MEMO REPORT(WAGE NEGOTIATIONS Incident Decision) Assignment

MEMO REPORT(WAGE NEGOTIATIONS Incident Decision) - Assignment Example The union has made it clear that if their demands are not met the employees will go on strike. The firm should avoid the strike scenario under all consequences. The proposed solution avoids the risk of a work stoppage caused by a worker’s strike. The optimal solution for the company is to settle with the union in order to resolve the incident. The negotiator send to talk will admit that the employees deserve a raise. The negotiator will explain to the union representatives that the increase in production of the company came due to a variety of factors including better equipment, optimal use of technology, and mastering the learning curve. The human factor also contributed directly to the increment in production. The firm will open its books to show the union that the company cannot afford such a high increment in salary. The proposed solution is to offer the employees an increase of $400 per

Non profit organizations Article Example | Topics and Well Written Essays - 1000 words

Non profit organizations - Article Example The main priority which is laid while performing the broad duties mostly reflects upon determining the interests of the law. Also, the duties that perform by high rank officers are framed in such a way that demonstrates legal forms of working behavior. However, the main concern in such type of organization is to generate a balanced working atmosphere. This particular aspect is developed through executing various principles related to corporate governance in non-profit organizations. The best feature about this sort of organization is that all the officers along with other employees perform their respective assigned tasks quite effectively. Also, the duties of officers in a non-profit organization are determined through following a broader framework which considers the basic objectives of such type of organizations. This way, the broad duties along with the responsibilities of all the members including the officers get prioritized in a formative manner (Twaits, 1998). This paper will broadly consider the major aspects pertaining to the broad duties of officers along with employees in non-profit organizations. In addition, the aspects will be critically analyzed, backed up with a proper review and a personal reflection of the concerned article. Review of the Item As per the studies undertaken by Andrew Twaits (1998), numerous researches and surveys have been conducted upon managing the non-profit organizations (NPOs) belonging to this modern day context. With increased level of globalization along with internationalization, NPOs have been viewed to support the community members in terms of serving their best interests effectively. It has been learned that NGOs can very well move in aligning with the needs of the society by a certain degree. With due analysis, it can be stated that the different activities of NPOs have been able to widen the expectation levels of shareholders in terms of fulfilling their respective desires. The management along with the operationa l activities that takes place in a NPO and the duties perform by the officers as well as the employees is often recognized to be quite broad. It can be apparently observed that the different tasks and the duties that are performed by the officers along with the employees deliver a high range of performance within the organizations. According to the article, it can be viewed that there exist two sorts of organization that mainly comprise ‘unincorporated association’ and ‘incorporated association’. These associations eventually lead towards governing along leading NPOs to attain their predetermined targets. In this regard, the term ‘unincorporated association’ signifies the meaning of a chamber, club, federation, society, council, league, institute, union or guild, which is fundamentally voluntary in nature. This form of association is viewed to serve the basic purpose or serving the interests of a group of people. The other form of association i .e. ‘incorporated association’ is regarded as a form of association which can be understood as a legal entity that possesses a perpetual succession and also a common seal. This form of association is considered to be highly recognizable in nature. This particular association is formed with the intent of considering all the legal attributes that are needed to be fulfilled while forming an ‘incorporated association’. Strong approval from the government is required for the formation of such

Review of the literature on risk management

Review of the literature on risk management This chapter reviews the literature on the risk management and corporate governance in the banking sector. Part of the literature also attempts to provide a relationship between the independence and financial knowledge of the board of directors and audit committee, and risk management practices by referring to both empirical and analytical research. 2.1 Risk Management in the banking sector When discussing the challenges faced by financial institutions in managing risk, it is important to have a consistent definition of the term risk. Risk can be defined as the volatility of a corporations market value. Risk management involves the protection of a firms assets and profits. Moreover, not only does it provide profitability but also other advantages like being in line with obedience function toward the rule, increasing the firms reputation and opportunity to attract more customers in building their portfolio of fund resources. Cebenoyan and Strahan (2004) suggest that [à ¢Ã¢â€š ¬Ã‚ ¦] the benefits of advances in risk management in banking may be greater credit availability, rather than reduced risk in the banking system (p.19). This means that banks will have a greater opportunity to increase their productive assets and profit. Only those banks that have efficient risk management system will survive in the market in the long run. They can follow a four-step routine to red uce their risk exposures and achieve their risk management objectives, as shown below. Figure 1-Steps for implementing risk management To properly manage risks, banks must firstly identify and classify the sources from which risk may arise at both transaction and portfolio levels. Risks inherent in lending activities include market risk, liquidity risk, credit risk and operational risk. Market risk is the risk resulting from adverse movements in the level of market prices of equities, currencies, interest rate instruments and commodities. Banks are always facing the risk of losses in on and off-balance-sheet positions arising from undesirable market movements. Banks are inherently vulnerable to liquidity risk due to their fundamental role of transforming of short-term deposits into long-term loans. The FSA has defined liquidity risk as: The risk that a firm, though solvent, either does not have sufficient financial resources available to enable it to meet its obligations as they fall due, or can secure them only at an excessive cost. Another risk that banks face is credit risk. It is the risk that can be incurred if the counterparty fails to meet its obligations in a timely manner. Loans are the most palpable source of credit risk in many of the banking systems; however, other sources of this risk originate through other activities of banks such as acceptances, trade financing, interbank transactions, financial futures, foreign exchange transactions, swaps, equities, options, bonds, and in the extension of commitments and guarantees, and the settlement of transactions. Operational risk, as its name suggests, is a risk arising from execution of a companys business functions. The Basel Committee has defined operational risk as: the risk of losses resulting from inadequate or failed internal processes, people and systems, or external events, such as the failure of computer systems or error and fraud on the part of staff. Apart from those risks mentioned above, the Federal Reserve System has also recognised two other risks: legal risk and reputational risk. Legal risk is the risk of loss caused by sanctions or penalties originating from court disputes due to breach of contract and legal obligation. Another legal risk relates to regulatory risk, i.e., the risk of loss resulting from sanctions and penalties pronounced by a regulatory body. Reputational risk may be defined as the risk of loss caused by a negative impact on the market positioning of the bank. It can be seen as the blowing up of an initial loss, arising from credit, market, liquidity or operational risks. However, banks hardly pay attention to these categories of risks. Once identified, the risks should be evaluated to determine their impact on the companys profitability and capital. This entails measuring them by using various techniques ranging from simple to sophisticated ones. For example, market risk can be measured by using Value at Risk. This stage also calls for estimating three dimensions of each exposure: the potential frequency of losses that exposures have produced or may produce, the potential impact on the organisation if a loss should occur and the potential variation in losses that will occur during the exposure period. Accurate and timely measurement of risk is necessary because with these types of data the risk manager can determine which exposes are most serious and which deserve the most immediate attention. After measuring risk, bank managers should establish and communicate risk limits through policies, standards, and procedures that define responsibility and authority. These limits should serve as a means to control the risks associated with the banking institutions activities. There is a variety of mitigating tools that banks may employ to minimise the loss exposures. These tools may be diversification, securitization and even derivative such as withdrawal option, Bermudan-style return put option, return swap, return swaption and liquidity option. The final step involves appraising the operation of the program regularly to be sure that it is achieving planned results. It helps the managers to evaluate the wisdom of their decision-making. To efficiently monitor risk, all material risk exposures should be identified and measured again. To facilitate this procedure, banks should put in place an effective management information system (MIS) that will provide directors and senior managers with timely reports on the operating performance, financial condition and risk exposure of the firm. If corrective action is indicated at this stage, the first three steps should be repeated. 2.1 Corporate Governance in the banking sector Corporate governance is a term that is now universally invoked wherever business and finance are discussed. Its purpose is to coordinate a conflict of interest among all parties relationship within the company and to develop a system that can reduce or eliminate the agency problems arising from the separation of ownership and control (OECD, 1997). Agency problem occurs when the agents of an organization (e.g. management) use their power to satisfy their own interests rather than those of the principals (e.g. shareholders). It may also refer to simple disagreement between agents and principals. For example, the board of directors may disagree with shareholders on how to best invest the companys assets, especially when the board of directors wishes to invest in securities that would favour their interests. Not merely does the term corporate governance carries different interpretations, its analysis also involves diverse disciplines and approaches. One of the most quoted definitions of corporate governance is the one given by Shleifer and Vishny (1997): corporate governance deals with the ways in which suppliers of finance to corporations assures themselves of getting a return on their investment. The Cadbury Report, however, defined corporate governance as the system by which companies are directed and controlled (para 2.5). Additionally, it recognised that a system of good governance allows the board of directors to be free to drive their companies forward, but exercise that freedom within a framework of effective accountability (para 1.1). The Hampel Report, whilst accepting the Cadbury definition of corporate governance, also noted that the single overriding objective of companies is the preservation and the greatest practical enhancement over time of their shareholders investment ( para 1.16). In a similar vein, Charkham (1994) identified two basic principles of corporate governance: That management must be able to drive the enterprise forward free from undue constraint caused by government interference, fear of litigation, or fear of displacement. That this freedom- to use managerial power or patronage- must be exercised with a framework of effective accountability. Nominal accountability is not enough. In the banking sector, however, corporate governance differs greatly with other economic sectors in terms of broader extent of claimants the banks assets and funds. In manufacturing corporations, the issue is to maximise the shareholders value but in banking, the risk involved for depositors assumes greater importance due to the fact that almost every bit of banks investment are financed by the depositors funds. If it goes bankrupt, it will be depositors savings that the bank will lose. Indeed, Macey and OHara (2001) states that a broader view of corporate governance should be adopted in the case of banking institutions, arguing that because of the peculiar contractual form of banking, corporate governance mechanisms for banks should encapsulate depositors as well as shareholders. Arun and Turner (2003) also support this argument. Furthermore, the involvement of government in the banking sector is discernibly higher compared to other economic sectors due to the larger interests of th e public (Caprio and Levine, 2002; Levine, 2004). Rational depositors require some form of guarantee before depositing their wealth in banks. Yet, it is relatively difficult for banks to provide these guarantees to them because communicating the value of a banks loan portfolio is quite impossible and very costly to reveal. As a consequence of this asymmetric information problem, bank managers can have an incentive to invest in riskier assets than they promised they would ex ante. To assure depositors that they will not expropriate them, banks could make investments in brand-name or reputational capital (Klein, 1974; Gorton, 1994; Demetz et al, 1996; Bhattacharya et al, 1998), but these schemes give depositors little confidence, especially when contracts have a finite nature and discount rates are sufficiently high (Hickson and Turner, 2003). The opaqueness of banks also makes it very costly for depositors to constrain managerial discretion through debt covenants (Capiro and Levine, 2002, p.2). As such, government interventions provide the lacking assurance to economic agents in the form of deposit insurance. Nevertheless, although the government provides deposit insurance, bank managers still have an incentive to opportunistically increase their risk-taking, but now it is mainly at the governments expense. Apart from supporting the argument that a broader approach to corporate governance should be adapted to banking institutions, Arun and Turner (2003) also argue that government intervention do restrain the behaviour of bank management. The Bank for International Settlements (BIS) has defined the governance in banks as the methods and approaches used to manage banks through the board of directors and senior management which determine how to put the banks objectives, operation and protect the interests of shareholders and stakeholders with a commitment to act in accordance with existing laws and regulations and to achieve the protection of the interests of depositors. The Table 1 below shows the general principles concerning corporate governance issued by the Basel Committee specifically for bank boards and senior management. Principle 1 Board members should be qualified for their positions, have a clear understanding of their role in corporate governance and be able to exercise sound judgment about the affairs of the bank. Principle 2 The board of directors should approve and oversee the banks strategic objectives and corporate values that are communicated throughout the banking organisation. Principle 3 The board of directors should set and enforce clear lines of responsibility and accountability throughout the organisation. Principle 4 The board should ensure that there is appropriate oversight by senior management consistent with board policy. Principle 5 The board and senior management should effectively utilise the work conducted by the internal audit function, external auditors, and internal control functions. Principle 6 The board should ensure that compensation policies and practices are consistent with the banks corporate culture, long-term objectives and strategy, and control environment. Principle 7 The bank should be governed in a transparent manner. Principle 8 The board and senior management should understand the banks operational structure, including where the bank operates in jurisdictions, or through structures, that impede transparency (i.e. know-your-structure). Table 1- Principles of corporate governance for bank boards and senior management 2.2 Corporate Governance Mechanism According to agency theory, the corporate governance mechanisms reduce the agency problem between investors and management (Jensen and Meckling, 1976; Gillan, 2006). Traditionally, these mechanisms can be classified as internal and external. Llewellyn and Sinha, (2000) states that internal corporate governance is about mechanism for the accountability, monitoring, and control of a firms management with respect to the use of resources and risk taking. Its main mechanisms are the board of directors, the ownership structure of the firm and the internal control system (Gillan, 2006). Whereas, external corporate governance controls encompass the controls external stakeholders exercise over the organisation and its primary external mechanisms are the takeover market and the legal/regulatory system. However for the purpose of this paper, we will mainly focus on some internal corporate governance mechanism such as the board of directors, more precisely on its independence and financial knowledge. Corporate governance best practices have also stressed in particular the key role played by the audit committee in reviewing a firms internal control system. Internal control systems contribute to the protection of shareholders interests by providing reasonable assurance on the reliability of financial reporting, effectiveness of operations and compliance with laws and regulations (COSO, 1994; 2004). As such, we will also draw some attention on the audit committee. 2.3 The boards independence The popular media as well as corporate governance experts have characterised boards largely as rubber stamps for management. They are the link between the shareholders of the firm and the managers entrusted with undertaking the day-to-day operations of the organisation (Monks and Minow, 1995; Forbes and Milliken, 1999). As stated in principle 4 above, bank boards should properly supervise the work of managers. Which type of directors can perform better this duty than independent director? In fact, such directors can bring additional experience as well as clarity of thought to deliberations independent of views of management. Moreover, since their careers are not tied to the firms CEO, outside directors are believed to be more powerful in keeping efficiently the firms top management (Fama, 1980; Fama and Jensen, 1983) and so could be associated with better performance. Some papers do support this theory. Baysinger and Butler (1985), being among the first studies, find that the relative independence of boards has a positive effect on the firms average return on equity by comparing 266 major US businesses over a ten-years period. Kesner (1987); Weisbach (1988); Rosenstein and Wyatt (1990); Peace and Zahra (1992); Ezzamel and Watson (1993); MacAvoy and Millstein (1999); Brown and Caylor (2004) and Ho (2005) also show that shareholder returns are enhanced by having a greater proportion of outside directors on the board. Research by Brickley, Coles, and Terry (1994) shows significantly higher returns to firms announcing poison pill  [1]  when outside directors dominate the board. Other studies supporting the benefit of the boards independence are Dechow and Sloan (1996); Beasely (1996) and Klein (2002) who state that as outside membership on the board increases the likelihood of financial statement fraud decreases. There is also Black et al. (2006) who reports that firms with 50% outside directors have approximately 40% higher share price by studying 515 Korean firms. And more recently, Staikouras C. K., Staikouras P. K. and Agoraki M. K. (2006) find that the percentage of independent directors is positively related with performance measured by Tobins Q on a sample of European banks. On the other hand, others find no convincing evidence that the level of outside directors on the board do add value to corporate performance. For instance, Fosberg (1989) finds that firms whose board is composed of a majority of outside directors do not have a higher performance as measured by the firms ROE or sales. Similarly, Hermalin and Weisbach (1991) find that non-executive directors have no impact on corporate performance in their sample of 142 NYSE firms. Pearce (1983) also find no relationship, as too Changanti et al. (1985) in their study of board composition and bankruptcy. The lack of relation between these two components has also been confirmed by Klein (1998), Bhagat and Black (2002) and Hayes, Mehran and Scott (2004). Other scholars refuting the effectiveness of outside directors on the board are Subrahmanyam et al. (1997) and Harford (2000) for the acquisition transactions, Core et al. (1999) for CEO compensation and Agrawal and Chadha (2005) for earnings restatements . It is normally the board of directors which overviews and approves the risk management policies. But, few papers have tried to link its independence to the firms risk management practices and hedging. By analysing a sample of bank holding companies, Whidbee and Wohar (1999) find that the likelihood of using derivatives seem to increase with the presence of external directors on the board but only when insiders hold a large proportion of the firms shares. Borokhovich et al. (2004) demonstrate that firms most active in hedging risk, especially when making use of interest rate derivatives usage, are those whose boards are dominated by external directors. Conversely, Dionne and Triki (2004); Mardsen and Prevost (2005) point out that outside directors has no impact on the firms risk management policy. Given the mixed empirical findings, it is quite difficult to assert whether the board independence contribute to corporate performance and the effectiveness of risk management. Although Fields and Keys (2003) assert that there is overwhelming support for independent directors providing superior monitoring and advisory functions to the firm, a unique and clear sign concerning the effect of the boards independence on any decision including the risk management one could not be predicted. 2.4 The financial knowledge of the board To adequately perform their supervision role, the board of directors must have financial knowledge  [2]  . Indeed, when board members are generalists and lack the technical financial knowledge to understand the complicated reports presented to them, they could vote for motions that increase the risks facing of the firm to a large extent. The company may collapse in this way and therefore hinder the shareholders interest. Because of the banks dominant position in the economy; they should possess some financial expertise directors on its board so as to make better decisions that will not lead the firm to go bankrupt. However, given its importance, the research on the value of the boards financial knowledge is quite scarce. At times, reports recognising the benefits of the boards independence also recommend financial literacy/expertise for directors in monitoring the firms performance. In fact, Booth and Deli (1999) and Guner, Malmendier and Tate (2004) suggest that commercial bankers on boards provide the financial skill needed to enable the business to contract more debt. Thus, this states that financial directors do add value to the firm. There is also Agrawal and Chadha (2005) who discover that there is lower earnings restatement in firms whose boards have accounting or financially knowledgeable independent directors. However, Rosenstein and Wyatt (1990) provide evidence that positive abnormal returns associated with the addition of an outsider to the board are higher when the latter is an officer of a financial firm. Later on, Lee, Rosenstein and Wyatt (1999) do come to the same conclusion. However, they were unable to make any statistically difference among the reaction of the three categories of financial directors they consider: commercial bankers, insurance company officers and investment bankers. To the best of our knowledge, researches on the boards financial knowledge have only been related with the firms performance and not specifically on its impact on risk management practices. As mentioned earlier in this study, the board of directors is usually responsible for the firms risk management policies. In other words, risk management is at the core of any board members charter. Financially knowledgeable directors will obviously make better decisions on risk management practices since they will have the technical background to understand the sophisticated tools involved in risk management transactions. As such, firms whose boards are composed of financially knowledgeable directors engage more actively in risk management. 2.5 The audit committee The audit committee is intended to provide a link between the board and the auditor independent of the companys management, which is responsible for the accounting system (IOD, 1995). The chief objectives of an audit committee are to improve the quality of financial reporting, to reduce the potential authority for the non-executive director, to improve the channel of communication with the external auditor and, perhaps most importantly, to review the adequacy of the companys financial control systems. Tricker (1984) defines audit committee as being an important vehicle for ensuring the supervision and accountability at board level. As such, audit committees are very important in banking to safeguard the shareholders interest as well as the public trust. Just as for the board of directors, independence is also considered important for an audit committee because outside directors can exercise their voice and be seen to make a valuable contribution since they are free of any influence arising from the firms CEO. Thus, the reported empirical evidence supports this argument. Klein (2002) shows that independent audit committees reduce the likelihood of earnings management, thus improving transparency. In addition, Abbott, Park and Parker (2002) argue that firms with audit committees comprising entirely of independent directors are less likely to have fraudulent or misleading reporting. Ho (2005) states that there is a strong positive link between independent audit committee and corporate competitiveness and also with return on equity after analyzing the international companies from 1997to 1999. Brown and Caylor (2004) do provide evidence that audit committees comprising of independent directors are positively related to dividend but not t o operating performance. On the other hand, some authors find a negative relationship or simply no relation at all between independent audit committee and the firms performance. Hayes, Mehran and Scott (2004) prove that the firms performance measured by the market to book ratio is not affected by the proportion of outside directors sitting on the audit committee. Agrawal and Chadha (2005) do come to the same conclusion by indicating that independent audit committee members are unrelated to earnings restatement. There are also Beasley (1996) who finds no apparent correlation between audit committees composition and financial statement fraud, and Klein (1998) who reports no relation between share prices and the audit committees composition. Yet, Carcello and Neal (2000) report a negative relationship between the probability of receiving a going-concern report and the proportion of outsiders on the audit committee. In addition to independence, the accounting and financial expertise of members of the audit committee has also received widespread attention from the media and regulators  [3]  . An audit committee with such characteristics is expected to provide effective monitoring as it possesses the skills needed to understand what is going on in the organisation. Interestingly, Agrawal and Chadha (2005) show that firms whose audit committees have an outside director with accounting background or financial knowledge are less likely to report earnings restatement while Abbott, Parker and Peters (2002) discover that the absence of a financially competent director on the audit committee is highly associated with an increased in financial misstatement and financial fraud. Xie, Davidson, and DaDalt (2003) find that the presence of investment bankers on the audit committee decreases discretionary accruals in a firm. Davidson et al. (2004) and Defond, Hann and Hu (2004) show that the market has a po sitive reaction following the announcement of directors with accounting /auditing experience on audit committees board. The audit committee is also responsible for evaluating the risk exposures and the measures taken to monitor and control these exposures. To our knowledge no paper has tried to link audit committees composition with risk management practices. Because of the mixed and conflicting argument on independence, it is quite difficult for us to attest whether audit committees independence encourage more corporate hedging. Furthermore, risk evaluation and risk management tools are quite difficult to use and thus understanding them requires a good grasp of mathematics and statistics. As such, we expect firms whose audit committees members are qualified as accounting/financial expert to engage more actively in risk management practices. Besides independence and accounting/financial knowledge, the Cadbury Report has insisted that all listed companies should have an audit committee comprising of at least three members. This is to urge firms to devote significant director resources to their audit committees so that audit committees monitor the firms management more efficiently. However, several studies support the idea that larger boards can be dysfunctional since they may be plagued with free rider, communication problem and monitoring problems  [4]  . Therefore, as long as the increase in the audit committees size does not pose these types of problems, firms complying with this requirement are expected to report a higher hedging ratio. Often, corporations, especially financial ones, create another committee named risk monitoring committees. This type of committee is often responsible of the risk monitoring of the firm. However, this does not imply that audit committee is no longer responsible for evaluating and managing risks. It must still discuss and evaluate risk management processes. In other words, the audit committee is there to review risk management processes proposed by the risk management committee. As such, we assume that the same characteristics as the audit committee should be applied to this type of committee to fulfil their duties well.

Story of a Different Hour :: Essays Papers

The Story of a Different Hour Mrs. Millard just found out that Mr. Millard was killed in a tragic train wreck. Because of a heart condition, Josephine (Mrs. Millard's sister) was hesitant to tell her what happened. Richard (Mr. Millard's good friend) was also there to comfort the newly widowed Mrs. Millard. Josephine was concerned for her sister. To everyone?s surprise Mrs. Millard was rather joyful rather than devastated of the tragic news about her husband. ?Free! Free! Free!?, ?Free! Body and free soul?. Everyone was a bit confused, why Louise was jumping for joy when she just received that her husband passed away few minutes ago. Something smells fishy in this story and who really is Richard? Is he a good friend of Mr. Millard or he is a lover of Louise?.. Well, we will modify some sentences in this story. We all knew what happened in the end. Mrs. Millard was having the time of her life because she just found out that her husband just died. Was Louise happy because of the hefty insurance money that her husband left her? We can?t tell. So as the door was being opened by a latchkey everyone ran through the long stair case and found ?Brently Millard who entered, a little travel-stained, composedly carrying his grip-sack and umbrella?, then Louise was so flabbergasted that she had a heart attack and eventually died. In my opinion the story could use a better ending than Louise dying at the end of the story. If only Chopin talked to me about this story before she published it in 1894 it would probably be a little different. We left of where before Brently opened the door. After Brently died, Louise was alone in her huge plantation. She asked Josephine to move in with her because she can?t bear to be alone any longer. One day Richard dropped by to check on Louise and to drop the title of the house, Richard is a prominent lawyer nowadays. Richard stayed for supper, and Louise told him ?

Jewish, Early Christian, Byzantine and Islamic Art

Teri Wilson March 1, 2010 Professor Hollinger Module 5 JEWISH, EARLY CHRISTIAN, BYZANTINE AND ISLAMIC ART Every religion has its own approach to art and architecture. An assessment between different traditions can offer an illuminating insight into the varying religious outlooks and theologies. Architecture, as well as art, is influenced by a number of forces in society, in the environment, in the psychology of the people who produce it, and in different institutions. It is an expression of inner feelings and beliefs and so naturally is influenced by religion in many societies. Religious architecture is created to experience the sacred, to provide a place into which spiritual energies flow and reflect a sense of the divine. Some religions speak of art directly or have tenets which influence what can and cannot be depicted in art. The scriptures of these religions are the theological basis and shape the way people in express themselves, and this includes how they express themselves through art and architecture. The architecture in Judaism, Christianity, Byzantine, and Islam has important similarities and differences that are a result of the teachings of these faiths. In the first centuries C. E. , Jewish communities could be found in every corner of the Roman Empire. The archaeological remnants and literary attestations of more than 150 synagogues throughout the empire make clear that Jews were integral to the urban landscape of late antiquity, well beyond the borders of Roman Palestine. Asia Minor, in particular, was one of the most prosperous, Jewish communities (Stokstad, 164) The third-century synagogue in the Roman garrison town of Dura-Europos, Syria, like the Christian meeting house and the shrine devoted to the Persian god Mithras that stood just yards away, was adorned with sumptuous painting. The Wall of Torah Niche had splendid murals with narrative scenes from the Bible covered the synagogue's walls; painted tiles of zodiacal symbols ornamented its ceiling (Stokstad, 165). Plaques with dedicatory inscriptions give some indication of the individuals and families who funded the building of such synagogues. In building their monuments, Jews often embraced the Greco-Roman practice of paving the floor with elaborate mosaics, many of which demonstrate an understanding of the second commandment injunction against image making that may surprise today's viewer. In early Byzantine synagogues such as Hamman Lif in North Africa and Beth Alpha, Hammath Tiberias, and Sepphoris in Israel, specifically Jewish symbols—shofarot (ram's horns), menorot (branched lamps), and Torah shrines—might appear alongside pomegranates, birds, lions, and fountains (metmuseum. rg). Zodiac wheels with human figures also find a prominent place in the pavements of several synagogues, dated from the fourth to the sixth centuries, as do scenes drawn from the Bible or allegorized images of the River Nile. After the destruction of the Second Temple by Roman emperor Titus in 70 C. E—an event commemorated on the Arch of Titus in Rome and in Jewish liturgy—images of the Temple's furnishings, especia lly the celebrated gold menorah, or seven-branched lamp, became emblematic of Jewish religion. Marble sarcophagi favored by wealthy Romans were adapted for Jewish use by incorporating a stylized relief image of a menorah (metmuseum. org). In the catacombs of Rome, Jews placed gold glass disks representing the menorah and Torah arks at their tombs, as well as symbols of the festival of Sukkot just as Christians placed glass disks showing saints All these images reference the destroyed Temple and invoke a hoped-for messianic age when the Temple would be restored. So wide-ranging are the contexts for the menorot that it is clear the symbol frequently served merely to distinguish a Jewish monument or a Jewish patron. Seven-branched candlesticks appear in Roman and Byzantine art: in graffiti in the catacombs, inscribed on plaques, as a motif on seals, as decoration on glass bottles and on clay lamps all further testimony to the integration of Jews into late Roman and early Byzantine society (metmuseum. org). With the adoption of Christianity as the official religion, art was able, so to speak, to come above ground in the old pagan city of Rome, and painting, instead of being restricted to the decoration of the walls of the Catacombs or of small chambers and chapels, came into use on a large scale in the new churches that were at once set up. At the same time patronage moved from the hands of the poorer classes to the richer, and artists of outstanding quality came to be employed as well as those of obscurer character, who would work for small fees (www. religion-online. org). To wall painting was added the more luxurious art of mosaic; numerous sculptures were done, and minor objects, often in expensive materials, were in addition produced in the service of the Church, so that art production became at the same time both more extensive and more luxurious (www. religion-online. org ). A great deal of the work that was done at this time has of course perished, more especially that in fragile materials, such as textiles or paintings on panels, but a few mosaics of the fourth century and a good many more of the fifth survive in Rome, and there is quite a lot of sculpture, both on a large scale in stone and on a small in ivory. Something has already been said about the ivories, more especially the Consular diptychs, which necessarily form a part of the general picture, though it is not always easy to be sure of where they were made, as they are in a diversity of styles (www. eligion-online. org). Here we are concerned not so much with these things as with works which are essentially Christian and also undoubtedly Roman, such as the mosaics and wall painting, which are necessarily immovable or stone sculptures on a large scale in a material which was carved on the spot and quarried in the neighborhood. The earliest of the mosaics are those in the church of Sta Constanz a, which was built as an octagonal martyrium or tomb sanctuary between 306 and 337. It was converted into a baptistery in the fifth century, when the lateral apses were added. Only the mosaics on the roofs of the vaulted aisles are of the same date as the original building. This roof is divided into eight compartments, and there are different designs in each, though only those on the three sets on each side survive; they are in pairs, balancing one another on each side. These mosaics, which consist in the main of scrolls and other diverse motifs shown in isolation against a white ground, are very classical in character; they are virtually floor mosaics transferred to the roof. The mosaics which decorated the central dome have not survived, though there is a sixteenth century painting of them in the Escorial. They included scenes from the Old and New Testaments, bordered below by a river and separated one from another by caryatid figures, not unlike the dividing panels in the Baptistery of the Orthodox at Ravenna. In the apses which terminate the sides of the octagon to the north and south are figural compositions of a rather different character, depicting the â€Å"Traditio Legis†, where Christ conveys future responsibility for preaching on one side to Peter and on the other to Paul. Our Lord stands in the centre of each apse, with the Apostle before Him, against a background of trees (catholic-resources. org). The mosaics are probably to be assigned to the time of the building's conversion for use as a baptistery in the fifth century. They have, however, been very much restored at subsequent dates, and to-day appear somewhat clumsy (catholic-resources. org). Those in the dome probably belonged to the same date as those in the vaults of the octagon. Another similar church of this kind is the Church of Santa Sabrina, a fifth-century basilica in Rome. The basilica, constructed by Bishop Peter of IIyria between 422 and 432 BC, is another must see (Stokstad, 170). Santa Sabrina, exterior is typical of the time, which is severe brickwork. In contrast, the interior displays a wealth of marble veneer and 24 fluted marble columns with Corinthian capitals acquired from a 2nd century building (Stokstad, 170). Christianity subject matter is the prime source of art up to the modern era. We find religious art in all styles and the major artists used Christianity in most of their paintings and built structures for Christian churches. In conclusion, it can be seen that art is not just one thing. It is a combination of devices which have taken thousands of years to grow and develop, through different religions, and through time. I personally feel that art is not something that we can define or even begin to describe. Art is to much a part of life to single out on its own or define, especially, religious art. Trying to write a summary on a general view of what art is is virtually impossible. Art, inside of every person is seen as something different and unique making the definition of art diversified for every person. Works Cited 1. www. metmuseum. org 2. www. catholic-resources. org 3. www. religion-online. org 4. Our book, â€Å"Art: A Brief History† by: Marilyn Stokstad

Om Heizer Om10 Ism 04

Chapter FORECASTING Discussion Questions 1.? Qualitative models incorporate subjective factors into the forecasting model. Qualitative models are useful when subjective factors are important. When quantitative data are difficult to obtain, qualitative models may be appropriate. 2.? Approaches are qualitative and quantitative. Qualitative is relatively subjective; quantitative uses numeric models. 3.? Short-range (under 3 months), medium-range (3 months to 3 years), and long-range (over 3 years). 4.? The steps that should be used to develop a forecasting system are: (a)?Determine the purpose and use of the forecast (b)? Select the item or quantities that are to be forecasted (c)? Determine the time horizon of the forecast (d)? Select the type of forecasting model to be used (e)? Gather the necessary data (f)? Validate the forecasting model (g)? Make the forecast (h)? Implement and evaluate the results 5.? Any three of: sales planning, production planning and budgeting, cash budgeting, analyzing various operating plans. 6.? There is no mechanism for growth in these models; they are built exclusively from historical demand values. Such methods will always lag trends. .? Exponential smoothing is a weighted moving average where all previous values are weighted with a set of weights that decline exponentially. 8.? MAD, MSE, and MAPE are common measures of forecast accuracy. To find the more accurate forecasting model, forecast with each tool for several periods where the demand outcome is known, and calculate MSE, MAPE, or MAD for each. The smaller error indicates the better forecast. 9.? The Delphi technique involves: (a)? Assembling a group of experts in such a manner as to preclude direct communication between identifiable members of the group (b)?Assembling the responses of each expert to the questions or problems of interest (c)? Summarizing these responses (d)? Providing each expert with the summary of all responses (e)? Asking each expert to study the summary of the responses and respond again to the questions or problems of interest. (f)? Repeating steps (b) through (e) several times as necessary to obtain convergence in responses. If convergence has not been obtained by the end of the fourth cycle, the responses at that time should probably be accepted and the process terminated—little additional convergence is likely if the process is continued. 0.? A time series model predicts on the basis of the assumption that the future is a function of the past, whereas an associative model incorporates into the model the variables of factors that might influence the quantity being forecast. 11.? A time series is a sequence of evenly spaced data points with the four components of trend, seasonality, cyclical, and random variation. 12.? When the smoothing constant, (, is large (close to 1. 0), more weight is given to recent data; when ( is low (close to 0. 0), more weight is given to past data. 13.? Seasonal patterns are of fixed duration a nd repeat regularly.Cycles vary in length and regularity. Seasonal indices allow â€Å"generic† forecasts to be made specific to the month, week, etc. , of the application. 14.? Exponential smoothing weighs all previous values with a set of weights that decline exponentially. It can place a full weight on the most recent period (with an alpha of 1. 0). This, in effect, is the naive approach, which places all its emphasis on last period’s actual demand. 15.? Adaptive forecasting refers to computer monitoring of tracking signals and self-adjustment if a signal passes its present limit. 16.?Tracking signals alert the user of a forecasting tool to periods in which the forecast was in significant error. 17.? The correlation coefficient measures the degree to which the independent and dependent variables move together. A negative value would mean that as X increases, Y tends to fall. The variables move together, but move in opposite directions. 18.? Independent variable (x) is said to explain variations in the dependent variable (y). 19.? Nearly every industry has seasonality. The seasonality must be filtered out for good medium-range planning (of production and inventory) and performance evaluation. 20.? There are many examples.Demand 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 becomes more difficult to make 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. Here are a few points to consider:  ¦ No one likes a system they don’t understand, and most college presidents would feel uncomfortable with this one. It does offer the advantage of depoliticizing the funds al- location if used wisely and fairly.But to do so means all parties must have 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 MAD) or could be based on input from experts on the board as well as the college.  ¦ Abuse of the system is tied to assigning alphas based on what results they yield, rather than what alphas make the most sense.  ¦ Regression is open to abuse as well. Models can use many years of data yielding one result or few years yielding a totally different forecast.Selection of associative variables can have a major impact on results as well. Active Model Exercises* ACTIVE MODEL 4. 1: Moving Averages 1.? What does the graph look like when n = 1? The forecast graph mirrors the data graph but one period later. 2.? What happens to the graph as the number of periods in the moving average increases? The forecast graph becomes shorter and smoother. 3.? What value for n minimizes the MAD for this data? n = 1 (a naive forecast) ACTIVE MODEL 4. 2: Exponential Smoothing 1.? Wha t happens to the graph when alpha equals zero? The graph is a straight line.The forecast is the same in each period. 2.? What happens to the graph when alpha equals one? The forecast follows the same pattern as the demand (except for the first forecast) but is offset by one period. This is a naive forecast. 3.? Generalize what happens to a forecast as alpha increases. As alpha increases the forecast is more sensitive to changes 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 absolute deviation (MAD) minimized? alpha = . 16 ACTIVE MODEL 4. 3: Exponential Smoothing with Trend Adjustment .? Scroll through different values for alpha and beta. Which smoothing constant appears to have the greater effect on the graph? alpha 2.? With beta set to zero, find the best alpha and observe the MAD. Now find the best beta. Observe the MAD. Does the addition of a trend improve the forecast? alpha = . 11, MAD = 2. 59; beta above . 6 changes the MAD (by a little) to 2. 54. ACTIVE MODEL 4. 4: Trend Projections 1.? What is the annual trend in the data? 10. 54 2.? Use the scrollbars for the slope and intercept to determine the values that minimize the MAD. Are these the same values that regression yields?No, they are not the same values. For example, an intercept of 57. 81 with a slope of 9. 44 yields a MAD of 7. 17. End-of-Chapter Problems [pic] (b) | | |Weighted | |Week of |Pints Used |Moving Average | |August 31 |360 | | |September 7 |389 |381 ( . 1 = ? 38. 1 | |September 14 |410 |368 ( . 3 = 110. 4 | |September 21 |381 |374 ( . 6 = 224. 4 | |September 28 |368 |372. | |October 5 |374 | | | |Forecast 372. 9 | | (c) | | | |Forecasting | Error | | |Week of |Pints |Forecast |Error |( . 20 |Forecast| |August 31 |360 |360 |0 |0 |360 | |September 7 |389 |360 |29 |5. 8 |365. 8 | |September 14 |410 |365. 8 |44. 2 |8. 84 |374. 64 | |September 21 |381 |374. 64 |6. 36 |1. 272 |375. 12 | |Se ptember 28 |368 |375. 912 |–7. 912 |–1. 5824 |374. 3296| |October 5 |374 |374. 3296 |–. 3296 |–. 06592 |374. 2636| The forecast is 374. 26. (d)? The three-year moving average appears to give better results. [pic] [pic] Naive tracks the ups and downs best but lags the data by one period. Exponential smoothing is probably better because it smoothes the data and does not have as much variation. TEACHING NOTE: Notice how well exponential smoothing forecasts the naive. [pic] (c)? The banking industry has a great deal of seasonality in its processing requirements [pic] b) | | |Two-Year | | | |Year |Mileage |Moving Average |Error ||Error| | |1 |3,000 | | | | | |2 |4,000 | | | | | |3 |3,400 |3,500 |–100 | |100 | |4 |3,800 |3,700 |100 | |100 | |5 |3,700 |3,600 |100 | |100 | | | |Totals| |100 | | |300 | | [pic] 4. 5? (c)? Weighted 2 year M. A. ith . 6 weight for most recent year. |Year |Mileage |Forecast |Error ||Error| | |1 |3,000 | | | | |2 |4,000 | | | | |3 |3,400 |3,600 |–200 |200 | |4 |3,800 |3,640 |160 |160 | |5 |3,700 |3,640 |60 |60 | | | | | | | 420 | | Forecast for year 6 is 3,740 miles. [pic] 4. 5? (d) | | |Forecast |Error ( |New | |Year |Mileage |Forecast |Error |( = . 50 |Forecast | |1 |3,000 |3,000 | ?0 | 0 |3,000 | |2 |4,000 |3,000 |1,000 |500 |3,500 | |3 |3,400 |3,500 | –100 |–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 Sales |X Period |X2 |XY | |January |20 |1 |1 |20 | |February |21 |2 |4 |42 | |March |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 |144 | |September |20 |9 |81 |180 | |October |20 |10 |100 |200 | |November |21 |11 |121 |231 | |December |23 |12 |144 |276 | |Sum | 18 |78 |650 |1,474 | |Average |? 18. 2 | 6. 5 | | | (a) [pic] (b)? [i]? NaiveThe coming January = December = 23 [ii]? 3-month moving (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]? Trend? [pic] [pic] Forecast = 15. 73? +?. 38(13) = 20. 67, where next January is the 13th month. (c)? Only trend provides an equation 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, there 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, then the forecast becomes 56. 3, or 56 patients. [pic] [pic] |Temperature |2 day M. A. | |Error||(Error)2| Absolute |% 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. 0 0| 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 about the same. [pic] 4. 12? t |Day |Actual |Forecast | | | | |Demand |Demand | | |1 |Monday |88 |88 | | |2 |Tuesday |72 |88 | | |3 |Wednesday |68 |84 | | |4 |Thursday |48 |80 | | |5 |Friday | |72 |( Answer | Ft = Ft–1 + ((At–1 – Ft–1) Let ( = . 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 |Absolute | |Year |Demand |Smoothing ( = 0. |Deviation | |1 |45 |41 |4. 0 | |2 |50 |41. 0 + 0. 6(45–41) = 43. 4 |6. 6 | |3 |52 |43. 4 + 0. 6(50–43. 4) = 47. 4 |4. 6 | |4 |56 |47. 4 + 0. 6(52–47. 4) = 50. 2 |5. 8 | |5 |58 |50. 2 + 0. 6(56–50. 2) = 53. 7 |4. 3 | |6 |? |53. 7 + 0. 6(58–53. 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(45–41) = 44. 6 |5. 4 | |3 |52 |44. 6 + 0. 9(50–44. 6 ) = 49. 5 |2. 5 | |4 |56 |49. 5 + 0. 9(52–49. 5) = 51. 8 |4. 2 | |5 |58 |51. 8 + 0. 9(56–51. 8) = 55. 6 |2. 4 | |6 |? |55. 6 + 0. 9(58–55. 6) = 57. 8 | | ( = 18. 5 MAD = 3. 7 (b)? 3-year moving average: | | |Three-Year |Absolute | |Year |Demand |Moving 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)? Trend projection: | | | |Absolute | |Year |Demand |Trend 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 | Then: (X = 15, (Y = 261, (XY = 815, (X2 = 55, [pic]= 3, [pic]= 52. 2 Therefore: [pic] (d)? Comparing the results of the forecasting methodologies for parts (a), (b), and (c). |Forecast Methodology |MAD | |Exponential smoothing, ( = 0. |5. 06 | |Exponential smoothing, ( = 0. 9 |3. 7 | |3-year moving average |6. 2 | |Trend projection |0. 64 | Based 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 Method 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 |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 2005–2009 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 = Ft–1 + ((At–1 – Ft–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 –2 = –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 | | |Unadjusted | |Adjusted | | | |Month |Income |Forecast |Trend |Forecast ||Error||Error2 | |February |70. 0 | 65. 0 | 0. 0 | 65 |? 5. 0 |? 25. 0 | |March |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. Note that all numbers are rounded. Note: 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 March is the February actual of 83, etc. |(a) | |Actual |Forecast ||Error| ||% Error| | | |March |101 |120 |19 |100 (19/101) = 18. 81% | | |April |? 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 manager’s technique is 14. 5, while 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-squares 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 following figure shows both the data and the resulting equation: [pic] (c) If there are nine performances by Stone Temple Pilots, the estimated sales are: (d) R = . 82 is the correlation 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 |180 | 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) = 105. 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 | |Winter |350 |300 |325. |250 |1. 30 |390 | |Spring |150 |165 |157. 5 |250 |0. 63 |189 | |Summer |300 |285 |292. 5 |250 |1. 17 |351 | 4. 27 | | Winter |Spring |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 |Quarterly |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 |12 0. 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 next 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 = price, 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. Each guest accounts for an additional $18 in bar sales. |Table for Problem 4. 33 | | | | | |Year |Transistors | | | | | | | |(x) |(y) |xy |x2 |126 + 18x |E rror |Error2 ||% Error| | | |? 1 |140 |? 140 |? 1 |144 |–4 |? 16 |100 (4/140)? = 2. 86% | | |? 2 |160 |? 320 |? 4 |162 |–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 |–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 price is $83,502, but this is the average price for a house 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 determination = (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 traveled ( 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 request is much higher than predicted by the model. This request 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 entertaining customers 4.? other transportation costs—cab, limousine, special 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 suggest that the model is not a particularly 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 |–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 | | | | | | | | | | | | | | | |MAD[pic]5. 00 | Cumulative error = 14. 05; MAD = 5? Tracking = 14. 05/5 ( 2. 82 4. 38? (a)? least squares equation: Y = –0. 158 + 0. 1308X (b)? Y = –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 |–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. 26—this is approximately 7% of the average number of patients and 10% of the minimum number of patients. We also see absolute deviations, for years 5, 6, and 7 in the range 5. 6–7. 3.The comparison of the MAD with the average and minimum number of patients and the comparatively large 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 specific year. 4. 40 | |Crime |Patients | | | | |Year |Rate 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 | |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 |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. One 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 chance to tackle a realistic problem in business, i. e. , not enough data to make a good forecast.As can be seen in the accompanying 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 next 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 = At–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 divide 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) Using 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 |Value |Value |Forecast |Value |Forecast | |t |A(t) |Ft (( = 0. 2) |Err or |Ft (( = 0. 6)|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 note 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 |–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. 105 | |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. 00 0 |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 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 significant improvement. 4. 45 |Month |At |Ft ||At – Ft | |(At – Ft) | |May |100 |100 | 0 | 0 | |June | 80 |104 |24 |–24 | |July |110 | 99 |11 |11 | |August |115 |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, while 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 average (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 = –9. 3495 Sales ( y) = –9. 349 + 0. 1121 (Contracts) (b) [pic] 4. 49? (a) |Method ( Exponential Smoothing | | | |0. 6 = ( | | | |Year |Deposits (Y) |Forecast ||E rror| |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. 0 0 |74. 5434 | 19. 4566 | 378. 561 | |TOTALS | |787. 30 | | | |150. 3 | | |1,513. 22 | |AVERAGE | 17. 8932 | | 3. 416 | 34. 39 | | | | |(MAD) |(MSE) | |Next period forecast = 86. 2173 |Standard error = 6. 07519 | Method ( Linear Regression (Trend Analysis) | |Year |Period (X) |Deposits (Y) |Forecast |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. 24 427 |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 | 4 2 |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–Simple Regression on GSP | | |a |b | | | | |–17. 636 |13. 936 | | | | |Coefficients: |GSP |Deposits | | | | |Year |(X) |(Y) |Forecast ||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. 2 6 |–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 |? 6 92. 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 |? 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) |? (MS E) | Given that one wishes to develop a five-year forecast, trend analysis is the appropriate choice. Measures of error and goodness-of-fit are really irrelevant.Exponential smoothing provides a forecast only of deposits for the next year—and thus does not address 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 models—one of which (the model for GSP) must be based solely on time as the independent 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 exclude data from roughly the first 25 years, the forecasts for the later year