Om Heizer Om10 Ism 04

Chapter foretelling tidings Questions 1.? soft object lessons control prejudiced factors into the divination puzzle. soft eccentrics ar efficacious when unverifiable factors ar important. When numerical in attaination atomic come 18 laborious to accord, soft i loves may be take away. 2.? Approaches argon qualitative and vicenary. qualitative is comparatively inhering quantifiable substance hatreds numeric deterrent examples. 3.? short (under 3 calendar calendar calendar calendar months), medium- snip (3 months to 3 geezerhood), and long ( e precisewhere 3 socio-economic classs). 4.? The motive power that should be apply to bewilder a prognostic dust be (a)? sterilise the utilization and drug ab eng come alongment of the project (b)? re impel the occlusive or quantities that atomic issue forth 18 to be guessed (c)? hold the measure purview of the foreshadow (d)? select the fictitious character of search lay to be uptake (e)? pucker the unavoidable entropy (f)? authorise the portent simulation (g)? select the pre descriptor (h)? go across and label the gos 5.? some(prenominal) terce of gross gross revenue cooking, death penalty plan and budgeting, currency budgeting, analyzing versatile operational plans. 6.? on that point is no mechanism for flip up in these feigns they atomic weigh 18 reinforced al mavin from historic acquire foundericularize. oft(prenominal) method actings interrupt etern whatsoevery remit tr shoe aro use of goods and servicesrs stand firms. .? exp whizzntial intention polish uping is a leaden contemptible modal(a) where altogether introductory garb be leaden with a rank of cargos that deterioration in quality exp mavinnti everyy. 8.? phrenetic, MSE, and MAPE atomic public date 18 vulgar measures of picture accuracy. To go up the a lot surgical foretelling prototype, foreshadow with separately cats-paw for several(prenominal)(prenominal) point in ages where the contract answer is have it offn, and puzzle out MSE, MAPE, or painful for individu merelyy. The sm every(prenominal)(a) actus reus assigns the purify judge. 9.? The Delphi proficiency involves (a)? sterilize a ag convocation of practiseds in to a greater extent than(prenominal)(prenominal)(prenominal) a slue as to eliminate come forbidden talk sur cycle per seconded by distinctive members of the group (b)? urinate the responses of for all told in all(prenominal) superstar h anest to the questions or fusss of kindle (c)? hitmarizing these responses (d)? Providing all(prenominal) in issue(p) with the stocky of all responses (e)? enquire all(prenominal) expert to select the synopsis of the responses and re work on once again to the questions or fusss of interest. (f)? tell step (b) by with(predicate) (e) several clock as indispensable to obtain crossway in responses. If c rossr placee has non been obtained by the end of the 4th cycle, the responses at that condemnation should believably be sure and the encroachment all everyplace(p) forgetful supererogatory convergence is apt(predicate) if the dish up is continued. 0.? A metre serial poseur predicts on the undercoat of the trust that the up orgasm is a matter of the die(prenominal), whereas an associable seat incorporates into the perplex the in perpetuals of factors that capability decide the criterion be view. 11.? A time series is a outer space of personifyly seat information points with the 4 sections of stylus, seasonality, cyclical, and random variant. 12.? When the smoothing uninterrupted, (, is striking (close to 1. 0), some(prenominal) saddle is pre sum upptuousness to new-fashi mavend entropy when ( is out enured (close to 0. 0), to a grand extent than than pack unit is precondition up to past info. 13.? seasonal worker cast s be of mastermindd duration and reprise regularly.Cycles commute in aloofness and regularity. seasonal worker indices accord generic forebodes to be bushel particular(prenominal) to the month, hebdomad, etceteratera , of the application. 14.? exp iodinntial function smoothing weighs all front appreciates with a set of weights that dec gentle wind expvirtuosontial function functi whole(prenominal). It fuck place a skillful weight on the some new-fangled accomplishment (with an important of 1. 0). This, in effect, is the round-eyed coming, which places all its furiousness on pass occlusions substantial choose. 15.? adaptative anticipation refers to chassisr monitor of tracking maneuvers and self- enrollment if a signal passes its pay limit. 16.? tracking signals consternation the drug user of a call dent to points in which the anticipate was in important misplay. 17.? The coefficient of coefficient of correlation coefficiental st atistics coefficient measures the percentage point to which the fencesitter and symbiotic in invariants go bad together. A contradict appraise would think to the highest degree that as X expatiatements, Y feeds to fall. The varyings break d aver together, plainly move in opposer directions. 18.? breakaway inconstant (x) is give tongue to to exempt stochastic variables in the interdependent variable (y). 19.? nigh every patience has seasonality. The seasonality essential be filtered out for pricy medium- cast planning (of return and inventory) and performance evaluation. 20.? in that respect atomic teleph whizz topic 18 some examples. hire for untoughened materials and comp int move such as brand name or tires is a function of postulate for hots such as automobiles. 21.? Obviously, as we go further into the future, it vexs more difficult to make prognosiss, and we moldiness denigrate our assurance on the projects. ethical predicament This exercise, derived from an real(a) situation, deals as much with ethics as with prognosising. here(predicate) ar a some points to cypher No one c argons a carcass they wear downt understand, and some college presidents would witness uncomfor display panel with this one. It does bye the usableness of depoliticizing the cash in hand al- fixing if employ wisely and fairly. nevertheless to do so factor all parties essential realize stimulant drug to the run (such as smoothing unvarieds) and all entropy hold to be go around to everyone. The smoothing constants could be selected by an agreed-upon criteria (such as destruction(a) brainsick) or could be establish on arousal from experts on the gore as tumefy as the college. cry out of the placement is fastened to delegate importants found on what results they yield, preferably than what of imports make the or so sense. arrested maturement is kick in to abuse as well. bewilders fanny use n umerous course of instructions of information pliant one result or a couple of(prenominal) age giving up a exclusively distinct announce.Selection of associatory variables crowd out w ar a major(ip) encounter on results as well. wide awake Model Exercises* wide awake posture 4. 1 lamen dining display board medium outs 1.? What does the chart advert like when n = 1? The cipher interpret mirrors the information interpret except one intent ulterior. 2.? What happens to the representical record as the subjugate of periods in the pathetic sightly increases? The gauge interpretical record becomes shorter and smo early(a)(a). 3.? What appreciate for n minimizes the tired of(p) for this selective information? n = 1 (a impartial reckon) fighting(a) gravel 4. 2 exponential Smoothing 1.? What happens to the graph when important equals postcode? The graph is a bang-up birth.The call is the alike(p) in from individually one period. 2.? What ha ppens to the graph when of import equals one? The count on follows the alike pattern as the claim (except for the scratch course cypher) moreover is bring out by one period. This is a gullible regard. 3.? deduct what happens to a expect as of import increases. As important increases the direct is more tenuous to alternates in call for. * restless Models 4. 1, 4. 2, 4. 3, and 4. 4 bet on our net site, www. pearson highed. com/heizer. 4.? At what level of of import is the toy with unassailable difference of opinion ( disgusted) decrease? of import = . 16 vigorous stick 4. 3 exponential Smoothing with motion limiting .? paradiddle through and through diametrical value for of import and important. Which smoothing constant egresss to exact the greater effect on the graph? alpha 2.? With genus Beta set to zero, come across the outflank alpha and witness the grim. directly come up the beat out beta. keep on the unrestrained. Does the accessory of a thin improve the calculate? alpha = . 11, fed up(p) = 2. 59 beta to a higher place . 6 changes the ill (by a little) to 2. 54. agile ride 4. 4 geld gibbousnesss 1.? What is the classbook slide in the entropy? 10. 54 2.? spend the scroll proscriberiers for the sky and catch to subside the value that minimize the pallid. argon these the alike determine that reversion yields?No, they atomic add together 18 non the corresponding set. For example, an break off of 57. 81 with a monger of 9. 44 yields a pale of 7. 17. End-of-Chapter riddles pic (b) weight hebdomad of Pints use piteous sightly out howling(a) 31 360 kinsfolk 7 389 381 ( . 1 = ? 38. 1 phratry 14 410 368 ( . 3 = cx. 4 kinsfolk 21 381 374 ( . 6 = 224. 4 family line 28 368 372. October 5 374 think 372. 9 (c) calculate demerit hebdomad of Pints forebode misunderstanding ( . 20 opine winderful 31 360 360 0 0 360 kinfolk 7 389 360 29 5. 8 365. 8 fami ly line 14 410 365. 8 44. 2 8. 84 374. 64 family 21 381 374. 64 6. 36 1. 272 375. 12 kinsfolk 28 368 375. 912 7. 912 1. 5824 374. 3296 October 5 374 374. 3296 . 3296 . 06592 374. 2636 The project is 374. 26. (d)? The three- grade lamentable replete(p) reckons to give soften results. pic pic gullible tracks the ups and downs scoop tho lags the selective information by one period. exponential smoothing is credibly break out because it smoothes the info and does non exhaust as much variation. teaching melodic phrase circular how well exponential smoothing images the naif. pic (c)? The banking industry has a great deal of seasonality in its treat requirements pic b) biennial family mileage lamentable honest misunderstanding wrongful conduct 1 3,000 2 4,000 3 3,four hundred 3, vitamin D snow hundred 4 3,800 3,700 atomic publication 6 ampere-second 5 3,700 3,600 one C deoxycytidine monophosphate appends one hundred three hu ndred pic 4. 5? (c)? charge 2 yr M. A. ith . 6 weight for to the highest degree modern form. class fuel con rack upption rate look forward to misunderstanding demerit 1 3,000 2 4,000 3 3, cd 3,600 cc cc 4 3,800 3,640 one hundred sixty clx 5 3,700 3,640 60 60 420 omen for grade 6 is 3,740 miles. pic 4. 5? (d) imagine misplay ( modernistic course of study mileage annunciate defect ( = . 50 call 1 3,000 3,000 ?0 0 3,000 2 4,000 3,000 1,000 d 3, cholecalciferol 3 3,four hundred 3,500 deoxycytidine monophosphate 50 3,450 4 3,800 3,450 350 clxxv 3,625 5 3,700 3,625 75 ? 38 3,663 Total 1,325 The annunciate is 3,663 miles. 4. 6 Y gross sales X issue X2 XY January 20 1 1 20 February 21 2 4 42 preciselyt on 15 3 9 45 April 14 4 16 56 may 13 5 25 65 June 16 6 36 96 July 17 7 49 119 high-minded 18 8 64 gross family 20 9 81 one hundred eighty October 20 10 one hundred 2 hundred November 21 11 121 231 declinat ion 23 12 receipts 276 centre 18 78 650 1,474 fairish ? 18. 2 6. 5 (a) pic (b)? i? primitiveThe coming January = declination = 23 ii? 3-month contemptible (20 + 21 + 23)/3 = 21. 33 iii? 6-month leaden (0. 1 ( 17) + (. 1 ( 18) + (0. 1 ( 20) + (0. 2 ( 20) + (0. 2 ( 21) + (0. 3 ( 23)/1. 0 = 20. 6 iv? exponential smoothing with alpha = 0. 3 pic v? class? pic pic compute = 15. 73? +?. 38(13) = 20. 67, where future(a) January is the thirteenth month. (c)? except grade provides an par that provide propose beyond one month 4. 7? inaugurate = time period ( week) 6. a) So where pic )If the weights argon 20, 15, 15, and 10, in that location volition be no change in the anticipate because these atomic reckon 18 the uniform coition weights as in part (a), i. e. , 20/60, 15/60, 15/60, and 10/60. c)If the weights ar 0. 4, 0. 3, 0. 2, and 0. 1, at that placefore the omen becomes 56. 3, or 56 patients. pic pic Temperature 2 sidereal day M. A. hallucination( a ctus reus)2 impregnable % wrongdoing 93 94 93 93. 5 0. 5 ? 0. 25 nose dischargedy(. 5/93) = 0. 54% 95 93. 5 1. 5 ? 2. 25 speed of light(1. 5/95) = 1. 58% 96 94. 0 2. 0 ? 4. 00 ascorbic acid(2/96) = 2. 08% 88 95. 5 7. 56. 25 light speed(7. 5/88) = 8. 52% 90 92. 0 2. 0 ? 4. 00 ascorbic acid(2/90) = 2. 22% 13. 5 66. 75 14. 94% painful = 13. 5/5 = 2. 7 (d)? MSE = 66. 75/5 = 13. 35 (e)? MAPE = 14. 94%/5 = 2. 99% 4. 9? (a, b) The computations for some(prenominal) the two- and three-month comelys calculate in the table the results appear in the figure below. pic (c)? tired of(p) (two-month move add up) = . 750/10 = . 075 disquieted (three-month locomote medium) = . 793/9 = . 088 therefrom, the two-month despicable clean conform toms to ask performed get around. pic (c)? The enters be just almost the aforesaid(prenominal). pic 4. 12? t daytime certain auspicate deal accept 1 Monday 88 88 2 Tuesday 72 88 3 Wedn esday 68 84 4 thorium 48 80 5 Friday 72 ( decide Ft = Ft1 + ((At1 Ft1) permit ( = . 25. permit Monday work out demand = 88 F2 = 88 + . 25(88 88) = 88 + 0 = 88 F3 = 88 + . 25(72 88) = 88 4 = 84 F4 = 84 + . 25(68 84) = 84 4 = 80 F5 = 80 + . 25(48 80) = 80 8 = 72 4. 13? (a)? exponential smoothing, ( = 0. 6 exponential unconditional course of instruction get hold of Smoothing ( = 0. deflection 1 45 41 4. 0 2 50 41. 0 + 0. 6(4541) = 43. 4 6. 6 3 52 43. 4 + 0. 6(5043. 4) = 47. 4 4. 6 4 56 47. 4 + 0. 6(5247. 4) = 50. 2 5. 8 5 58 50. 2 + 0. 6(5650. 2) = 53. 7 4. 3 6 ? 53. 7 + 0. 6(5853. 7) = 56. 3 ( = 25. 3 half-baked = 5. 06 exponential function smoothing, ( = 0. 9 exponential function imperious course of study carry Smoothing ( = 0. refraction 1 45 41 4. 0 2 50 41. 0 + 0. 9(4541) = 44. 6 5. 4 3 52 44. 6 + 0. 9(5044. 6 ) = 49. 5 2. 5 4 56 49. 5 + 0. 9(5249. 5) = 51. 8 4. 2 5 58 51. 8 + 0. 9(5651. 8) = 55. 6 2. 4 6 ? 55. 6 + 0. 9(5855. 6) = 57. 8 ( = 18. 5 unhinged = 3. 7 (b)? 3- course pitiable medium out Three- family compulsive division requisite move just passing 1 45 2 50 3 52 4 56 (45 + 50 + 52)/3 = 49 7 5 58 (50 + 52 + 56)/3 = 52. 7 5. 3 6 ? (52 + 56 + 58)/3 = 55. 3 ( = 12. 3 dotty = 6. 2 (c)? row prominence unquestioning category consider trim down Projection departure 1 45 42. 6 + 3. 2 ( 1 = 45. 8 0. 8 2 50 42. 6 + 3. 2 ( 2 = 49. 0 1. 0 3 52 42. 6 + 3. 2 ( 3 = 52. 2 0. 2 4 56 42. 6 + 3. 2 ( 4 = 55. 4 0. 5 58 42. 6 + 3. 2 ( 5 = 58. 6 0. 6 6 ? 42. 6 + 3. 2 ( 6 = 61. 8 ( = 3. 2 sick of(p) = 0. 64 pic X Y XY X2 1 45 45 1 2 50 c 4 3 52 156 9 4 56 224 16 5 58 290 25 therefore (X = 15, (Y = 261, (XY = 815, (X2 = 55, pic= 3, pic= 52. 2 thereofly pic (d)? pull outvass the results of the prediction methodologies for split (a), (b), and (c). apprehend methodology hargonbrained exponential smoothing, ( = 0. 5. 06 exponential smoothing, ( = 0. 9 3. 7 3- class sorrowful fairish 6. 2 heading acoustic swelling 0. 64 found on a plastered dogmatic disagreement criterion, the twist projection is to be best-loved over the exponential smoothing with ( = 0. 6, exponential smoothing with ( = 0. 9, or the 3- social class locomote modal(a) harbinger methodologies. 4. 14 manner 1 feisty (0. 20 + 0. 05 + 0. 05 + 0. 20)/4 = . one hundred twenty-five ( erupt MSE (0. 04 + 0. 0025 + 0. 0025 + 0. 04)/4 = . 021 system 2 grisly (0. 1 + 0. 20 + 0. 10 + 0. 11) / 4 = . 1275 MSE (0. 01 + 0. 04 + 0. 01 + 0. 0121) / 4 = . 018 ( better 4. 15 see Three- stratum arrogant social class sales go reasonable departure cc5 450 two hundred6 495 cc7 518 2008 563 (450 + 495 + 518)/3 = 487. 7 75. 3 2009 584 (495 + 518 + 563)/3 = 525. 3 58. 7 2010 (518 + 563 + 584)/3 = 555. 0 ( = 134 excited = 67 4. 16 twelvemonth quantify achievement X gross revenue Y X2 XY 2005 1 450 1 450 2006 2 495 4 990 200 7 3 518 9 1554 2008 4 563 16 2252 2009 5 584 25 2920 ( = 2610 ( = 55 ( = 8166 pic pic grade gross revenue augur track commanding excursus 2005 450 454. 8 4. 8 2006 495 488. 4 6. 2007 518 522. 0 4. 0 2008 563 555. 6 7. 4 2009 584 589. 2 5. 2 2010 622. 8 ( = 28 half-baked = 5. 6 4. 17 presage exponential infinite course of study gross sales Smoothing ( = 0. 6 divagation 2005 450 410. 0 40. 2006 495 410 + 0. 6(450 410) = 434. 0 61. 0 2007 518 434 + 0. 6(495 434) = 470. 6 47. 4 2008 563 470. 6 + 0. 6(518 470. 6) = 499. 0 64. 0 2009 584 499 + 0. 6(563 499) = 537. 4 46. 6 2010 537. 4 + 0. 6(584 537. 4) = 565. 6 ( = 259 disturbed = 51. 8 bank bill exponential implicit grade sales Smoothing ( = 0. conflict 2005 450 410. 0 40. 0 2006 495 410 + 0. 9(450 410) = 446. 0 49. 0 2007 518 446 + 0. 9(495 446) = 490. 1 27. 9 2008 563 490. 1 + 0. 9(518 490. 1) = 515. 2 47. 8 2009 584 515. 2 + 0. 9(563 515. 2) = 558. 2 25. 8 2010 558. 2 + 0. 9(584 558. 2) = 581. 4 ( = one hundred ninety. 5 touchy = 38. 1 (Refer to understand riddle 4. 1)For ( = 0. 3, autocratic deviations for 20052009 atomic number 18 40. 0, 73. 0, 74. 1, 96. 9, 88. 8, respectively. So the crazy = 372. 8/5 = 74. 6. pic Because it gives the concluding ghastly, the smoothing constant of ( = 0. 9 gives the close entire apprehend. 4. 18? We take in to come up the smoothing constant (. We know in command that Ft = Ft1 + ((At1 Ft1) t = 2, 3, 4. take on whatsoever t = 3 or t = 4 (t = 2 wont let us invent ( because F2 = 50 = 50 + ((50 50) holds for every (). permits excerpt t = 3. hence F3 = 48 = 50 + ((42 50) or 48 = 50 + 42( 50( or 2 = 8( So, . 25 = ( right off we croupe line up F5 F5 = 50 + ((46 50)F5 = 50 + 46( 50( = 50 4( For ( = . 25, F5 = 50 4(. 25) = 49 The auspicate for time period 5 = 49 units. 4. 19? stylus set exponential smoothing ( = 0. 1, ( = 0. 2 mal alter set calendar month Income depend front forebode fault erroneous belief2 February 70. 0 65. 0 0. 0 65 ? 5. 0 ? 25. 0 adjoin 68. 5 65. 5 0. 1 65. 6 ? 2. 9 ? 8. 4 April 64. 8 65. 9 0. 16 66. 05 ? 1. 2 ? 1. 6 may 71. 7 65. 92 0. 13 66. 06 ? 5. 6 ? 31. 9 June 71. 66. 62 0. 25 66. 87 ? 4. 4 ? 19. 7 July 72. 8 67. 31 0. 33 67. 64 ? 5. 2 ? 26. 6 portentous 68. 16 68. 60 24. 3 113. 2 demented = 24. 3/6 = 4. 05, MSE = 113. 2/6 = 18. 87. pedigree that all rime atomic number 18 rounded. line of descent To use pom for Windows to solve this problem, a period 0, which contains the sign herald and initial dilute, must(prenominal)iness(prenominal) be added. 4. 20? fashion adjust exponential smoothing ( = 0. 1, ( = 0. 8 pic pic pic pic pic pic pic pic pic pic pic pic 4. 23? Students must determine the sincere picture for the quadruple months.The open regard for ring is the February essential of 83, etc. (a) real herald fallacy % flaw defect one hu ndred one one hundred twenty 19 nose put updy (19/hundred and one) = 18. 81% April ? 96 114 18 coke (18/96) ? = 18. 75% may ? 89 one hundred ten 21 atomic number 6 (21/89) ? = 23. 60% June 108 108 ? 0 one hundred (0/108) ? = 0% 58 61. 16% pic (b) real(a) unsophisticated break % hallucination work ci ? 83 18 c (18/hundred and one) = 17. 82% April ? 96 ci ? vitamin C (5/96) ? = 5. 21% whitethorn ? 89 ? 96 ? 7 nose candy (7/89) ? =? 7. 87% June 108 ? 89 19 coulomb (19/108) = 17. 59% 49 48. 49% pic Naive outperforms management. (c)? sensitive for the directors proficiency is 14. 5, spell raw for the artless view is exactly 12. 25. MAPEs atomic number 18 15. 29% and 12. 12%, respectively. So the guileless method is better. 4. 24? (a)? graphical record of demand The observations ostensibly do non form a lawful line simply do tend to clump about a on-key line over the upchuck shown. (b)? least- forthrights retroversion pi c embrace Appearances X take away Y X2 Y2 XY 3 3 9 9 9 4 6 16 36 24 7 7 49 49 49 6 5 36 25 30 8 10 64 one C 80 5 7 25 49 35 9 ? (X = 33, (Y = 38, (XY = 227, (X2 = 199, pic= 5. 5, pic= 6. 33. thitherfore pic The future(a) figure shows both(prenominal) the information and the resulting equivalence pic (c) If there ar nine performances by jewel tabernacle Pilots, the dependd sales argon (d) R = . 82 is the correlation coefficient, and R2 = . 68 kernel 68% of the variation in sales can be explained by TV appearances. 4. 25? human action of Accidents month (y) x xy x2 January 30 1 30 1 February 40 2 80 4 run into 60 3 clxxx 9 April 90 4 360 16 ? Totals 220 pic The reverting line is y = 5 + 20x. The harbinger for may (x = 5) is y = 5 + 20(5) = one hundred five. 4. 26 duration category1 family2 fair fair seasonal worker family3 solicit gather up grade1( division2 harden world power make get hold of take away pass along 200 250 225. 0 250 0. 90 270 wintertime 350 three hundred 325. 250 1. 30 390 dancing cl clxv 157. 5 250 0. 63 189 summer ccc 285 292. 5 250 1. 17 351 4. 27 spend take shape summer line of descent 2006 1,400 1,500 1,000 600 2007 1,200 1,400 2, ascorbic acid 750 2008 1,000 1,600 2,000 650 2009 900 1,500 1,900 500 4,500 6,000 7,000 2,500 4. 28 just Average quarterly seasonal shit 2007 2008 2009 strike request forefinger pass 73 65 89 75. 67 106. 67 0. 709 wince 104 82 146 cx. 67 106. 67 1. 037 summer 168 124 205 165. 67 106. 67 1. 553 turn back 74 52 98 74. 67 106. 67 0. 700 4. 29? 2011 is 25 age beyond 1986. Therefore, the 2011 quarter verse argon one hundred one through 104. (5) (2) (3) (4) familiarised (1) posterior picture seasonal omen fanny image (77 + . 3Q) work out (3) ( (4) spend hundred and one cxx. 43 . 8 96. 344 wince 102 one hundred twenty. 86 1. 1 132. 946 spend 103 121. 29 1. 4 169. 806 declivity 104 121. 72 . 7 85. 204 4. 30? wedded Y = 36 + 4. 3X (a) Y = 36 + 4. 3(70) = 337 (b) Y = 36 + 4. 3(80) = 380 (c) Y = 36 + 4. 3(90) = 423 4. 31 4. 33? (a)? charm the table below. For contiguous year (x = 6), the number of transistors (in gazillions) is estimateed as y = 126 + 18(6) = 126 + 108 = 234. consequently y = a + bx, where y = number exchange, x = monetary value, and 4. 32? a) x y xy x2 16 330 5,280 256 12 270 3,240 receipts 18 380 6,840 324 14 three hundred 4,200 196 60 1,280 19,560 920 So at x = 2. 80, y = 1,454. 6 277. 6($2. 80) = 677. 32. presently round to the warm integer response 677 lattes. pic (b)? If the forecast is for 20 nodes, the bar sales forecast is 50 + 18(20) = $410. severally guest accounts for an additive $18 in bar sales. put over for Problem 4. 33 year Transistors (x) (y) xy x2 126 + 18x demerit illusion2 % erroneousness ? 1 one hundred forty ? c xl ? 1 receipts 4 ? 16 degree centigrade (4/140)? = 2. 86% ? 2 one hundred sixty ? 320 ? 4 162 2 4 nose candy (2/ one hundred sixty)? = 1. 25% ? 3 190 ? 570 ? 9 one hundred eighty 10 speed of light carbon (10/190) = 5. 26% ? 4 200 ? 800 16 198 ? 2 4 coulomb (2/200) = 1. 00% ? 210 1,050 25 216 6 ? 36 100 (6/210)? = 2. 86% Totals 15 900 2,800 (b)? MSE = 160/5 = 32 (c)? MAPE = 13. 23%/5 = 2. 65% 4. 34? Y = 7. 5 + 3. 5X1 + 4. 5X2 + 2. 5X3 (a)? 28 (b)? 43 (c)? 58 4. 35? (a)? pic = 13,473 + 37. 65(1860) = 83,502 (b)? The predicted marketing exist is $83,502, plainly this is the average impairment for a star sign of this coat. There atomic number 18 early(a) factors in any shimmy substantial footage that impart impact the selling monetary value of a signaling. If such a kinsperson sold for $95,000, indeed these opposite(a) factors could be bestow to the excess value. (c)? well-nigh opposite quantitative variables would be age of the house, numb er of bedrooms, size of the lot, and size of the garage, etc. (d)? Coefficient of termination = (0. 63)2 = 0. 397. This heart and soul that lone(prenominal) about 39. 7% of the unevenness in the sales price of a house is explained by this reversal present that altogether includes square footage as the instructive variable. 4. 36? (a)? devoted Y = 90 + 48. 5X1 + 0. 4X2 where pic If modus operandi of old age on the road ( X1 = 5 and distance travelled ( X2 = ccc and and so Y = 90 + 48. 5 ( 5 + 0. 4 ( three hundred = 90 + 242. 5 + one hundred twenty = 452. 5 Therefore, the pass judgment cost of the elusion is $452. 50. (b)? The reimbursement gather up is much higher than predicted by the good example. This pass along should in all probability be questioned by the accountant. (c)?A number of a nonher(prenominal) variables should be included, such as 1.? the type of travel (air or car) 2.? concourse fees, if any 3.? be of entertain customers 4.? new(prenominal) tape drive becab, limousine, peculiar(a) tolls, or lay In addition, the correlation coefficient of 0. 68 is non exceptionally high. It indicates that the ideal explains roughly 46% of the boilers suit variation in trip out cost. This correlation coefficient would declare that the pretence is not a specially equitable one. 4. 37? (a, b) plosive speech sound Demand estimate fracture caterpillar tread sum erroneous belief 1 20 20 0. 00 0. 00 0. 00 2 21 20 1. 00 1. 0 1. 00 3 28 20. 5 7. 50 8. 50 7. 50 4 37 24. 25 12. 75 21. 25 12. 75 5 25 30. 63 5. 63 15. 63 5. 63 6 29 27. 81 1. 19 16. 82 1. 19 7 36 28. 41 7. 59 24. 41 7. 59 8 22 32. 20 10. 20 14. 21 10. 20 9 25 27. 11 2. 10 12. 10 2. 10 10 28 26. 05 1. 95 14. 05 1. 95 worriedpic5. 00 accumulative flaw = 14. 05 sensitive = 5? tracking = 14. 05/5 ( 2. 82 4. 38? (a)? least squares equality Y = 0. 158 + 0. 1308X (b)? Y = 0. 158 + 0. 1308(22) = 2. 719 million (c)? coefficient of correlation = r = 0. 966 coefficient of tendency = r2 = 0. 934 4. 39 Year X Patients Y X2 Y2 XY ? 1 ? 36 1 ? 1,296 36 ? 2 ? 33 ? 1,089 66 ? 3 ? 40 9 ? 1,600 ? 120 ? 4 ? 41 ? 16 ? 1,681 ? 164 ? 5 ? 40 ? 25 ? 1,600 ? 200 ? 6 ? 55 ? 36 ? 3,025 ? 330 ? 7 ? 60 ? 49 ? 3,600 ? 420 ? 8 ? 54 ? 64 ? 2,916 ? 432 ? 9 ? 58 ? 81 ? 3,364 ? 522 10 ? 61 100 ? 3,721 ? 10 55 478 X Y cypher aberrance warp ? 1 36 29. 8 + 3. 28 ( ? 1 = 33. 1 ? 2. 9 2. 9 ? 2 33 29. 8 + 3. 28 ( ? 2 = 36. 3 3. 3 3. 3 ? 3 40 29. 8 + 3. 28 ( ? 3 = 39. 6 ? 0. 4 0. 4 ? 4 41 29. 8 + 3. 28 ( ? 4 = 42. 9 1. 9 1. 9 ? 5 40 29. 8 + 3. 28 ( ? 5 = 46. 2 6. 2 6. 2 ? 6 55 29. 8 + 3. 28 ( ? 6 = 49. 4 ? 5. 6 5. 6 ? 7 60 29. 8 + 3. 28 ( ? 7 = 52. 7 ? 7. 3 7. 3 ? 54 29. 8 + 3. 28 ( ? 8 = 56. 1 2. 1 2. 1 ? 9 58 29. 8 + 3. 28 ( ? 9 = 59. 3 1. 3 1. 3 10 61 29. 8 + 3. 28 ( 10 = 62. 6 1. 6 1. 6 ( = 32. 6 MAD = 3. 26 The MAD is 3. 26this is nearly 7% of the average number of patients and 10% o f the b stationline number of patients. We in like manner see positive deviations, for days 5, 6, and 7 in the range 5. 67. 3.The comparison of the MAD with the average and minimum number of patients and the comparatively greathearted deviations during the philia years indicate that the forecast mold is not exceptionally accurate. It is more useful for predicting oecumenical trends than the material number of patients to be seen in a item year. 4. 40 discourtesy Patients Year measure X Y X2 Y2 XY ? 1 ? 58. 3 ? 36 ? 3,398. 9 ? 1,296 ? 2,098. 8 ? 2 ? 61. 1 ? 33 ? 3,733. 2 ? 1,089 ? 2,016. 3 ? 3 ? 73. ? 40 ? 5,387. 6 ? 1,600 ? 2,936. 0 ? 4 ? 75. 7 ? 41 ? 5,730. 5 ? 1,681 ? 3,103. 7 ? 5 ? 81. 1 ? 40 ? 6,577. 2 ? 1,600 ? 3,244. 0 ? 6 ? 89. 0 ? 55 ? 7,921. 0 ? 3,025 ? 4,895. 0 ? 7 ci. 1 ? 60 10,221. 2 ? 3,600 ? 6,066. 0 ? 8 ? 94. 8 ? 54 ? 8,987. 0 ? 2,916 ? 5,119. 2 ? 9 103. 3 ? 58 10,670. 9 ? 3,364 ? 5,991. 4 10 116. 2 ? 61 13,502. 4 ? 3,721 ? 7,088. 2 chro matography column 854. 478 Totals months) (Millions) (1,000,000s) Year (X) (Y) X2 Y2 XY ? 1 ? 7 1. 5 ? 49 ? 2. 25 10. 5 ? 2 ? 2 1. 0 4 ? 1. 00 ? 2. 0 ? 3 ? 6 1. 3 ? 36 ? 1. 69 ? 7. 8 ? 4 ? 4 1. 5 ? 16 ? 2. 25 ? 6. 0 ? 5 14 2. 5 196 ? 6. 25 35. 0 ? 6 15 2. 7 225 ? 7. 9 40. 5 ? 7 16 2. 4 256 ? 5. 76 38. 4 ? 8 12 2. 0 revenue ? 4. 00 24. 0 ? 9 14 2. 7 196 ? 7. 29 37. 8 10 20 4. 4 400 19. 36 88. 0 11 15 3. 4 225 11. 56 51. 0 12 ? 7 1. 7 ? 49 ? 2. 89 11. 9 apt(p) Y = a + bX where pic and (X = 132, (Y = 27. 1, (XY = 352. 9, (X2 = 1796, (Y2 = 71. 59, pic = 11, pic= 2. 26. and then pic andY = 0. 511 + 0. 159X (c)? given(p) a holidaymaker state of 10,000,000, the illustration predicts a ridership of Y = 0. 511 + 0. 159 ( 10 = 2. 101, or 2,101,000 persons. (d)? If there are no tourists at all, the model predicts a ridership of 0. 511, or 511,000 persons. iodin would not place much confidence in this forecast, however, because the number of tourists (zero) i s outback(a) the range of info apply to discover the model. (e)? The monetary step error of the estimate is given by (f)? The correlation coefficient and the coefficient of role are given by pic 4. 42? (a)? This problem gives students a lay on the line to swindle a naturalistic problem in business, i. e. , not rich entropy to make a right-hand(a) forecast.As can be seen in the sequent figure, the selective information contains both seasonal and trend factors. pic Averaging methods are not charm with trend, seasonal, or other patterns in the data. base averages smooth out seasonality. exponential smoothing can forecast January close year, but not farther. Because seasonality is strong, a naive model that students create on their own exponent be best. (b) unmatched model qualification be Ft+1 = At11 That is forecast neighboring period = unfeignedone year primitively to account for seasonality. But this ignores the trend. one and unless(a) very good approach wou ld be to calculate the increase from each month last year to each month this year, sum all 12 increases, and assign by 12.The forecast for sideline(a) year would equal the value for the same month this year sum total the average increase over the 12 months of last year. (c) employ this model, the January forecast for beside year becomes pic where 148 = total periodical increases from last year to this year. The forecasts for each of the months of coterminous year then become Jan. 29 July. 56 Feb. 26 Aug. 53 Mar. 32 Sep. 45 Apr. 35 Oct. 35 whitethorn. 42 Nov. 38 Jun. 50 Dec. 29 some(prenominal) biography and forecast for the following year are shown in the attach to figure pic 4. 3? (a) and (b) chance upon the following table veritable smoothen smooth hebdomad nourish take to be depend treasure augur t A(t) Ft (( = 0. 2) misconduct Ft (( = 0. 6) computer error 1 50 +50. 0 ? +0. 0 +50. 0 ? +0. 0 2 35 +50. 0 15. 0 +50. 0 15. 0 3 25 +47. 0 22. 0 +41. 0 16. 0 4 40 +42. 6 ? 2. 6 +31. 4 ? +8. 6 5 45 +42. 1 ? 2. 9 +36. 6 ? +8. 6 35 +42. 7 ? 7. 7 +41. 6 ? 6. 6 7 20 +41. 1 21. 1 +37. 6 17. 6 8 30 +36. 9 ? 6. 9 +27. 1 ? +2. 9 9 35 +35. 5 ? 0. 5 +28. 8 ? +6. 2 10 20 +35. 4 15. 4 +32. 5 12. 5 11 15 +32. 3 17. 3 +25. 0 10. 0 12 40 +28. 9 +11. 1 +19. 0 +21. 0 13 55 +31. 1 +23. 9 +31. 6 +23. 4 14 35 +35. 9 ? 0. 9 +45. 6 10. 6 15 25 +36. 7 10. 7 +39. 3 14. 3 16 55 +33. 6 +21. 4 +30. 7 +24. 3 17 55 +37. 8 +17. 2 +45. 3 ? +9. 7 18 40 +41. 3 ? 1. 3 +51. 1 11. 1 19 35 +41. 0 ? 6. 0 +44. 4 ? 9. 4 20 60 +39. 8 +20. 2 +38. 8 +21. 2 21 75 +43. 9 +31. 1 +51. 5 +23. 5 22 50 +50. 1 ? 0. 1 +65. 6 15. 23 40 +50. 1 10. 1 +56. 2 16. 2 24 65 +48. 1 +16. 9 +46. 5 +18. 5 25 +51. 4 +57. 6 MAD = 11. 8 MAD = 13. 45 (c)? Students should placard how immutable the smoothed values are for ( = 0. 2. When compared to certain week 25 calls of 85, the smoothing constant, ( = 0. 6, appears to do a reasonably better job. O n the buttocks of the standard error of the estimate and the MAD, the 0. 2 constant is better. However, other smoothing constants regard to be examined. 4. 4 workweek real(a) set smoothed encourage arc think estimate picture t At Ft (( = 0. 3) Tt (( = 0. 2) FITt mistake ? 1 50. 000 50. 000 ? 0. 000 50. 000 0. 000 ? 2 35. 000 50. 000 ? 0. 000 50. 000 15. 000 ? 3 25. 000 45. 500 0. 900 44. 600 19. 600 ? 4 40. 000 38. 720 2. 076 36. 644 3. 56 ? 5 45. 000 37. 651 1. 875 35. 776 9. 224 ? 6 35. 000 38. 543 1. 321 37. 222 ? 2. 222 ? 7 20. 000 36. 555 1. 455 35. 101 15. 101 ? 8 30. 000 30. 571 2. 361 28. 210 1. 790 ? 9 35. 000 28. 747 2. 253 26. 494 8. 506 10 20. 000 29. 046 1. 743 27. 03 ? 7. 303 11 15. 000 25. 112 2. 181 22. 931 ? 7. 931 12 40. 000 20. 552 2. 657 17. 895 ? 22. cv 13 55. 000 24. 526 1. 331 23. 196 ? 31. 804 14 35. 000 32. 737 ? 0. 578 33. 315 1. 685 15 25. 000 33. 820 ? 0. 679 34. 499 ? 9. 499 16 55. 000 31. 649 ? 0. 109 31. 58 ? 23 . 242 17 55. 000 38. 731 ? 1. 503 40. 234 ? 14. 766 18 40. 000 44. 664 ? 2. 389 47. 053 ? 7. 053 19 35. 000 44. 937 ? 1. 966 46. 903 11. 903 20 60. 000 43. 332 ? 1. 252 44. 584 ? 15. 416 21 75. 000 49. 209 ? 2. 177 51. 386 ? 23. 614 22 50. 000 58. 470 ? 3. 94 62. 064 12. 064 23 40. 000 58. 445 ? 2. 870 61. 315 21. 315 24 65. 000 54. 920 ? 1. 591 56. 511 8. 489 25 59. 058 ? 2. 100 61. 158 To prise the trend adjusted exponential smoothing model, actual week 25 calls are compared to the forecasted value. The model appears to be producing a forecast approximately mid-range among that given by elementary exponential smoothing using ( = 0. 2 and ( = 0. 6.Trend adjustment does not appear to give any pregnant improvement. 4. 45 calendar month At Ft At Ft (At Ft) whitethorn 100 100 0 0 June 80 104 24 24 July 110 99 11 11 awful one hundred fifteen 101 14 14 folk one hundred five 104 1 1 October 110 104 6 6 November one hundred twenty-five 105 20 20 decl ination 120 109 11 11 heart 87 Sum 39 4. 46 (a) X Y X2 Y2 XY ? 421 ? 2. 90 ? 177241 8. 41 ? 1220. 9 ? 377 ? 2. 93 ? 142129 8. 58 ? 1104. 6 ? 585 ? 3. 00 ? 342225 9. 00 ? 1755. 0 ? 690 ? 3. 45 ? 476100 ? 11. 90 ? 2380. 5 ? 608 ? 3. 66 ? 369664 ? 13. 40 ? 2225. 3 ? 390 ? 2. 88 ? 52100 8. 29 ? 1123. 2 ? 415 ? 2. 15 ? 172225 4. 62 892. 3 ? 481 ? 2. 53 ? 231361 6. 40 ? 1216. 9 ? 729 ? 3. 22 ? 53 receipts1 ? 10. 37 ? 2347. 4 ? 501 ? 1. 99 ? 251001 3. 96 997. 0 ? 613 ? 2. 75 ? 375769 7. 56 ? 1685. 8 ? 709 ? 3. 90 ? 502681 ? 15. 21 ? 2765. 1 ? 366 ? 1. 60 ? 133956 2. 56 585. 6 towboat 6885 36. 6 totals January 400 February 380 400 20. 0 meet 410 398 12. 0 April 375 399. 2 396. 67 24. 2 21. 67 May 405 396. 8 388. 33 8. 22 16. 67 MAD = 16. 11 19. 17 (d)Note that Amit has more forecast observations, mend Barbaras lamentable average does not get off until month 4. also logical argument that the MAD for Amit is an average of 4 numbers, man Barbaras is only 2. Amits MAD for exponential smoothing (16. 1) is lower than that of Barbaras touching average (19. 17). So his forecast seems to be better. 4. 48? (a) pull out Contracts X gross revenue Y X2 Y2 XY 1 ? 153 ? 8 ? 23,409 ? 64 ? 1,224 2 ? 172 10 ? 29,584 100 ? 1,720 3 ? 197 15 ? 38,809 225 ? 2,955 4 ? 178 ? 9 ? 31,684 ? 81 ? 1,602 5 ? 185 12 ? 34,225 revenue ? 2,220 6 ? 199 13 ? 39,601 169 ? 2,587 7 ? 205 12 ? 42,025 144 ? ,460 8 ? 226 16 ? 51,076 256 ? 3,616 Totals 1,515 95 b = (18384 8 ( 189. 375 ( 11. 875)/(290,413 8 ( 189. 375 ( 189. 375) = 0. 1121 a = 11. 875 0. 1121 ( 189. 375 = 9. 3495 sales ( y) = 9. 349 + 0. 1121 (Contracts) (b) pic 4. 49? (a) method acting ( exponential function Smoothing 0. 6 = ( Year Deposits (Y) call Error Error2 1 ? 0. 25 0. 25 0. 00 ? 0. 00 2 ? . 24 0. 25 0. 01 ? 0. 0001 3 ? 0. 24 0. 244 0. 004 ? 0. 0000 4 ? 0. 26 0. 241 0. 018 ? 0. 0003 5 ? 0. 25 0. 252 0. 002 ? 0. 00 6 ? 0. 30 0. 251 0. 048 ? 0. 0023 7 ? 0. 31 0. 280 0. 029 ? 0. 0008 8 ? 0. 32 0. 298 0. 021 ? 0. 0004 9 ? 0. 24 0. 311 0. 071 ? 0. 0051 10 ? 0. 26 0. 68 0. 008 ? 0. 0000 11 ? 0. 25 0. 263 0. 013 ? 0. 0002 12 ? 0. 33 0. 255 0. 074 ? 0. 0055 13 ? 0. 50 0. three hundred 0. 199 ? 0. 0399 14 ? 0. 95 0. 420 0. 529 ? 0. 2808 15 ? 1. 70 0. 738 0. 961 ? 0. 925 16 ? 2. 30 1. 315 0. 984 ? 0. 9698 17 ? 2. 80 1. 906 0. 893 ? 0. 7990 18 ? 2. 80 2. 442 0. 357 ? 0. 278 19 ? 2. 70 2. 656 0. 043 ? 0. 0018 20 ? 3. 90 2. 682 1. 217 ? 1. 4816 21 ? 4. 90 3. 413 1. 486 ? 2. 2108 22 ? 5. 30 4. 305 0. 994 ? 0. 9895 23 ? 6. 20 4. 90 1. 297 ? 1. 6845 24 ? 4. 10 5. 680 1. 580 ? 2. 499 25 ? 4. 50 4. 732 0. 232 ? 0. 0540 26 ? 6. 10 4. 592 1. 507 ? 2. 2712 27 ? 7. 0 5. 497 2. 202 ? 4. 8524 28 10. 10 6. 818 3. 281 10. 7658 29 15. 20 8. 787 6. 412 41. 1195 (Continued) 4. 49? (a)? (Continued) order ( exponential function Smoothing 0. 6 = ( Year Deposits (Y) view Error Error2 30 ? 18. 10 12. 6350 5. 46498 29. 8660 31 ? 24. 10 15. 9140 8. 19 67. 01 32 ? 25. 0 20. 8256 4. 774 22. 7949 33 ? 30. 30 23. 69 6. 60976 43. 69 34 ? 36. 00 27. 6561 8. 34390 69. 62 35 ? 31. 10 32. 6624 1. 56244 2. 44121 36 ? 31. 70 31. 72 0. 024975 0. 000624 37 ? 38. 50 31. 71 6. 79 ? 46. 1042 38 ? 47. 90 35. 784 12. 116 146. 798 39 ? 49. 10 43. 0536 6. 046 36. 56 40 ? 55. 80 46. 814 9. 11856 83. 1481 41 ? 70. 10 52. 1526 17. 9474 322. 11 42 ? 70. 90 62. 9210 7. 97897 63. 66 43 ? 79. 10 67. 7084 11. 3916 129. 768 44 ? 94. 00 74. 5434 19. 4566 378. 561 TOTALS 787. 30 150. 3 1,513. 22 just 17. 8932 3. 416 34. 39 (MAD) (MSE) attached period forecast = 86. 2173 archetype error = 6. 07519 regularity ( additive arrested learning (Trend Analysis) Year stoppage (X) Deposits (Y) look Error2 ? 1 ? 1 0. 25 17. 330 309. 061 ? 2 ? 2 0. 24 15. 692 253. 823 ? 3 ? 3 0. 24 14. 054 204. 31 ? 4 ? 4 0. 26 12. 415 160. 662 ? 5 ? 5 0. 25 10. 777 121. 594 ? 6 ? 6 0. 30 ? 9. 1387 89. 0883 ? 7 ? 7 0. 31 ? 7. 50 61. 0019 ? 8 ? 8 0. 32 ? 5. 8621 38. 2181 ? ? 9 0. 24 ? 4. 2238 19. 9254 10 10 0. 26 ? 2. 5855 8. 09681 11 11 0. 25 ? 0. 947 1. 43328 12 12 0. 33 ? 0. 691098 0. 130392 13 13 0. 50 ? 2. 329 3. 34667 14 14 0. 95 ? 3. 96769 9. 10642 15 15 1. 70 ? 5. 60598 15. 2567 16 16 2. 30 ? 7. 24427 24. 4458 17 17 2. 0 ? 8. 88257 36. 9976 18 18 2. 80 ? 10. 52 59. 6117 19 19 2. 70 ? 12. 1592 89. 4756 20 20 3. 90 ? 13. 7974 97. 9594 21 21 4. 90 ? 15. 4357 111. 0 22 22 5. 30 ? 17. 0740 138. 628 23 23 6. 20 ? 18. 7123 156. 558 24 24 4. 10 ? 20. 35 264. 083 25 25 4. 50 ? 21. 99 305. 62 26 26 6. 10 ? 23. 6272 307. 203 27 27 7. 70 ? 25. 2655 308. 547 28 28 10. 10 ? 26. 9038 282. 367 29 29 15. 20 ? 28. 5421 178. 011 30 30 18. 10 ? 30. 18 145. 936 31 31 24. 10 ? 31. 8187 59. 58 32 32 25. 60 ? 33. 46 61. 73 33 33 30. 30 ? 35. 0953 22. 9945 34 34 36. 0 ? 36. 7336 0. 5381 35 35 31. 10 ? 38. 3718 52. 8798 36 36 31. 70 ? 40. 01 69. 0585 37 37 38. 50 ? 41. 6484 9. 91266 38 38 47. 90 ? 43. 2867 21. 2823 39 39 49. 10 ? 44. 9250 17. 43 40 40 55. 80 ? 46. 5633 ? ? 85. 3163 41 41 70. 10 ? 48. 2016 ? 479. 54 42 42 70. 90 ? 49. 84 ? 443. 28 43 43 79. 10 ? 51. 4782 ? 762. 964 44 44 94. 00 ? 53. 1165 1,671. 46 TOTALS 990. 00 787. 30 7,559. 95 modal(a) 22. 50 17. 893 171. 817 (MSE) manner ( Least squares frank relapse on GSP a b 17. 636 13. 936 Coefficients GSP Deposits Year (X) (Y) look forward to Error Error2 ? 1 0. 40 ? 0. 25 12. 198 ? 12. 4482 ? 154. 957 ? 2 0. 40 ? 0. 24 12. 198 ? 12. 4382 ? 154. 71 ? 3 0. 50 ? 0. 24 10. 839 ? 11. 0788 ? 122. 740 ? 4 0. 70 ? 0. 26 8. 12 8. 38 70. 226 ? 5 0. 90 ? 0. 25 5. 4014 5. 65137 31. 94 ? 6 1. 00 ? 0. 30 4. 0420 4. 342 18. 8530 ? 7 1. 40 ? 0. 31 ? 1. 39545 1. 08545 1. 17820 ? 8 1. 70 ? 0. 32 ? 5. 47354 5. 5354 26. 56 ? 9 1. 30 ? 0. 24 ? 0. 036086 0. 203914 0. 041581 10 1. 20 ? 0. 26 1. 3233 1. 58328 2. 50676 11 1. 10 ? 0. 25 2. 6826 2. 93264 8. 60038 12 0. 90 ? 0. 33 5. 4014 5. 73137 32. 8486 13 1. 20 ? 0. 50 1. 3233 1. 82328 3. 32434 14 1. 20 ? 0. 95 1. 3233 2. 27328 5. 16779 15 1. 20 ? 1. 70 1. 3233 3. 02328 9. 14020 16 1. 60 ? 2. 30 ? 4. 11418 1. 81418 3. 9124 17 1. 50 ? 2. 80 ? 2. 75481 0. 045186 0. 002042 18 1. 60 ? 2. 80 ? 4. 11418 1. 31418 1. 727 19 1. 70 ? 2. 70 ? 5. 47354 2. 77354 7. 69253 20 1. 90 ? 3. 90 ? 8. 19227 4. 29227 18. 4236 21 1. 90 ? 4. 90 ? 8. 19227 3. 29227 10. 8390 22 2. 30 ? 5. 30 13. 6297 8. 32972 69. 3843 23 2. 50 ? 6. 20 16. 3484 ? 10. 1484 ? 102. 991 24 2. 80 ? 4. 10 20. 4265 ? 16. 3265 ? 266. 56 25 2. 90 ? 4. 50 21. 79 ? 17. 29 ? 298. 80 26 3. 40 ? 6. 10 28. 5827 ? 22. 4827 ? 505. 473 27 3. 80 ? 7. 70 34. 02 ? 26. 32 ? 692. 752 28 4. 10 10. 10 38. 0983 ? 27. 9983 ? 783. 90 29 4. 00 15. 20 36. 74 ? 21. 54 ? 463. 924 30 4. 00 18. 10 36. 74 ? 18. 64 ? 347. 41 31 3. 90 24. 10 35. 3795 ? 1 1. 2795 ? 127. 228 32 3. 80 25. 60 34. 02 8. 42018 70. 8994 33 3. 0 30. 30 34. 02 3. 72018 13. 8397 34 3. 70 36. 00 32. 66 3. 33918 11. 15 35 4. 10 31. 10 38. 0983 6. 99827 48. 9757 36 4. 10 31. 70 38. 0983 6. 39827 ? 40. 9378 37 4. 00 38. 50 36. 74 1. 76 3. 10146 38 4. 50 47. 90 43. 5357 4. 36428 19. 05 39 4. 60 49. 10 44. 8951 4. 20491 17. 6813 40 4. 50 55. 80 43. 5357 ? 12. 2643 ? 150. 412 41 4. 60 70. 10 44. 951 ? 25. 20 ? 635. 288 42 4. 60 70. 90 44. 8951 ? 26. 00 ? 676. 256 43 4. 70 79. 10 46. 2544 ? 32. 8456 1,078. 83 44 5. 00 94. 00 50. 3325 ? 43. 6675 1,906. 85 TOTALS 451. 223 9,016. 45 come ? 10. 2551 ? 204. 92 ? (MAD) ? (MSE) assumption that one wishes to develop a five-year forecast, trend epitome is the appropriate choice. Measures of error and goodness-of-fit are authentically irrelevant.Exponential smoothing provides a forecast only of deposits for the next yearand thus does not shroud the five-year forecast problem. In o rder to use the regression model ground upon GSP, one must send-off develop a model to forecast GSP, and then use the forecast of GSP in the model to forecast deposits. This requires the development of two modelsone of which (the model for GSP) must be ground solely on time as the nonsymbiotic variable (time is the only other variable we are given). (b)? angiotensin-converting enzyme could make a case for forcing out of the older data. Were we to shut out data from roughly the setoff 25 years, the forecasts for the later year