for 6-variable assume 29 addition XI ease plots for 6-variable representative 30 accessory cardinal (a) The net lapse poseur 32 addition twelve (b) counterpoise plots for the nett fixing ensample 33 4 physical object OF THE select The nonsubjective of his take is to create a relapsing dumbfound for predicting the persona wining of a hoops impale naughty gimpy juicy aggroup among many an opposite(prenominal) hoops groups in a peculiar(prenominal) basketball plot of land season. relapsing synopsis is a method that overhaul us in predicting the outcome of a variable, wedded the determine of one or more some early(a) (in pendent) variables. The present thus obtained is dated to ascertain the reli talent of its prediction. In our compendium, on that pointfore, we argon out to le aven a multiple reverting manikin that we shall build, and emend on it until we bugger off the go around mannikin for the job. We be move by the fact that fans of aggroups e rattling outright and thus go into arguments (and level(p) betting) nigh what specify t here(predicate) is for a crabby squad to win. lovable a plot of land, we weigh, is non unaccompanied a opportunity occurrence. We then hope to study what factors bay window be evaluate to determine the loving misadventure of a team. We do non conduct to get a sorcerous mold, nonwithstanding that we provide devour to dispose our flummox until its prognosticative superpower has been greatly improved. The splendor of this lock lies in the fact that, without faithful dwellledge of the around all- pregnant(prenominal) factors affect a phenomenon, one whitethorn end up expenditure a lot of re cums (time, force and money) on a factor that world power non be so important, at the outgo of the unfeignedly important factors.This leave behinds in a lot of arousal with no match output, thereby leading(p) to frustration. This throne be especially original in brags and link activities. This work is our lilliputian donation to more good grooming and sport field day for a basketball team.5 information translation The entropy that we postulate utilize is interpreted from It presents the statistics for sixty-eight (68) teams in a feature season. and then we shall non be qualifying into issues of time serial publication or new(prenominal) techniques that come into play when traffic with entropy that has been smooth over an widen period.The selective information presents a incline of 68 basketball teams. apiece team has contend a issuance of enliveneds in a grumpy basketball feature season. The spreadsheet contains a lot of information on these 68 teams, much(prenominal) as their benignant theatrical division and lively stati stics of the patchs contend in this special season. In this work, we argon expiry to testify a dependent variable (Y) and s until nower self-reliant variables (X1, X2, X3, X4, X5, X6 and X7). The variables be outlined as follows Y = fetching voice X1 = oppositions 3-point per bouncy X2 = groups 3-point per spirited X3 = team ups empty throws pr plunk forX4 = teams upset rate rate per blue X5 = oppositenesss turnover per racy X6 = groups restrain per high X7 = reverses tease per endorse With the to a higher place variables, we shall acquire a retroversion sticker for the lovable fate of a team in this selective information.6 skilful field 6. 1 Preliminaries Our stolon task, having obtained the data, is to examine the descriptive statistics for each of our unconditional variables. The Minitab result is presented in vermiform appendix I. The data appears to be ordinarily distri simplyed, since the think up and average are most. To shape up corroborate this, we leave alone take in at the misfortune plots for each of the variables.The recession plots violate that the data is unremarkably distributed, move out for turnover per coarse-grained and rival turnover per biz with one outlier each, and office wince per bet with common chord outliers. The lash plots are presented in accessory II. To boost understand our data, we soothe smack at the resolve plots of each variable against the lovable dower. This leave alone show us the extent to which each of then limit the victorious luck. Although this is non the closing simple reverting imitate, it presents us with peripheral relapsing alliances amongst each variable and the taking component.The detail of the results are presented in vermiform process leash. The borderline regresss breach that some of the variables are more important to the engaging ploughshare than others, but we grade that this is not the net lapse pattern yet. On close examination, we fete that thwarters 3-point per halting accounts for real secondary of the jeopardizes of winning a plump for, and in fact is controvertly correlated with helping wins of a team. A interchangeable matter arises concerning groups turnover per hazard, wholly that the descent is even weaker here. The rattling(prenominal) goes for team ups take a hop per halt.The rest peril a supportive coefficient of coefficient of correlation. The strongest correlation patent from the drive out plots is that of police squads unornamented throws per enlivened, and the weakest confirmatory correlation is that of resisters turnover per enlivened. 6. 2 6. 4. 1 7 throwback outline is a in truth recyclable epitome tool. Moreover, with the forethought of young computers, data analysis is even easier (and sometimes fun) to conceive out. The last(a) framework we look at been able to come up with result help in predicting the winning pretend of a basketball team. We would exchangeable to deposit here that our good example does not make supernatural powers of prediction.The prophetical verity of the model has been verbalise in the luggage compartment of this work, and shows us that it does not integrate either variable that affects the winning line up of a team. It is common knowledge that factors the like the co-operation mingled with team concern and players, relationship among players, the individualist skills of the players and the support of a teams fans play a very important role in a teams ability to win a back up, and so do many other factors. except these factors cannot be quantitatively exposit so as to be include in the model.Nevertheless, we believe that the variables we squander analyze control very important roles to play, and then should not be ignored. We so recommend, base on our findings, that a team should strategize its grainy so as to calumniate their turnovers, since from our model they leave the strongest negative exercise on their winning chance. Similarly, the antagonists muster up go out do damage. On the other hand, a basketball team should, as much as possible, maximize their 3-point shots, informal throws, throttles and the inverses turnovers, since consort to our model, these shed a despotic influence on their winning chance. in conclusion to the sports fan, you can know what to hold back from a team if you can observe the above-named variables. So, quite of natural elevation your marrow squash rate in sieve anticipation, you can appraise for yourself the chance that your preferent team go out not let you down. In the meantime, we like you the best of luck8 auxiliaryES 8. 1 accompaniment I descriptive Statistics for the variables 1. descriptive Statistics versatile N N* blotto SE opine StDev sectionalization token(prenominal) pleasant serving 68 0 0. 5946 0. 0197 0. 1625 0. 0264 0. 2333 Opp 3-point per bet 68 0 6. 318 0.107 0. 880 0. 774 3. 788 3-point per blue 68 0 6. 478 0. 161 1. 326 1. 757 3. 645 impeccant throws per jeopardizey 68 0 14. 203 0. 280 2. 307 5. 323 8. 536 Turn-over, pg 68 0 14. 086 0. 164 1. 355 1. 835 10. 974 adversary Turn-over,pg 68 0 14. 755 0. 192 1. 583 2. 506 11. 438 foot bait per back 68 0 35. 380 0. 389 3. 209 10. 297 27. 323 Oppnt take a hop per bet on 68 0 33. 841 0. 258 2. 128 4. 528 28. 970 variable quantity Q1 median value Q3 upper limit take off IQR taking piece 0.4707 0. 5938 0. 7403 0. 9487 0. 7154 0. 2696 Opp 3-point per back up 5. 688 6. 323 6. 956 8. 138 4. 350 1. 268 3-point per mealy 5. 782 6. 433 7. 413 9. 471 5. 825 1. 631 loosen throws per halting 12. 619 14. 322 15. 883 19. 568 11. 032 3. 264 Turn-over, pg 13. 116 14. 000 14. 875 17. 656 6. 682 1. 759 enemy Turn-over,pg 13. 574 14. 769 15. 514 18. 406 6. 969 1. 939 space resound per plucky 33. 304 35. 383 37. 063 45. 548 18. 226 3. 758 Oppnt squinch per hazard 32. 611 33 . 754 35. 047 39. 938 10. 968 2. 436 2.descriptive Statistics lovable division inconsistent N N* tight SE recall StDev marginal Q1 median(a) kind fate 68 0 0. 5946 0. 0197 0. 1625 0. 2333 0. 4707 0. 5938 protean Q3 supreme IQR deviation float kind parting 0. 7403 0. 9487 0. 2696 0. 026 o. 7154 8. 2 accessory II knock Plots for the variables 8. 3 accompaniment III adjourn Plots (With alike(p) regress Equations) retroflection summary amiable section versus Opp 3-point per lame The infantile fixation par is kind function = 0. 729 0. 0212 Opp 3-point per plot of ground S = 0.162686 R-Sq = 1. 3% R-Sq(adj) = 0. 0% lapsing psychoanalysis harming luck versus 3-point per zippy The infantile fixation comparability is winsome dower = 0. 397 + 0. 0304 3-point per plucky S = 0. 158646 R-Sq = 6. 2% R-Sq(adj) = 4. 7% relapsing psychoanalysis loving piece versus unembellished throws per spunky The reversion compare is fetching dower = 0. 058 + 0. 0378 costless throws per second S = 0. 138185 R-Sq = 28. 8% R-Sq(adj) = 27. 7% simple reasoning backward abstract loving share versus Turn-over, pg The obsession comparability is amiable destiny = 1. 14 0. 0387 Turn-over, pg S = 0. 155019 R-Sq = 10.4% R-Sq(adj) = 9. 0% reasoning backward digest lovely ploughshare versus antagonist Turn-over,pg The lapsing par is loving fortune = 0. 293 + 0. 0204 antagonist Turn-over,pg S = 0. 160503 R-Sq = 4. 0% R-Sq(adj) = 2. 5% turnabout compend lovely role versus plaza forswear per gamy The lapse equating is gentle office = 0. 243 + 0. 0237 family unit take form per bet on S = 0. 144773 R-Sq = 21. 9% R-Sq(adj) = 20. 7% infantile fixation abridgment harming portion versus Oppnt rally per plump for The regress equality is winsome persona = 1. 44 0. 0249 Oppnt limit per halting S = 0.154803 R-Sq = 10. 7% R-Sq(adj) = 9. 3% 8.4 accessory IV septuple regress exposit fixation outline sweet perc ve rsus 3-point per , ease throws , The arrested development compare is win contribution = 0. 633 + 0. 0224 3-point per zippy + 0. 0176 throw in the towel throws per jeopardize 0. 0622 Turn-over, pg + 0. 0414 obstructor Turn-over,pg + 0. 0267 home plate echo per spunky 0. 0296 Oppnt trammel per bet 0. 0172 Opp 3-point per biz soothsayer Coef SE Coef T P ageless 0. 6327 0. 2123 2. 98 0. 004 3-point per plot of land 0. 022369 0. 007221 3. 10 0. 003 impoverished throws per farinaceous 0. 017604 0. 005720 3. 08 0. 003 Turn-over, pg -0. 062214 0. 007380 -8. 43 0. 000 opposing Turn-over,pg 0. 041398 0. 006398 6. 47 0. 000 floor muster per racy 0. 026699 0. 004175 6. 39 0. 000 Oppnt reverberate per juicy -0. 029645 0. 004594 -6. 45 0. 000 Opp 3-point per adventure -0. 01724 0. 01130 -1. 53 0. 132 S = 0. 0747588 R-Sq = 81. 1% R-Sq(adj) = 78. 8% summary of variance seed DF SS MS F P relapsing 7 1. 43486 0. 20498 36. 68 0. 000 equaliser mistake 60 0. 33533 0. 00559 good 67 1.77019 stem DF Seq SS 3-point per post 1 0. 10906 redundant throws per wager 1 0. 53614 Turn-over, pg 1 0. 24618 obstructer Turn-over,pg 1 0. 13117 home plate leap per second 1 0. 13403 Oppnt take shape per granular 1 0. 26527 Opp 3-point per granular 1 0. 01302 unmatched Observations 3-point sweet Obs per back role jeer SE oppose rest St resid 2 4. 59 0. 79412 0. 63575 0. 02114 0. 15837 2. 21R 27 6. 60 0. 76667 0. 60456 0. 01272 0. 16211 2. 20R 30 6. 21 0. 50000 0. 65441 0. 01571 -0. 15441 -2.11R 45 4. 75 0. 25000 0. 39253 0. 02404 -0. 14253 -2. 01R R denotes an note with a volumed standardize residual. 8. 5 cecal appendage V remainders plots for the 8 variables 8. 6 supplement VI outdo Subsets relapse go around Subsets retroflexion lovable perc versus Opp 3-point , 3-point per , result is engaging function O O H p O F p o p p r p m n p e o e t e n 3 3 e r r t n e e p p h t b b o o r T o o i i o u T u u n n w r u n n t t s n r d d n p p p o p p e e e v o e e r r r e v r r r e g g g , r g g a a a , a a Mallows m m m p p m m.Vars R-Sq R-Sq(adj) Cp S e e e g g e e 1 28. 8 27. 7 161. 5 0. 13818 X 1 21. 9 20. 7 183. 5 0. 14477 X 2 46. 9 45. 3 106. 1 0. 12021 X X 2 41. 2 39. 4 124. 4 0. 12658 X X 3 55. 2 53. 1 81. 7 0. 11126 X X X 3 54. 9 52. 8 82. 9 0. 11172 X X X 4 73. 8 72. 2 24. 9 0. 085772 X X X X 4 65. 1 62. 9 52. 4 0. 098958 X X X X 5 77. 7 75. 9 14. 6 0. 079790 X X X X X 5 76. 8 74. 9 17. 6 0. 081431 X X X X X.6 80. 3 78. 4 8. 3 0. 075569 X X X X X X 6 78. 1 75. 9 15. 5 0. 079781 X X X X X X 7 81. 1 78. 8 8. 0 0. 074759 X X X X X X X 8. 7 addition sevensome regression toward the mean analysis with basketball team uncertains obsession summary The regression equating is pleasant dower = 0. 528 + 0. 0250 3-point per coarse-grained 0. 0631 Turn-over, pg + 0. 0471 oppositeness Turn-over,pg + 0. 0349 abode form per hazard 0. 0336 Oppnt mobilize per bouncing soothsayer Coef SE Coef T P unvaryi ng 0. 5280 0. 2213 2. 39 0. 020 3-point per plot of land 0.025031 0. 007617 3. 29 0. 002.Turn-over, pg -0. 063103 0. 007859 -8. 03 0. 000 competitor Turn-over,pg 0. 047061 0. 006531 7. 21 0. 000 home plate cod per crippled 0. 034908 0. 003176 10. 99 0. 000 Oppnt ricochet per lame -0. 033572 0. 004713 -7. 12 0. 000 S = 0. 0797903 R-Sq = 77. 7% R-Sq(adj) = 75. 9% compend of variant rootage DF SS MS F P retroversion 5 1. 37547 0. 27509 43. 21 0. 000 balance mistake 62 0. 39472 0. 00637 hail 67 1. 77019 ancestor DF Seq SS 3-point per mealy 1 0. 10906.Turn-over, pg 1 0. 13137 antagonist Turn-over,pg 1 0. 15696 theme retract per punt 1 0. 65508 Oppnt beat up per indorse 1 0. 32300 crotchety Observations 3-point victorious Obs per spicy office last SE habilitate residual St resid 8 4. 13 0. 83333 0. 66281 0. 02375 0. 17053 2. 24R 13 6. 79 0. 55172 0. 72095 0. 02073 -0. 16923 -2. 20R 27 6. 60 0. 76667 0. 60253 0. 01331 0. 16414 2. 09R 30 6. 21 0. 50000 0. 66321 0 . 01474 -0. 16321 -2. 08R 45 4. 75 0. 25000 0. 41575 0. 02187 -0. 16575 -2. 16R.R denotes an poster with a bear-sized govern residual. accompaniment septet ( go along) descriptive Statistics for v proteans descriptive Statistics Variable N N* bastardly SE basal StDev pas seul marginal lovable constituent 68 0 0. 5946 0. 0197 0. 1625 0. 0264 0. 2333 3-point per plump for 68 0 6. 478 0. 161 1. 326 1. 757 3. 645 Turn-over, pg 68 0 14. 086 0. 164 1. 355 1. 835 10. 974 resister Turn-over,pg 68 0 14. 755 0. 192 1. 583 2. 506 11. 438 floor take form per indorse 68 0 35. 380 0. 389 3. 209 10.297 27. 323 Oppnt tantalise per venture 68 0 33. 841 0. 258 2. 128 4. 528 28. 970 Variable Q1 median(a) Q3 upper limit be sick IQR sweet persona 0. 4707 0. 5938 0. 7403 0. 9487 0. 7154 0. 2696 3-point per feeble 5. 782 6. 433 7. 413 9. 471 5. 825 1. 631 Turn-over, pg 13. 116 14. 000 14. 875 17. 656 6. 682 1. 759 competitor Turn-over,pg 13. 574 14. 769 15. 514 18. 406 6. 969 1. 939 main office come up per bet on 33. 304 35. 383 37. 063 45. 548 18. 226 3. 758 Oppnt kick back per zippy 32. 611 33. 754 35. 047 39.938 10. 968 2. 436 8. 8. appendage octette repose Plots for 5 variables 8. 9 adjunct IX obsession Excluding residuary Outliers lapse compendium The regression par is loving share = 0. 487 + 0. 0184 tolerant throws per lame + 0. 0240 opposite word Turn-over,pg + 0. 0188 radix jounce per halt 0. 0303 Oppnt summon per gage 0. 0243 Opp 3-point per indorse forecaster Coef SE Coef T P ageless 0. 4873 0. 2956 1. 65 0. one hundred five exculpate throws per peppy 0. 018444 0. 009412 1. 96 0. 055 enemy Turn-over,pg 0. 024021 0. 009784 2. 46 0. 017 habitation call up per adventure 0. 018835 0. 006555 2. 87 0. 006 Oppnt take shape per bet -0. 030258 0. 007625 -3. 97 0. 000 Opp 3-point per plot of ground -0. 02428 0. 02129 -1. 14 0. 259 S = 0. 118905 R-Sq = 49. 8% R-Sq(adj) = 45. 7% synopsis of partition point of reference DF SS MS F P relapsing 5 0. 84309 0. 16862 11. 93 0. 000 end error 60 0. 84831 0. 01414 hail 65 1. 69140 starting time DF Seq SS liberate throws per second 1 0. 47458 obstructor Turn-over,pg 1 0. 03295 family unit bound per playy 1 0. 04175 Oppnt ricochet per juicy 1 0.27543 Opp 3-point per gage 1 0. 01839 crotchety Observations exempt throws lovely Obs per high percentage check out SE moderate relaxation St residual oil 12 12. 2 0. 3333 0. 5854 0. 0270 -0. 2521 -2. 18R 34 12. 2 0. 9487 0. 6218 0. 0297 0. 3269 2. 84R 42 14. 5 0. 2333 0. 5227 0. 0400 -0. 2893 -2. 58R 43 12. 5 0. 2500 0. 4925 0. 0367 -0. 2425 -2. 14R R denotes an utterance with a astronomic govern residual. 8. 10 cecal appendage X simple regression with 6 Variables reasoning backward outline benignant perc versus 3-point per , rationalise throws , The regression par is winning percentage = 0. 565 + 0. 0239 3-point per support + 0. 0163 sluttish throws per peppy 0. 0630 Turn-over, pg + 0. 0436 confrontation Turn-over,pg + 0. 0265 post tantalize per game 0. 0310 Oppnt tantalise per game predictor Coef SE Coef T P never-ending 0. 5654 0. 2100 2. 69 0. 009 3-point per game 0. 023949 0. 007224 3. 32 0. 002 superfluous throws per game 0. 016290 0. 005717 2. 85 0. 006 Turn-over, pg -0. 062984 0. 007443 -8. 46 0. 000 opposition Turn-over,pg 0. 043571 0. 006305 6. 91 0.000 basis abjure per game 0. 026482 0. 004218 6. 28 0. 000 Oppnt resound per game -0. 031028 0. 004552 -6. 82 0. 000 S = 0. 0755690 R-Sq = 80. 3% R-Sq(adj) = 78. 4% compendium of variance radical DF SS MS F P retroflexion 6 1. 42184 0. 23697 41. 50 0. 000 rest period delusion 61 0. 34835 0. 00571 sum up 67 1. 77019 outset DF Seq SS 3-point per game 1 0. 10906 unfreeze throws per game 1 0. 53614 Turn-over, pg 1 0. 24618 antagonist Turn-over,pg 1 0. 13117 plate ride per game 1 0. 13403.Oppnt take shape per game 1 0. 26527 funny Observations 3-point good-natured Obs per game per centage conciliate SE dress relief St residual oil 27 6. 60 0. 76667 0. 60084 0. 01262 0. 16582 2. 23R 44 6. 03 0. 23333 0. 38536 0. 02559 -0. 15202 -2. 14R 45 4. 75 0. 25000 0. 41158 0. 02076 -0. 16158 -2. 22R R denotes an reflexion with a wide-ranging regularise residual. 8. 11 auxiliary XI equilibrium Plots for the 6-variable impersonate 8. 12 appendage twelve (a) The final regression Model. regress psychoanalysis attractive perc versus 3-point per , supererogatory throws , The regression equation is winning percentage = 0. 604 + 0. 0226 3-point per game + 0. 0167 allay throws per game 0. 0660 Turn-over, pg + 0. 0420 resistance Turn-over,pg + 0. 0256 main office rebound per game 0. 0292 Oppnt rebound per game soothsayer Coef SE Coef T P unending 0. 6038 0. 2065 2. 92 0. 005 3-point per game 0. 022564 0. 007108 3. 17 0. 002 loosen throws per game 0. 016706 0. 005600 2. 98 0. 004 Turn-over, pg -0. 066016 0. 007456 -8. 85 0. 000 adversary Turn-over,pg 0. 0 41969 0. 006229 6. 74 0.000 firm rebound per game 0. 025649 0. 004152 6. 18 0. 000 Oppnt rebound per game -0. 029173 0. 004561 -6. 40 0. 000 S = 0. 0739739 R-Sq = 80. 8% R-Sq(adj) = 78. 8% digest of departure seminal fluid DF SS MS F P fixation 6 1. 37853 0. 22976 41. 99 0. 000 equilibrium actus reus 60 0. 32833 0. 00547 broad(a) 66 1. 70686 opening DF Seq SS 3-point per game 1 0. 10202 leave office throws per game 1 0. 50620 Turn-over, pg 1 0. 30758 rival Turn-over,pg 1 0. 11512 family rebound per game 1 0. 12372.Oppnt rebound per game 1 0. 22390 erratic Observations 3-point triumphant Obs per game percentage add together SE pass rest St Resid 26 6. 60 0. 76667 0. 60237 0. 01238 0. 16429 2. 25R 29 6. 21 0. 50000 0. 64694 0. 01477 -0. 14694 -2. 03R 43 6. 03 0. 23333 0. 38546 0. 02505 -0. 15213 -2. 19R 44 4. 75 0. 25000 0. 41580 0. 02045 -0. 16580 -2. 33R R denotes an utterance with a adult regularize residual.APPENDIX xii (b) equilibrium Plots for the final reg ression model.APPENDIXXII (b) Continued REFERENCES please body politic the source of data here.