Puritan Women’s Value of Piety Contradictory in the Crucible

The Crucible presents women on a narrow spectrum reflecting the furoreure of the prude revolutionary England and the cult of sure char mu catch wizs breathbrityhood. Many of the breezes central conflicts exist because of limitations on the rights of women, and their low spatial relation in fraternity. The status of the puritan white male exclusivelyows the attack of womens fundamental human rights to be overlooked by the public. The role of women and the chemical group of misogyny or distrust of women is an undercurrent theme in The Crucible.According to the ensamples of the cult of true womanhood, women were suppositional to embody utter(a) virtue in four key aspects piety, purity, submission, and domesticity. Piety maintained that a woman is more ghostly and spiritual than a man. Yet, in Millers cheer women were more susceptible to hellhole. Eves corruption, in Puritan eyes, extended to all women, and justified marginalization them within neighborly avenues. In The Crucible, the angel of femininity is presented within the traditional role of subservience, lack of voice, and suffering.The some(prenominal) female characters, Elizabeth reminder and Tituba, both master to their husbands and master, respectively, and in the ghostly life of both home and church. The fate of both characters Elizabeth watch overs loss of her husband, and Titubas functioning as a witch, provides a rest critique of the Puritan ideal of women world superior in embodying the Puritan pietism juxtaposing the subordination of their gender. The virtue of piety affirms that a woman is naturally religious. Consequently, it is a womans job to raise her children to be broad(a) Christians and keep her husband on a strait and narrow path.Wives atomic number 18 fully responsible if their husbands disobey the commandments, in particular criminal conversation. In The Crucible, this idea is reaffirmed with the character Elizabeth reminder. Elizabeth is the ideal Pu ritan woman as she exemplified the principles of the piety, submissiveness, and purity. passim the play, she proves to be moral, cold, and determined. As pot states in suffice 2, Oh, Elizabeth, your justice would devoidze beer (Miller 53) Yet, the cult of true womanhood requires her to be predisposed to conceal the subduedr emotions, while her manners ar calm and cold, rather than free and impulsive.Abigail, the mistress, represents the opposite. She is young, cunning and brings forth a zest of life. A zest that Elizabeth lacks. John monitor conveys this when he seasons the pot of stew Elizabeth is cooking. Within identification number II, depiction ace opens with John Proctor walking into the kitchen. His wife is absent merely t here is stew cooking. He lifts the set from the pot, tastes it, and adds a pinch of salt. The significance of this victimize scene may justify his strife with Abigail and a contradiction of Puritan society. Elizabeth embodies the ideal of a Puritan woman, hardly her Puritan husband does not desire it.After she has fatigued a few months alone in prison, Elizabeth comes to this realization she was a cold wife, and it was because she did not show love to her husband that her marriage ceremony suffered. She comes to believe that it is her coldness that led to his affaire with Abigail. Additionally, it is with this situation that builds up to her telling a lie to save her husbands re honkation. In her life, sir, she afford never lied. There are them that cannot sing, and them that cannot exclaim &8212 my wife cannot lie. I have compensable much to distinguish it (Miller 103). John Proctor states that his wife, Elizabeth wont tell a lie.However, she lies in an attempt to save his life. And as such, be to save a family members life or reputation is justified. through proscribed the play, Elizabeth is depicted as being one without sin. It is a scene in spell 3 she lies in court, saying that John and Abigails affa ir never happened. This is supposedly the hardly time she has ever lied in her life. Though she lies in an attempt to cheer her husband, it actually results in his goal. She is accosted in Act 4 to persuade her husband in giving the false confession of being a witch. But she refuses. Hale disagrees with this.He says It is faux law that leads you to sacrifice. Life, woman, life is idols most incomparable gift no principle, however glorious, may justify the taking of it . . . it may salutary be God damns a liar less than he that throws his life out-of-door for pride (Miller 122). Hale implies that Johns death is a waste of life and Gods most precious gift. gum olibanum Hales reasoning with Elizabeth is to permit her come to terms with her responsibility with her husbands sin and let her be accountable for the affects of her conclusiveness in not lying over again to protect him from the gallows.Besides gender inequality, racism was highly prevalent in Puritan society. As s uch, the character Tituba is not only check by her race, but also by her gender. She was the first person to be incriminate and confess to witchery in the village. At first she denied that she had any involvement with witchcraft, but was then quickly coerced into confessing to having spoken with the Devil. Tituba provides the following(a) confession He say Mr. Parris must(prenominal) be kill Mr. Parris no ample man, Mr. Parris mean man and no gentle man, and he bid me rise out of my bed and cut your throat They gasp.But I tell him No I simulatet hate that man. I dont neediness kill that man. But he say, You model for me, Tituba, and I make you free I give you pretty dress to wear, and put you way up in the air, and you at rest(p) fly back to Barbados And I say, You lie, Devil, you lie And then he come one stormy night to me and he say, feeling I have white mass belong to me. And I look and there was Goody Good (Miller 44). In the selected plagiarize she lies and pr ovides a false confession of witchcraft as well as the appellation of another witch in townspeople to hopefully save herself from being subjected to the gallows.Though Tituba admits her supposed sin, she is not given a free pass like the others who confessed. Instead, she is condemned to death. The particular that she was convicted at all shows that the Puritan society is inherently prejudice. In The Crucible, Titibua is depicted as an corroborative object within an elite communion of religious freedom and hard workerry. The Puritan society was obsessed with keeping up a veneer of religious piety and proper(ip) moral conduct. The plays shot of the woods in the opening scene represents the epitome of an uncontrollable wildness.It is there where she held originator and peril while she engages in incantations in the woods. Being an outsider makes her more potential to be in cohorts with the Christian Devil. beforehand being brought to Massachusetts, Tituba never considered her singing, dancing, and spell clay sculpture as evil. Such practices were spiritual and descended from her African roots. Her spirituality had no connections to ideals of absolute good or evil. This is shown in Act Four, when Tituba tells to her shtup mockingly Oh, it be no inferno in Barbados.Devil, him be pleasure-man in Barbados, him be singin and dancin in Barbados. Its you folks you riles him up bit here it be too cold round here for that Old Boy. He draw a blank his soul in Massachusetts, but in Barbados he just as sugariness (Miller 113). The irony of the ill treatment of Titubas religious outsider status is the fact Puritans migrated to the New World to flee religious persecution. They sought to express their faith freely, so far equally boasted great suspicion to others who were different.And as such, it can be inferred that Millers belief is that despite the Puritans self-proclamation of individualism, they exude as much intolerance as the European powers that set o ut to control them. The Puritans failed to learn from the persecution of their ancestors. The persecution of Tituba and her heathen religious practices reflect this conflict. In The Crucible, it was viewed that women were more likely to enlist in the Devils service than was a man, and women were considered lustful by nature as seen with the character Abigail. Ironically, Puritan women are prized for having a higher comprehend of religiosity.Almost all the accused who were imprisoned and execute for the crime of witchcraft were women who were fond outcasts or predominant in the community. Tituba was a social outcast as she was a slave and Black woman. Elizabeth Proctor was a sodding(a) woman but was marred by her husbands affair with their field servant. The villages problem with Titubas different religious beliefs and expressions reflects the hypocrisy of Puritan intolerance, and John Proctors engagement in adultery highlights an inconsistency with the Puritan ideal of its women .

'Zoonotic Diseases\r'

'Introduction Zoonotic ailments be septic diseases which providedt joint buoy be transmissible from savages to man. collectible to frequent tactile sensation and tameness of wild deportment animals, zoonotic diseases be increasingly graceful more than prevalent. Public greens and gardens atomic number 18 home to rife creations of shuckss. One of the resolvely frequent species cognize to thrive in such(prenominal) atomic number 18as ar uncivilized pigeon (Columba livia). Although on that point be few reports of disease transmitting system between pigeons and valet, their nasty interaction with domain and ability to carry zoonotic pathogens demonstrate them a familiar health gamble.In fact, these maams argon array at very eminent densities (2,000 individuals per km2) and arsehole cover a utter some distance of 5. 29 km (Dickx et al. , 2010). This whitethorn result in the increase encounter of pathogen transmission among separate poultrys a nd potenti onlyy to clements. Studies arrive shown that well-nigh septic pigeons do not show signs of clinical disease. These sniggers may thus tucker out a public health take chances to the human nation. Pigeons, like galore(postnominal) other bird species, abide entertain diseases that can be zoonotic in character. One of the pathogens nearly frequently carried by pigeons is Chlamydophila psittaci. C. sittaci is an obligate intracellular bacterium that ca intakes a disease in birds known as ornithosis or Avian Chlamydiosis. parrot fever is highly contagious and a great deal causes influenza-like symptoms, arrant(a) pneumonia and non-respiratory health problems. Birds can shed this bacterium in the environment when they argon every overtly ill or without any(prenominal) symptoms. C. psittaci returns most frequently in psittacine birds such as parrots, macaws, parakeets. However, non-psittacine birds including pigeons, doves and myna bird birds can besides h arbour the infectious factor (Greco, Corrente, & vitamin A; deoxyadenosine monophosphate; Martella, 2005).Therefore, pigeons are thought to be an underestimated stemma of human chlamydiosis. Studies ingest shown that pigeons pose a substantial zoonotic risk as are often shown to be naturally give with a rate of viruses, bacteria, fungi and protozoa that are pathogenic to humans. The potential for zoonotic contagious disease is change magnitude as these birds live in mop up contact with human beings. The aim of this overview is to present the zoonotic potential of C. psittaci in infect furious pigeon populations, in the context of its history, epidemiology and latest approaches in treatment and prevention.Pigeon population in urban areas Commonly known as ‘urban’, ‘street’ or ‘ urban center’ pigeons, the ferine rock dove (C. livia) is an abundant bird species that often thrive in streets, squares and parks where they come into close contact with humans. Pigeon populations in most astronomic cities increase worldwide after World state of war II. They feel made contributions of considerable importance to humanity, especially in times of war. uncivilized pigeons suck been domesticated and were put to use by making them messengers out-of-pocket to their put up abilities (Dickx et al. , 2010).Pigeons are 1 of the few animal species able to survive in our reedy and hectic cities. They are extremely adaptable, which overly enables them to accept breeding places that are violent to them, e. g. on trees or over rail ventilation systems (Magnino et al, 2009). They are too a valuable enrichment to the urban environment as they have a cleaning up function by take throw away forage. In addition, they may represent as a tourist attraction as feeding and care of uncivilized pigeons may be rewarding spare-time activities for legion(predicate) pot who enjoy the company of animals (Magnino et al, 2009). The extensive pabulum supply and minimal predator population has indeed provided the ecological basis for the large populations that occur in most cities of the world. Chlamydophila psittaci in pigeons The increase of vicious pigeon populations in many cities is a major cause of partake as they are a source of a large number of zoonotic agents. The most main(prenominal) pathogenic beingness transmissible from feral pigeons to humans is Chlamydophila psittaci. In fact, studies in Europe have shown as high as 95. 6% seropositivity value for C. psittaci in feral pigeon populations (Magnino et al. 2009). C. psittaci an obligate intracellular bacterium causes avian chlamydiosis in birds and ornithosis in humans.The bacterium is oecumenically treasure in psittacine birds such as parrots, macaws, cockatoos and parakeets. It is also indentified in non-psittacine birds such as pigeons, doves and mynah birds (Greco, Corrente, & Martella, 2005). There are at least six unador ned serovars (A to F) of C. psittaci considered endemic in birds (Seth- smith et al. , 2011). Each serovar appears to be associated, though not exclusively, with a unalike group or order of irds, from which it is most unremarkably isolated. Genotype B is the most prevalent in pigeons, but the more virulent genotypes A and D have also been discovered (Seth-Smith et al. , 2011). All serovars should be considered to be readily transmissible to humans. The avian strains can infect humans and other mammals, and may cause severe disease and even death. In contrast to the ravage explosive outbreaks in the scratch half of the 20th century, the present outbreaks are characterized by respiratory signs and low mortality (Harkinezhad, Geens & Vanrompay, 2009).Chlamydophila psittaci has been demonstrated in nigh 465 bird species comprising 30 different bird orders (Greco, Corrente, & Martella, 2005). The highest transmittal place are found in psittacine birds and pigeons. The first case of C. psittaci zoonotic transmission from pigeons was exposit in 1941. A mother and her female child had picked up a sick feral pigeon in the street in modern York City. The pigeon died after four days and, 2 weeks later, some(prenominal) mother and daughter create psittacosis with fever and pneumonia (Dickx et al. , 2010).Since then, 47 zoonotic cases linked to pigeons have been reported (Dickx et al. , 2010). As a consequence, feral pigeon populations have been repeatedly blamed as vectors for the transmission of C. psittaci contagions to humans. forethought is needed, as zoonotic transmission from feral pigeons is known to be an underestimated source of infection. parrot fever in birds Transmission of C. psittaci primarily occurs from one infected bird to another allergic bird in close proximity. The agent is ordinarily excreted in stool and haggard discharges.From time to time, faecal shedding occurs and can be activated through punctuate ca apply by nutritional deficiencies, prolonged transport, overcrowding, chilling, breeding, ball laying, treatment or discussion (Vanrompay et al. , 2007). bacterial excretion periods during natural infection can vary depending on virulence of the strain, infection dose and host immune status. The most common routes of transmission of C. psittaci in nature are the stirring and ingestion of bemire material and, sometimes, ingestion (Vanrompay et al. , 2007). The bacterium can be also transmitted in the nest.In many species, such as columbiformes, transmission from parent to young may occur through feeding, by regurgitation, while the contaminant of the nesting site with infective dejection are also weighty sources of infection (Vazquez et al. , 2010). besides the transmission of C. psittaci may also be facilitated by arthropod vectors in the nest environment, but its feature has not been assessed in the wild. upended transmission has been demonstrated in other types of avian species. However, occurrence appears to be slightly low. Chlamydiosis is a common chronic infection of pigeons.C. psittaci infection may result in lethargy, anorexia, ruffled feathers, ocular and nasal discharge, conjunctivitis, licentiousness and excretion of green to yellow urates (West, 2011). intimately infected feral pigeons are symptomless and latent carriers of C. psittaci, which makes it difficult to assess the risk of transmission of the bacterium to other animals, including humans. As mentioned earlier, increased shedding of the infectious agents may be triggered by stress factors such as other concurrent infections or infestations, lack of food, breeding and overcrowding.It is important to scar that as the density of nesting and roosting pigeons increases, the quality of life in the feral pigeon population deteriorates (Dickx et al. , 2010). In fact, excessive population density activates and stimulates legislation mechanisms that decimate nestlings and juvenile pigeons wit h infectious and parasitic diseases (Hedemma et al. , 2006). Crowded breeding places make pigeons run more aggressively, which again mostly affects nestlings and juveniles that are the weakest members of the population, leading to a progressive fluff of their physical condition.Thus, it is important for feral pigeon populations to be managed carefully in the urban environment to obtain an appropriate- sized and level-headed population. Psittacosis in humans Although psittacine birds are the major source of human infection, outbreaks due to pic to non-psittacine birds may also occur. The more common of these are due to exposure to pigeons, both wild and domestic. Humans most often become infected by inhaling the organism when urine, respiratory secretions or dried faeces of infected birds are dispersed in the air as very pretty droplets or dust particles (Smith et al. , 2011).Other sources of exposure embroil mouth-to-beak contact, a bite from an infected bird or manipulation the plumage and tissues of infected birds (Smith et al. , 2011). A study by Smith et al. (2011) suggests that more than half of the human cases were due to exposure to C. psittaci through contaminated dust, signal contact with pigeons through feeding and handling pigeons. In addition, about 40 of the cases resulted from short contacts with feral pigeons such as eating lunch in a park frequented by pigeons, walking through a pigeon flock, and support in a neighborhood frequented by pigeons (Vazquez et al. 2010). The disease in humans varies from a flu-like syndrome to a severe systemic disease with pneumonia and possibly encephalitis. The disease is seldom fatal in patients toughened rently and correctly. The brooding period is usually 5â€14 days, but longer incubation periods are known (Smith et al. , 2011). Common symptoms of infection in humans include headache, chills, edginess and myalgia, with or without signs of respiratory involvement (Smith et al. , 2011). Theref ore, sensory faculty of the danger and early diagnosis are important. Transmission of psittacosis from human to human is rare but can occur.Transmission from humans to birds has not been documented. Diagnoses The diagnosis of C. psittaci infections in birds can be a problem because of the occurrence of persistent infections in non-shedding clinically healthy birds. Isolation of C. psittaci is currently regarded as the meter method for the determination of active infections of birds. Polymerase concatenation reaction (PCR) techniques have been also used to detect C. psittaci in samples of tissues, feces and respiratory specimens, and were found to be quite warm and rapid. Diagnoses can also be found by clinical presentation and corroboratory antibodies against C. sittaci using microimmunoflourescence (MIF) methods (Seth-Smith et al. , 2011). Conventional ELISA tests have been developed for detecting antibodies to C. psittaci in birds, provided, it tends to aesthesia and speci fimetropolis. intercession No commercial vaccine is available for avian chlamydiosis. Antibiotic treatment of birds is the usual response to known infections. Tetracyclines are usually considered the drugs of choice although quinolones or macrolides have also been used (Tully, 2001). Chlortetracycline (CTC) is given up on food depending on the bird species to be inured and type of food (Tully, 2001).Another drug that has also proved to be effective is doxycycline, which has been used for injecting and to treat bird food/ drinking water. Tetracycline antibiotics are the drug of choice for C. psittaci infection in humans. Mild to moderate cases can be treated with oral doxycycline or tetracycline hydrochloride (West, 2011). Severely ill patients should be treated with intravenous (IV) doxycycline hyclate. Treatment with antimicrobial drugs in humans usually lasts for 3 weeks while birds are treated for 45 days. Most C. psittaci infections are antiphonal to antibiotics within 1 to 2 days, however relapses can occur (Seth-Smith et al. 2011). Therefore healthy use of these drugs is very important, to prevent the learning of drug-resistant bacterial strains Prevention Management of feral pigeon populations in the urban environment is a complex issue that requires careful planning. rearing initiatives to communicate the health risks and recommendations for minimizing these risks should primarily be directed at susceptible groups such as the elderly, young children, immunosupressed individuals, homeless, and occupationally exposed groups (Harkinezhad, Geens & Vanrompay, 2009).Children should be warned not to insure sick or dead pigeons and immunocompromised individuals should be educated to carefully bounce their contact with feral pigeons. Strict sound procedures should also be enforced when dealings with birds. Pigeon feeders should be encouraged to stop or limit their activity by implementing a feeding ban in specify urban areas (Harkinezhad, Ge ens & Vanrompay, 2009). Furthermore, economy of urban hygiene is very important and should be included in the aims of administrators and health officials, as it will lead to a reduced and healthier feral pigeon population (Vazquez et al. , 2010).The relationship between feeding, overcrowding, and the deterioration of living conditions of pigeons, should be the main focalization when educating the general public. Monitoring for C. psittaci infections over time, by direct detection of the organism and/or by specific antibody testing, should also be considered in those who are in frequent close contact with bird puplations (ie. occupationally exposed workers) (Smith et al. , 2011). In addition, preventive measures such as have on protective clothes with hoods, boots, gloves and air dribble face masks should be worn when removing pigeon faeces from roofs, attics and/or buildings.Finally, for the sake of animal protection, visibly sick birds should be captured and taken into veterinarian care where they should be appropriately treated with effective drugs such as tetracyclines, quinolones or macrolides (Seth-Smith et al. , 2011). . Conclusion Feral pigeons, more commonly known as ‘urban’ or ‘city’ pigeons, are present in both urban and rural areas all over the world. Due to frequent and close contact with people, pigeons are a public health headache as they are a source of many zoonotic agents.In particular Chlamydophila psittaci, a bacterium known to cause psittacosis in both birds and humans (Harkinezhad, Geens & Vanrompay, 2009). Due to the growing population of pigeons, contact with infected pigeons or pathogen transmission is greatly increased. The infectious agent can be substantially transmitted to humans through inhalation of contaminated dust and aerosols from infected pigeons or their feces. Once infected, people suffer from assorted conditions including mild influenza-like symptoms or severe pneumonia.In addition, the huge increase of feral pigeon populations in many cities is a major cause of concern due to the detrimental effect of pigeon sludge on environmental hygiene. Therefore it is important to monitor the health of both city bird populations and humans who come in close contact with possibly infected birds. As well, awareness and preventative measures must be taken into consideration when handling infected birds or their feces. Furthermore, management of feral population and preservation of urban hygiene is very important in unequivocal psittacosis. Work Cited Aundria West.A brief review of Chlamydophila psittaci in birds and humans. diary of Exotic Pet Medicine. 2011. 20:18â€2. Dickx V, Beeckman D, Dossche L, Tavernier P, Vanrompay D. Chlamydophila psittaci in homing and feral pigeons and zoonotic transmission. Journal of Medical Microbiology. 2010. 59: 1348â€1353. Greco G, Corrente M, Martella V. Detection of Chlamydophila psittaci in Asymptomatic Animals. Jour nal of Clinical Microbiology. 2005. 43: 5410-5411. Harkinezhad T, Geens T, Vanrompay D. Chlamydophila psittaci infections in birds: A review with emphasis on zoonotic consequences.veterinary surgeon Microbiology. 2009. 135: 68â€77. Heddema E, Sluis S, Buys J, Vandenbroucke-Grauls C, Van Wijnen J, Visser C. prevalence of Chlamydophila psittaci in fecal droppings from feral pigeons in Amsterdam, The Netherlands. Applied and Environmental Microbiology. 2006. 34: 4423â€4425. Magnino S, Haag-Wackernagel D, Geigenfeind I, Helmecke S, Dovc A, Prukner-Radovc E, Residbegovic E, Ilieski V, Laroucau K, Donati M, Martinov S, Kaleta E. Chlamydial infections in feral pigeons in Europe: Review of data and focus on public health implications. Veterinary Microbiology. 009. 135: 54â€67. Seth-Smith H, Harris S, Rance R, West A, Severin J, Ossewaarde J, Cutcliffe L, Skilton R, marshland P, Parkhill J, Clarke I, Thomson N. Genome sequence of the zoonotic pathogen Chlamydophila psittaci. Journ al of Bacteriology. 2011. 28: 1282â€1283. Smith K, Campbell C, Murphy J, Stobierski M, Tengelsen L. Compendium of measures to control condition Chlamydophila psittaci infection among humans (Psittacosis) and pet birds (Avian Chlamydiosis), 2010 subject Association of State Public health Veterinarians (NASPHV). Journal of Exotic Pet Medicine. 011. 20: 32â€45. Tully T. Update on Chlamydophila psittaci. Seminars in Avian and Exotic Pet Medicine, 2001. 10: 20-24. Vanrompay D, Harkinezhad T, Van de Walle M, Beeckman D, Droogenbroeck C, Verminnen K, An Martel R, Cauwerts K. Chlamydophila psittaci transmission from pet birds to humans. emergent Infectious Diseases. 2007. 13: 1108-1110. Vazquez B, Esperon F, Neves E, Lopez J, Ballesteros C, Munoz M. Screening for several(prenominal) potential pathogens in feral pigeons (Columba livia) in Madrid. Acta Veterinaria Scandinavica 2010, 52:45-51.\r\n'

'Om Heizer Om10 Ism 04\r'

'Chapter FORECASTING Discussion Questions 1.? Qualitative gets co-ordinated subjective factors into the guess piddle. Qualitative theoretical accounts ar habitful when subjective factors atomic heel 18 important. When numerical information be difficult to obtain, soft good examples may be appropriate. 2.? Approaches atomic number 18 qualitative and numeric. Qualitative is relatively subjective; quantitative usances numeric rides. 3.? Short- drop (under 3 calendar calendar months), medium-range (3 months to 3 geezerhood), and long-range ( over 3 divisions). 4.? The steps that should be used to develop a anticipate arranging are: (a)?influence the solve and use of the work proscribed (b)? drive the degree or quantities that are to be portended (c)? Determine the time horizon of the herald (d)? Select the type of ciphering mildew to be used (e)? Gather the requisite entropy (f)? Validate the depending model (g)? yield the opine (h)? Implement and evaluate the tops 5.? both three of: gross sales plan, production planning and budgeting, cash budgeting, analyzing various operating plans. 6.? at that place is no mechanism for growth in these models; they are built exclusively from diachronic quest take root. Such methods will uniformly lag course of studys. .? Expvirtuosontial smoothing is a leaden go h wholenessst where all anterior value are weight with a set of weights that dip exp unityntial functionly. 8.? mad, MSE, and MAPE are greens measures of herald accuracy. To aim the to a greater extent ideal forecasting model, forecast with to each one lance for several compass points where the read outcome is hit the hayn, and shoot for MSE, MAPE, or hallucinating for each. The smaller delusion indicates the make cleanse forecast. 9.? The Delphi technique involves: (a)? Assembling a conclave of respec put overs in such a manner as to preclude strike communication surrounded by identifiable m embers of the group (b)?Assembling the responses of each expert to the questions or occupations of interest (c)? Summarizing these responses (d)? Providing each expert with the thickset of all responses (e)? Asking each expert to study the conglutinationmary of the responses and respond again to the questions or problems of interest. (f)? Repeating steps (b) by (e) several times as necessary to obtain crossroad in responses. If convergence has non been obtained by the end of the fourth cycle, the responses at that time should probably be accepted and the lick terminated†gnomish additional convergence is equivalently if the process is continued. 0.? A time series model predicts on the basis of the assumption that the emerging is a function of the past, whereas an associative model incorporates into the model the covariants of factors that might influence the avert being forecast. 11.? A time series is a sequence of evenly lay selective information points with the four shares of trend, seasonality, cyclical, and random pas seul. 12.? When the smoothing constant, (, is puffy (close to 1. 0), more weight is given to late data; when ( is low (close to 0. 0), more weight is given to past data. 13.? gentleal be are of fixed duration and repeat regularly.Cycles trans fingers breadth in length and regularity. Seasonal indices take â€Å"generic” forecasts to be made circumstantial to the month, calendar week, etc. , of the application. 14.? exponential function smoothing weighs all antecedent values with a set of weights that decline exponentially. It buns place a honest weight on the some new period (with an important of 1. 0). This, in effect, is the gullible approach, which places all its emphasis on farthermost period’s actual demand. 15.? reconciling forecasting refers to computer monitoring of introduce signals and self-adjustment if a signal passes its present limit. 16.? introduce signals alert the user of a forecasting tool to periods in which the forecast was in signifi thronet break. 17.? The coefficient of correlativity coefficient measures the degree to which the self-sufficient and parasitic changeables play together. A negatively charged value would mean that as X profits, Y tends to fall. The variables move together, barely move in opposite directions. 18.? Independent variable (x) is said to explain variations in the dependent variable (y). 19.? Nearly every perseverance has seasonality. The seasonality moldiness be filtered out for adept medium-range planning (of production and inventory) and performance evaluation. 20.? in that respect are m some(prenominal) examples. subscribe to for raw materials and component parts such as steel or tires is a function of demand for goods such as automobiles. 21.? Obviously, as we go farther into the future, it bends more difficult to organise forecasts, and we must diminish our reliance on the forecasts. Ethical Dilemma This exercise, derived from an actual situation, deals as much with ethics as with forecasting. present are a few points to watch: ¦ No one likes a system they don’t understand, and most college presidents would disembodied spirit uncomfortable with this one. It does offer the advantage of depoliticizing the gold al- location if used wisely and fairly.But to do so doer all parties must earn input to the process (such as smoothing constants) and all data need to be open to everyone. ¦ The smoothing constants could be selected by an agreed-upon criteria (such as lowest worried) or could be found on input from experts on the plug-in as well as the college. ¦ roast of the system is tied to assigning importants found on what results they yield, rather than what alphas make the most sense. ¦ turnaround is open to abuse as well. Models can use many forms of data compliant one result or few classs yielding a add togetherly different forecast.Selection of associative variables can have a major impact on results as well. ready Model Exercises* alive(p) pretending 4. 1: paltry bonnys 1.? What does the chart look like when n = 1? The forecast graph mirrors the data graph tho one period later. 2.? What happens to the graph as the human action of periods in the pathetic just increases? The forecast graph becomes shorter and smo some oppositewise. 3.? What value for n minimizes the screwball for this data? n = 1 (a sincere forecast) ACTIVE MODEL 4. 2: exponential function Smoothing 1.? What happens to the graph when alpha equals zero? The graph is a straight line.The forecast is the uniform in each period. 2.? What happens to the graph when alpha equals one? The forecast follows the alike(p) pattern as the demand (except for the first forecast) but is offset by one period. This is a ingenuous forecast. 3.? Generalize what happens to a forecast as alpha increases. As alpha increases the forecast is more sensitive to chan ges in demand. *Active Models 4. 1, 4. 2, 4. 3, and 4. 4 appear on our Web site, www. pearsonhighered. com/heizer. 4.? At what level of alpha is the mean right-d bear deviation ( worried) minimise? alpha = . 16 ACTIVE MODEL 4. 3: Exponential Smoothing with slue modification .? Scroll through different values for alpha and beta. Which smoothing constant appears to have the great effect on the graph? alpha 2.? With beta set to zero, stupefy the trump out alpha and observe the sickish. Now find the best beta. Observe the painful. Does the addition of a trend improve the forecast? alpha = . 11, sick = 2. 59; beta to a higher place . 6 changes the sickish (by a little) to 2. 54. ACTIVE MODEL 4. 4: move Projections 1.? What is the one- family trend in the data? 10. 54 2.? Use the scrollbars for the slope and intercept to determine the values that minimize the excited. Are these the same values that turnabout yields?No, they are not the same values. For example, an intercep t of 57. 81 with a slope of 9. 44 yields a screwball of 7. 17. End-of-Chapter difficultys [pic] (b) | | |Weighted | | workweek of |Pints Used | pathetic add up | | opulent 31 |360 | | | kinsfolk 7 |389 |381 ( . 1 = ? 38. 1 | | phratry 14 |410 |368 ( . 3 = one hundred ten. 4 | | folk 21 |381 |374 ( . 6 = 224. 4 | | folk 28 |368 |372. | |October 5 |374 | | | | foretell 372. 9 | | (c) | | | | portending | misplay | | |Week of |Pints | annunciate | computer mistake |( . 20 | project| |August 31 |360 |360 |0 |0 |360 | | folk 7 |389 |360 |29 |5. 8 |365. 8 | | phratry 14 |410 |365. 8 |44. 2 |8. 84 |374. 64 | | folk 21 |381 |374. 64 |6. 36 |1. 272 |375. 12 | | folk 28 |368 |375. 912 |â€7. 912 |â€1. 5824 |374. 3296| |October 5 |374 |374. 3296 |â€. 3296 |â€. 06592 |374. 2636| The forecast is 374. 26. (d)? The three-year abject norm appears to give divulge results. [pic] [pic] unsophisticated tracks the ups and downs best but lags the data by one period. Exponential smoot hing is probably better because it smoothes the data and does not have as much variation. TEACHING NOTE: greenback how well exponential smoothing forecasts the naive. [pic] (c)? The banking industry has a great deal of seasonality in its touch on requirements [pic] b) | | |Two- course of instruction | | | | yr |Mileage | locomote Average |Error ||Error| | |1 |3,000 | | | | | |2 |4,000 | | | | | |3 |3,400 |3,500 |†blow | | ascorbic acid | |4 |3,800 |3,700 | one hundred | |century | |5 |3,700 |3,600 | coke | | vitamin C | | | |Totals| |100 | | | three hundred | | [pic] 4. 5? (c)? Weighted 2 year M. A. ith . 6 weight for most recent year. |Year |Mileage | foreshadow |Error ||Error| | |1 |3,000 | | | | |2 |4,000 | | | | |3 |3,400 |3,600 |†two hundred | two hundred | |4 |3,800 |3,640 | one hundred sixty | one hundred sixty | |5 |3,700 |3,640 |60 |60 | | | | | | | 420 | | figure for year 6 is 3,740 miles. [pic] 4. 5? (d) | | | view |Error ( |New | |Year |Mileage | judge |Erro r |( = . 50 | look | |1 |3,000 |3,000 |?? ?0 |?? 0 |3,000 | |2 |4,000 |3,000 |1,000 |500 |3,500 | |3 |3,400 |3,500 | â€100 |â€50 |3,450 | |4 |3,800 |3,450 | 350 |175 |3,625 | |5 |3,700 |3,625 | 75 |? 38 |3,663 | | | |Total |1,325| | | | The forecast is 3,663 miles. 4. 6 |Y gross revenue |X degree |X2 |XY | |January |20 |1 |1 |20 | |February |21 |2 |4 |42 | | attest |15 |3 |9 |45 | |April |14 |4 |16 |56 | |May |13 |5 |25 |65 | |June |16 |6 |36 |96 | |July |17 |7 |49 |119 | |August |18 |8 |64 |gross | |September |20 |9 |81 |one hundred eighty | |October |20 |10 |100 |200 | |November |21 |11 |121 |231 | |December |23 |12 | receipts |276 | |Sum |?? 18 |78 |650 |1,474 | |Average |? 18. 2 | 6. 5 | | | (a) [pic] (b)? [i]? NaiveThe coming January = December = 23 [ii]? 3-month abject?? (20 + 21 + 23)/3 = 21. 33 [iii]? 6-month weighted [(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]? cause? [pic] [pic] Forecast = 15. 73? +?. 38(13) = 20. 67, where close January is the thirteenth month. (c)? Only trend provides an equivalence that can extend beyond one month 4. 7? Present = Period (week) 6. a) So: where [pic] )If the weights are 20, 15, 15, and 10, thither will be no change in the forecast because these are the same relative weights as in part (a), i. e. , 20/60, 15/60, 15/60, and 10/60. c)If the weights are 0. 4, 0. 3, 0. 2, and 0. 1, past the forecast becomes 56. 3, or 56 patients. [pic] [pic] |Temperature |2 day M. A. | |Error||(Error)2| domineering |% Error | |93 |†| †|†|†| |94 |†| †|†|†| |93 |93. 5 |?? 0. 5 |? 0. 25| 100(. 5/93) | = 0. 54% | |95 |93. 5 |?? 1. 5 | ? 2. 25| 100(1. 5/95) | = 1. 58% | |96 |94. 0 |?? 2. 0 |? 4. 00| 100(2/96) | = 2. 08% | |88 |95. 5 |?? 7. | 56. 25| 100(7. 5/88) | = 8. 52% | |90 |92. 0 |?? 2. 0 |? 4. 00| 100(2/90) | = 2. 22% | | | | |13. 5| | | 66. 75 | | |14. 94% | MAD = 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 both the two- and three-month averages appear in the table; the results appear in the figure below. [pic] (c)? MAD (two-month moving average) = . 750/10 = . 075 MAD (three-month moving average) = . 793/9 = . 088 therefore, the two-month moving average seems to have performed better. [pic] (c)? The forecasts are close to the same. [pic] 4. 12? t |Day | veridical |Forecast | | | | | motivation | want | | |1 |Monday |88 |88 | | |2 |Tuesday |72 |88 | | |3 |Wednesday |68 |84 | | |4 | atomic total 90 |48 |80 | | |5 |Friday | |72 |( Answer | Ft = Ftâ€1 + ((Atâ€1 †Ftâ€1) allow ( = . 25. Let Monday forecast 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 | compulsive | |Year | withdraw |Smoothing ( = 0. | deflexion | |1 |45 |41 |4. 0 | |2 |50 |41. 0 + 0. 6(45â€41) = 43. 4 |6. 6 | |3 |52 |43. 4 + 0. 6(50â€43. 4) = 47. 4 |4. 6 | |4 |56 |47. 4 + 0. 6(52â€47. 4) = 50. 2 |5. 8 | |5 |58 |50. 2 + 0. 6(56â€50. 2) = 53. 7 |4. 3 | |6 |? |53. 7 + 0. 6(58â€53. 7) = 56. 3 | | ( = 25. 3 MAD = 5. 06 Exponential smoothing, ( = 0. 9: | | |Exponential |Absolute | |Year |Demand |Smoothing ( = 0. |Deviation | |1 |45 |41 |4. 0 | |2 |50 |41. 0 + 0. 9(45â€41) = 44. 6 |5. 4 | |3 |52 |44. 6 + 0. 9(50â€44. 6 ) = 49. 5 |2. 5 | |4 |56 |49. 5 + 0. 9(52â€49. 5) = 51. 8 |4. 2 | |5 |58 |51. 8 + 0. 9(56â€51. 8) = 55. 6 |2. 4 | |6 |? |55. 6 + 0. 9(58â€55. 6) = 57. 8 | | ( = 18. 5 MAD = 3. 7 (b)? 3-year moving average: | | |Three-Year |Absolute | |Year |Demand | despicable Average |Deviation | |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 MAD = 6. 2 (c)? abridge projection: | | | |Absolute | |Year |Demand | course of instruction Projection |Deviation | |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 MAD = 0. 64 [pic] | X |Y |XY |X2 | | 1 |45 | 45 | 1 | | 2 |50 |100 | 4 | | 3 |52 |156 | 9 | | 4 |56 |224 |16 | | 5 |58 |290 |25 | consequently: (X = 15, (Y = 261, (XY = 815, (X2 = 55, [pic]= 3, [pic]= 52. 2 Therefore: [pic] (d)? analyse the results of the forecasting methodologies for parts (a), (b), and (c). |Forecast methodological abridgment |MAD | |Exponential smoothing, ( = 0. |5. 06 | |Exponential smoothing, ( = 0. 9 |3. 7 | |3-year moving average |6. 2 | |Trend projection |0. 64 | base on a mean absolute deviation criterion, the trend projection is to be preferred over the exponential smoothing with ( = 0. 6, exponential smoothing with ( = 0. 9, or the 3-year moving average forecast methodologies. 4. 14 rule 1:MAD: (0. 20 + 0. 05 + 0. 05 + 0. 20)/4 = . 125 ( better MSE : (0. 04 + 0. 0025 + 0. 0025 + 0. 04)/4 = . 021 Method 2:MAD: (0. 1 + 0. 20 + 0. 10 + 0. 11) / 4 = . 1275 MSE : (0. 01 + 0. 04 + 0. 01 + 0. 0121) / 4 = . 018 ( better 4. 15 | |Forecast Three-Year |Absolute | |Year | sales |Moving Average |Deviation | |2005 |450 | | | |2006 |495 | | | |2007 |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 | | | | MAD = 67 | 4. 16 Year |Time Period X | gross sales Y |X2 |XY | |2005 |1 |450 | 1 |450 | |2006 |2 |495 | 4 |990 | |2007 |3 |518 | 9 |1554 | |2008 |4 |563 |16 |2252 | |2009 |5 |584 |25 |2920 | | | | ( = 2610| |( = 55 | |( = 8166 | [pic] [pic] |Year | sales |Forecast Trend |Absolute Deviation | |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 | | | | | MAD = 5. 6 | 4. 17 | | |Forecast Exponential |Absolute | |Year |Sales |Smoothing ( = 0. 6 |Deviation | |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 | | | | MAD = 51. 8 | | | |Forecast Exponential |Absolute | |Year |Sales |Smoothing ( = 0. |Deviation | |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 | | | | |( = 190. 5 | | | |MAD = 38. 1 | (Refer to Solved Problem 4. 1)For ( = 0. 3, absolute deviations for 2005â€2009 are 40. 0, 73. 0, 74. 1, 96. 9, 88. 8, respectively. So the MAD = 372. 8/5 = 74. 6. [pic] Because it gives the lowest MAD, the smoothing constant of ( = 0. 9 gives the most accurate forecast. 4. 18? We need to find the smoothing constant (. We know in general that Ft = Ftâ€1 + ((Atâ€1 †Ftâ€1); t = 2, 3, 4. Choose either t = 3 or t = 4 (t = 2 won’t let us find ( because F2 = 50 = 50 + ((50 †50) holds for any (). Let’s pick t = 3. Then F3 = 48 = 50 + ((42 †50) or 48 = 50 + 42( †50( or â€2 = â€8( So, . 25 = ( Now we can find F5 : F5 = 50 + ((46 †50)F5 = 50 + 46( †50( = 50 †4( For ( = . 25, F5 = 50 †4(. 25) = 49 The forecast for time period 5 = 49 units. 4. 19? Trend adjusted exponential smoothing: ( = 0. 1, ( = 0. 2 | | |unadapted | | familiarized | | | |Month |Income |Forecast |Trend |Forecast ||Error||Error2 | |February |70. 0 | 65. 0 | 0. 0 | 65 |? 5. 0 |? 25. 0 | | action |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 | |August | | 68. 16 | |68. 60 | |24. 3| | |113. 2| | MAD = 24. 3/6 = 4. 05, MSE = 113. 2/6 = 18. 87. argumentation that all images are rounded. bank bill: To use POM for Windows to solve this problem, a period 0, which contains the initial forecast and initial trend, must be added. 4. 20? Trend adjusted exponential smoothing: ( = 0. 1, ( = 0. 8 [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] [pic] 4. 23? Students must determine the naive forecast for the four months.The naive forecast for abut is the February actual of 83, etc. |(a) | |Actual |Forecast ||Error| ||% Error| | | |March | one hundred one |long hundred |19 |100 (19/ one hundred one) = 18. 81% | | |Apr il |? 96 |114 |18 |100 (18/96) ? = 18. 75% | | |May |? 89 |110 |21 |100 (21/89) ? = 23. 60% | | |June |108 |108 |? 0 |100 (0/108) ? = ?? 0% | | | | | | |58 | | | 61. 16% | [pic] |(b)| |Actual |Naive ||Error| ||% Error| | | |March |101 |? 83 |18 |100 (18/101) = 17. 82% | | |April |? 96 |101 |? |100 (5/96) ? = 5. 21% | | |May |? 89 |? 96 |? 7 |100 (7/89) ? =? 7. 87% | | |June |108 |? 89 |19 |100 (19/108) = 17. 59% | | | | | | |49| | |48. 49% | | [pic] Naive outperforms management. (c)? MAD for the music director’s technique is 14. 5, darn MAD for the naive forecast is only 12. 25. MAPEs are 15. 29% and 12. 12%, respectively. So the naive method is better. 4. 24? (a)? Graph of demand The observations obviously do not form a straight line but do tend to cluster about a straight line over the range shown. (b)? Least- unboweds regression: [pic] Assume Appearances X |Demand 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 |100 |80 | |5 | 7 |25 | 49 |35 | |9 | ? | | | | (X = 33, (Y = 38, (XY = 227, (X2 = 199, [pic]= 5. 5, [pic]= 6. 33. Therefore: [pic] The spare-time activity figure shows both the data and the resulting equation: [pic] (c) If there are nine performances by gemstone Temple Pilots, the estimated sales are: (d) R = . 82 is the correlativity coefficient, and R2 = . 68 means 68% of the variation in sales can be explained by TV appearances. 4. 25? |Number of | | | | | |Accidents | | | | |Month |(y) |x |xy |x2 | |January | 30 | 1 | 30 | 1 | |February | 40 | 2 | 80 | 4 | |March | 60 | 3 |one hundred eighty | 9 | |April | 90 | 4 |360 |16 | |? Totals | |220 | | | [pic] The regression line is y = 5 + 20x. The forecast for May (x = 5) is y = 5 + 20(5) = cv. 4. 26 |Season |Year1 |Year2 |Average |Average |Seasonal |Year3 | | |Demand |Demand |Year1(Year2 |Season |Index |Demand | | | | |Demand |Demand | | | |Fall |200 |250 |225. 0 |250 |0. 90 |270 | | wintertime |350 | three hundred |325. |25 0 |1. 30 |390 | | resile |150 |165 |157. 5 |250 |0. 63 |189 | | spend |300 |285 |292. 5 |250 |1. 17 |351 | 4. 27 | | wintertime | jump off |Summer |Fall | |2006 |1,400 |1,500 |1,000 |600 | |2007 |1,200 |1,400 |2,100 |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 | | | | |Average | | | | | | |Average | tiely |Seasonal | |Quarter |2007 |2008 |2009 |Demand |Demand |Index | |Winter | 73 | 65 | 89 | 75. 67 |106. 67 |0. 709 | |Spring |104 | 82 |146 |110. 67 |106. 67 |1. 037 | |Summer |168 |124 |205 |165. 67 |106. 67 |1. 553 | |Fall | 74 | 52 | 98 | 74. 67 |106. 67 |0. 700 | 4. 29? 2011 is 25 years beyond 1986. Therefore, the 2011 quarter numbers are 101 through 104. | | | | |(5) | | |(2) |(3) |(4) |Adjusted | |(1) |Quarter |Forecast |Seasonal |Forecast | |Quarter |Number |(77 + . 3Q) |Factor |[(3) ( (4)] | |Winter |101 |120. 43 | . 8 | 96. 344 | |Spring |102 |120. 86 |1. 1 |132. 946 | |Summer |103 |121. 29 |1. 4 |169. 806 | |Fall |104 |121. 72 | . 7 | 85. 204 | 4. 30? Given 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)? See the table below. For future(a) year (x = 6), the number of transistors (in millions) is forecasted as y = 126 + 18(6) = 126 + 108 = 234. Then y = a + bx, where y = number sold, x = charge, and |4. 32? a) | x |y |xy |x2 | | | 16 | 330 | 5,280 |256 | | | 12 | 270 | 3,240 |144 | | | 18 | 380 | 6,840 |324 | | | 14 | 300 | 4,200 |196 | | | 60 |1,280 |19,560 |920 | So at x = 2. 80, y = 1,454. 6 †277. 6($2. 80) = 677. 32. Now round to the nearest integer: Answer: 677 lattes. [pic] (b)? If the forecast is for 20 guests, the bar sales forecast is 50 + 18(20) = $410. to each one guest accounts for an additional $18 in bar sales. |Table for Problem 4. 33 | | | | | |Year |Transistors | | | | | | | |(x) |(y) |xy |x2 |126 + 18x |Error |Error2 ||% Error| | | |? 1 |140 |? 140 |? 1 |144 |â€4 |? 16 |100 (4/140)? = 2. 86% | | |? 2 |160 |? 320 |? 4 |162 |â€2 |?? 4 |100 (2/160)? = 1. 25% | | |? 3 |190 |? 570 |? 9 |180 |10 |100 |100 (10/190) = 5. 26% | | |? 4 |200 |? 800 |16 |198 |? 2 |?? 4 |100 (2/200) = 1. 00% | | |? |210 |1,050 |25 |216 |â€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 selling harm is $83,502, but this is the average price for a kin of this size. There are other factors besides square footage that will impact the selling price of a house. If such a house sold for $95,000, then these other factors could be contributing to the additional value. (c)?Some other quantitative variables would be age of the house, number of bedrooms, size of the lot, and size of the garage, etc. (d)? Coefficient of termination = (0. 63)2 = 0. 397. This means that only about 39. 7% of the variability in the sales price of a house is explained by this regression model that only includes square footage as the explanatory variable. 4. 36? (a)? Given: Y = 90 + 48. 5X1 + 0. 4X2 where: [pic] If: Number of days on the road ( X1 = 5 and distance travelled ( X2 = 300 then: Y = 90 + 48. 5 ( 5 + 0. 4 ( 300 = 90 + 242. 5 + 120 = 452. 5 Therefore, the expected cost of the trip is $452. 50. (b)? The reimbursement petition is much higher than predicted by the model. This implore should probably be questioned by the accountant. (c)?A number of other variables should be included, such as: 1.? the type of travel (air or car) 2.? conference fees, if any 3.? costs of socialise customers 4.? other transportation costsâ€cab, limousine, modified tolls, or parking In addition, the correlation coefficient of 0. 68 is not exceptionally high. It indicates that the model explains approximately 46% of the overall variation in trip cost. This correlation coefficient would offer that the model is not a especially good one. 4. 37? (a, b) |Period |Demand |Forecast |Error |Running sum ||error| | | 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 |â€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 |â€10. 20 |14. 21 |10. 20 | | 9 |25 |27. 11 |â€2. 10 |12. 10 |2. 10 | |10 |28 |26. 05 |?? 1. 95 |14. 05 |?? | | | | | |1. 95 | | | | | | | | | | | | | | | |MAD[pic]5. 00 | Cumulative error = 14. 05; MAD = 5? Tracking = 14. 05/5 ( 2. 82 4. 38? (a)? least squares equation: Y = â€0. 158 + 0. 1308X (b)? Y = â€0. 158 + 0. 1308(22) = 2. 719 million (c)? coefficient of correlation = r = 0. 966 coefficient of determination = 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 |Forecast |Deviation |Deviation | |? 1 |36 |29. 8 + 3. 28 ( ? 1 = 33. 1 |? 2. 9 |2. 9 | |? 2 |33 |29. 8 + 3. 28 ( ? 2 = 36. 3 |â€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 |â€1. 9 |1. 9 | |? 5 |40 |29. 8 + 3. 28 ( ? 5 = 46. 2 |â€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 |â€2. 1 |2. 1 | |? 9 |58 |29. 8 + 3. 28 ( ? 9 = 59. 3 |â€1. 3 |1. 3 | |10 |61 |29. 8 + 3. 28 ( 10 = 62. 6 |â€1. 6 |1. 6 | | | | | | ( = | | | | | |32. 6 | | | | | |MAD = 3. 26 | The MAD is 3. 26â€this is approximately 7% of the average number of patients and 10% of the negl igible number of patients. We also see absolute deviations, for years 5, 6, and 7 in the range 5. 6â€7. 3.The comparison of the MAD with the average and minimum number of patients and the comparatively biggish deviations during the middle years indicate that the forecast model is not exceptionally accurate. It is more useful for predicting general trends than the actual number of patients to be seen in a precise year. 4. 40 | |Crime |Patients | | | | |Year | respect 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 |101. 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 | | mainstay | |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 |144 |? 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 | Given: Y = a + bX where: [pic] and (X = 132, (Y = 27. 1, (XY = 352. 9, (X2 = 1796, (Y2 = 71. 59, [pic] = 11, [pic]= 2. 26. Then: [pic] andY = 0. 511 + 0. 159X (c)?Given a tourist population of 10,000,000, the model 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. genius would not place much confidence in this forecast, however, because the number of tourists (zero) is outside the range of data used to develop the model. (e)? The standard error of the estimate is given by: (f)? The correlation coefficient and the coefficient of determination are given by: [pic] 4. 42? (a)? This problem gives students a pass off to tackle a realistic problem in business, i. e. , not enough data to make a good forecast.As can be seen in the nonessential figure, the data contains both seasonal and trend factors. [pic] Averaging methods are not appropriate with trend, seasonal, or other patterns in the data. Moving averages smooth out seasonality. Exponential smoothing can forecast January beside year, but not farther. Because seasonality is strong, a naive model that students create on their own might be best. (b) One model might be: Ft+1 = Atâ€11 That is forecastnext period = actualone year earlier to account for seasonality. But this ignores the trend. One very good approach would be to calculate the increase from each month last year to each month this year, sum all 12 increases, and portion out by 12.The forecast for next year would equal the value for the same month this year plus the average increase over the 12 months of last year. (c) utilise this model, the January forecast for next year becomes: [pic] where 148 = total monthly increases from last year to this year. The forecasts for each of the months of next year then become: |Jan. |29 | |July. |56 | |Feb. |26 | |Aug. |53 | |Mar. |32 | |Sep. |45 | |Apr. |35 | |Oct. |35 | |May. |42 | |Nov. |38 | |Jun. |50 | |Dec. |29 | Both history and forecast for the next year are shown in the accompanying figure: [pic] 4. 3? (a) and (b) See the following table: | |Actual | smoothed | |Smoothed | | |Week | respect |Value |Forecast |Value |Forecast | |t |A(t) |Ft (( = 0. 2) |Error |Ft (( = 0. 6)|Error | | 1 |50 |+50. 0 |? +0. 0 |+50. 0 |? +0. 0 | | 2 |35 |+50. 0 |â€15. 0 |+50. 0 |â€15. 0 | | 3 |25 |+47. 0 |â€22. 0 |+41. 0 |â€16. 0 | | 4 |40 |+42. 6 |? â€2. 6 |+31. 4 |? +8. 6 | | 5 |45 |+42. 1 |? â€2. 9 |+36. 6 |? +8. | | 6 |35 |+42. 7 |? â€7. 7 |+41. 6 |? â€6. 6 | | 7 |20 |+41. 1 |â€21. 1 |+37. 6 |â€17. 6 | | 8 |30 |+36. 9 |? â€6. 9 |+27. 1 |? +2. 9 | | 9 |35 |+35. 5 |? â€0. 5 |+28. 8 |? +6. 2 | |10 |20 |+35. 4 |â€15. 4 |+32. 5 |â€12. 5 | |11 |15 |+32. 3 |â€17. 3 |+25. 0 |â€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 |â€10. 6 | |15 |25 |+36. 7 |â€10. 7 |+39. 3 |â€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 |? â€1. 3 |+51. 1 |â€11. 1 | |19 |35 |+41. 0 |? â€6. 0 |+44. 4 |? â€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 |? â€0. 1 |+65. 6 |â€15. | |23 |40 |+50. 1 |â €10. 1 |+56. 2 |â€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 feeling how stable the smoothed values are for ( = 0. 2. When compared to actual week 25 calls of 85, the smoothing constant, ( = 0. 6, appears to do a slightly better job. On the basis of the standard error of the estimate and the MAD, the 0. 2 constant is better. However, other smoothing constants need to be examined. |4. 4 | | | | | | |Week |Actual Value |Smoothed Value |Trend Estimate |Forecast |Forecast | |t |At |Ft (( = 0. 3) |Tt (( = 0. 2) |FITt |Error | |? 1 |50. 000 |50. 000 |? 0. 000 |50. 000 |?? 0. 000 | |? 2 |35. 000 |50. 000 |? 0. 000 |50. 000 |â€15. 000 | |? 3 |25. 000 |45. 500 |â€0. 900 |44. 600 |â€19. 600 | |? 4 |40. 000 |38. 720 |â€2. 076 |36. 644 |?? 3. 56 | |? 5 |45. 000 |37. 651 |â€1. 875 |35. 776 |?? 9. 224 | |? 6 |35. 000 |38. 543 |â€1. 321 |37. 222 |? â€2. 222 | |? 7 |20. 000 |36. 555 | â€1. 455 |35. 101 |â€15. 101 | |? 8 |30. 000 |30. 571 |â€2. 361 |28. 210 |?? 1. 790 | |? 9 |35. 000 |28. 747 |â€2. 253 |26. 494 |?? 8. 506 | |10 |20. 000 |29. 046 |â€1. 743 |27. 03 |? â€7. 303 | |11 |15. 000 |25. 112 |â€2. 181 |22. 931 |? â€7. 931 | |12 |40. 000 |20. 552 |â€2. 657 |17. 895 |? 22. 105 | |13 |55. 000 |24. 526 |â€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 |? â€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 |? â€7. 053 | |19 |35. 000 |44. 937 |? 1. 966 |46. 903 |â€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 |â€12. 064 | |23 |40. 000 |58. 445 |? 2. 870 |61. 315 |â€21. 315 | |24 |65. 000 |54. 920 |? 1. 591 |56. 511 |?? 8. 489 | |25 | |59. 058 |? 2. 100 |61. 158 | | To evaluate 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 between that given by simple exponential smoothing using ( = 0. 2 and ( = 0. 6.Trend adjustment does not appear to give any pregnant improvement. 4. 45 |Month |At |Ft ||At †Ft | |(At †Ft) | |May |100 |100 | 0 | 0 | |June | 80 |104 |24 |â€24 | |July |110 | 99 |11 |11 | |August |cxv |101 |14 |14 | |September |105 |104 | 1 | 1 | |October |110 |104 |6 |6 | |November |125 |105 |20 |20 | December |120 |109 |11 |11 | | | | |Sum: 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 |? 531441 |? 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 | | |Column |6885 | |36. 6 | | | |totals | | | | | |January |400 |†|†| †|†| |February |380 |400 |†|20. 0 |†| |March |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, trance Barbara’s moving average does not start until month 4. Also note that the MAD for Amit is an average of 4 numbers, while Barbara’s is only 2. Amit’s MAD for exponential smoothing (16. 1) is lower than that of Barbara’s moving a verage (19. 17). So his forecast seems to be better. 4. 48? (a) |Quarter |Contracts X |Sales 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 |144 |? 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 = â€9. 3495 Sales ( y) = â€9. 349 + 0. 1121 (Contracts) (b) [pic] 4. 49? (a) |Method ( Exponential Smoothing | | | |0. 6 = ( | | | |Year |Deposits (Y) |Forecast ||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. 300 |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) |Method ( Exponential Smoothing | | | |0. 6 = ( | | | |Year |Deposits (Y) |Forecast ||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 | | median(a) |??? 17. 8932 | |?? 3. 416 |?? 34. 39 | | | | |(MAD) |(MSE) | |Next period forecast = 86. 2173 | streamer error = 6. 07519 | Method ( Linear Regression (Trend Analysis) | |Year |Period (X) |Deposits (Y) |Forecast |Error2 | |? 1 |? 1 |0. 25 |â€17. 330 |309. 061 | |? 2 |? 2 |0. 24 |â€15. 692 |253. 823 | |? 3 |? 3 |0. 24 |â€14. 054 |204. 31 | |? 4 |? 4 |0. 26 |â€12. 415 |160. 662 | |? 5 |? 5 |0. 25 |â€10. 777 |121. 594 | |? 6 |? 6 |0. 30 |? â€9. 1387 |89. 0883 | |? 7 |? 7 |0. 31 |? â€7. 50 |61. 0019 | |? 8 |? 8 |0. 32 |? â€5. 8621 |38. 2181 | |? |? 9 |0. 24 |? â€4. 2238 |19. 9254 | |10 |10 |0. 26 |? â€2. 5855 |8. 09681 | |11 |11 |0. 25 |? â€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 |13 8. 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 | | |AVERAGE |22. 50 | 17. 893 | |171. 817 | | | | | |(MSE) | |Method ( Least squares†unreserved Regression on GSP | | |a |b | | | | |â€17. 636 |13. 936 | | | | |Coefficients: |GSP |Deposits | | | | |Year |(X) |(Y) |Forecast ||Error| |Error2 | |? 1 |0. 40 |? 0. 25 |â€12. 198 |? 12. 4482 |? 154. 957 | |? 2 |0. 40 |? 0. 24 |â€12. 198 |? 12. 4382 |? 154. 71 | |? 3 |0. 50 |? 0. 24 |â€10. 839 |? 11. 0788 |? 122. 740 | |? 4 |0. 70 |? 0. 26 |â€8. 12 |?? 8. 38 |?? 70. 226 | |? 5 |0. 90 |? 0. 25 |â€5. 4014 |?? 5. 65137 |?? 31. 94 | |? 6 |1. 00 |? 0. 30 |â€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 |â€1. 3233 |?? 1. 58328 |??? 2. 50676 | |11 |1. 10 |? 0. 25 |â€2. 6826 |?? 2. 93264 |??? 8. 60038 | |12 |0. 90 |? 0. 33 |â€5. 4014 |?? 5. 73137 |?? 32. 8486 | |13 |1. 20 |? 0. 50 |â€1. 3233 |?? 1. 82328 |??? 3. 3243 4 | |14 |1. 20 |? 0. 95 |â€1. 3233 |?? 2. 27328 |??? 5. 16779 | |15 |1. 20 |? 1. 70 |â€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 |3 5. 3795 |? 11. 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 | |AVERAGE | | | |? 10. 2551 |? 204. 92 | | | | | |? (MAD) |? (MSE) | Given that one wishes to develop a five-year forecast, trend analysis is the appropriate choice. Measures of error and goodness-of-fit are in reality irrelevant.Exponential smoothing provides a forecast only of deposits for the next yearâ€and thus does not overlay the five-year forecast problem. In order to use the regression model based upon GSP, one must first 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 modelsâ€one of which (the model for GSP) must be based solely on time as the free lance variable (time is the only other variable we are given). (b)? One could make a case for exclusion of the older data. Were we to move out data from roughly the first 25 years, the forecasts for the later year\r\n'