Coal As A Fossil Fuel - 1706 Words

Coal is a fossil fuel and is the result of the altered remains of prehistoric vegetation that originally accumulated in swamps and peat bogs. The material that formed fossil fuels varied greatly over time as each layer was buried. As a result of these variations and the length of time the coal was forming, several types of coal were created. Depending upon its composition, each type of coal burns differently and releases different types of emissions. The first step of coal formation occurs when peat is transformed physically and chemically. This process is known as coalification. During the process of coalification, peat endures a plethora of changes due to bacterial decay, compaction, heat, and time. Peat deposits differ in content from one another and can contain everything from pristine plant parts such as roots, bark, spores, etc. to decayed plants, decay products, and even charcoal if the peat caught fire during accumulation. Coal is formed in anoxic swamp areas with a plethora of vegetation. In such an environment, the accumulation of plant debris exceeds the rate of bacterial decay of the debris. The bacterial decay rate is reduced because the available oxygen in organic-rich water is completely used up by the decaying process. Anaerobic (without oxygen) decay is much slower than aerobic decay. In order for the peat to turn into coal, it is necessary for the peat to be covered by sediment. The peat is compacted and as a result, much water is squeezed out during theShow MoreRelatedCoal Is A Fossil Fuel1705 Words   |  7 PagesCoal is a fossil fuel and is the result of altered remains of prehistoric vegetation that originally accumulated in swamps and peat bogs. The material that formed fossil fuels varied greatly over time as each layer was buried. As a result of these variations and the length of time the coal was forming, several types of coal were created. Depending upon its composition, each type of coal burns differently and releases different types of emissions. The first step of coal formation occurs when peatRead MoreCoal Is A Fossil Fuel1555 Words   |  7 PagesCoal is a fossil fuel that provides energy to be used for multiple purposes, provides many jobs, and supplies the U.S. with a strong export. People in America are unaware of what coal actually is, what it is used for, and what kind of jobs it supplies in the United States. Carbon gives coal most of its energy. Coal is made from peat, which is material that is formed from plants that have accumulated at the bottom of swampy areas. As peat is buried by sedimentary rock and sandstone, moisture is squeezedRead More The Fossil Fuel Coal Essay1914 Words   |  8 Pages Coal, an amazing fossil fuel Abstract Coal has had a tremendous effect on the world. It produces the most electricity when compared to other fuels. The US generates more than half of their electricity from coal. This black or brownish†black fossil fuel, formed by the energy in plants hundreds of millions of years ago, is made up of mostly carbon, hydrogen, and small traces of other elements like sulfur. Coal has four main types of categories. Mining is the method used to extract coal fromRead MoreCoal Is A Nonrenewable Fossil Fuel766 Words   |  4 Pagespower plants run on the same primary fuel. With that said, I hope you carefully consider my recommendations, as they are essential in maintaining the current and future state of our country. Although using coal as our primary energy resource has minor sociopolitical and scientific complications, the strategies to address these problems and the social, political, scientific, and economic advantages greatly outweigh the setbacks. While coal is a nonrenewable fossil fuel, it will still provide our countryRead MoreFossil Fuels : Oil, Coal And Gas1640 Words   |  7 PagesFossil Fuels: Oil, Coal and Gas Fossil fuels are essential to life on earth as we know it today. Our world would certainly be much different if it weren’t for such seemingly simple things such as coal, oil, and natural gas. These basic elements of life on earth may not seem like a major concern to some people until we put into perspective how they have shaped our world today. Civilizations have been built, economies have risen and crumbled, and even wars have been fought over these precious fossilRead MoreFossil Fuels Coal, Petroleum, And Natural Gas756 Words   |  4 PagesFossil fuels—coal, petroleum (oil), and natural gas — are concentrated organic compounds found in the Earth’s crust. They are created from the remains of plants and animals that lived millions of years ago in the form of concentrated biomass. According to the US Energy Information Administration (EIA), fossil fuels meet 81 percent of U.S. energy demand. Scattered records of the use of coal date to at least 1100 BC. By the middle Ages, small mining operations began to spread in Europe, where coalRead MoreFossil Fuels ( Oil, Coal, Natural Gas )1743 Words   |  7 Pages Fossil Fuels (Oil, Coal, Natural Gas) Debbie Burrell SCI2000 Gwynedd Mercy University Abstract Fossil fuels are non-renewable sources of energy that were form billions of years ago. The three different types of fossil fuels in the world include: oil, coal and natural gas. Although each of the three types of fossil fuels are extracted differently they are all processed and used as the world’s primary sources of energy. Being the world’s primary sources of energy, fossil fuel experienceRead MoreFossil Fuels : Coal, Oil And Natural Gas1867 Words   |  8 PagesThe three type of major fossil fuels are coal, oil and natural gas. These fossil fuels are considered non-renewable energy because of the length of time it will take for the natural processes to create these resources. It will take millions of years for them to form. Most of our coal was formed about 300 million years ago, when a majority of the earth was covered by steamy swamps. As the plants and the trees died, the remaining of the plants and trees sank to the bottom of the swap which accumulatedRead Mor eTypes Of Fossil Fuels : Coal, Oil And Natural Gas2944 Words   |  12 PagesThere are three major forms of fossil fuels: coal, oil and natural gas. All three were formed many hundreds of millions of years ago before the time of the dinosaurs, which is why the name fossil fuels. The age they were formed is called the Carboniferous Period. It was part of the Paleozoic Era. Carboniferous gets its name from carbon, the basic element in coal and other fossil fuels. The Carboniferous Period occurred from about 360 to 286 million years ago. At the time, the land was covered withRead MoreThe worlds fossil fuels are running out. With the average amount of time it takes for coal to form1000 Words   |  4 PagesThe worlds fossil fuels are running out. With the average amount of time it takes for coal to form being 300 billion years, the earth can only renew them so fast. Fossil fuels, like coal and oil take the earth billions of years to reproduce so an effective alternate energy source must be explored. Fossil fuels or crude oil has been around for a long time and can be refined to form a number of products such as gas, gasoline, kerosene, gas oil or diesel. We are also running out of oil which is also

Comparing Bram Stoker’s Dracula and the 1972 Film...

Bram Stoker’s Dracula is not only a classic story of men and monsters, but a dramatic reactionary work to the perceived threats to Victorian society in nineteenth century England. In modern times there have been many film adaptations of the novel, each developing a unique analysis or criticism of the literary text within the framework of the society and time period in which it was created. The 1972 film Blacula is one of the most culturally specific variations on the story of Dracula, and highlights many of the themes and messages found in Stoker’s original text. Among the primary similarities between the novel and the film is the portrayal of race, sexuality, nationality, and culture, and the characterization in each work speaks to the†¦show more content†¦Dracula is of mixed racial heritage and blood â€Å"in the whirlpool of European races,† a concept which would have been fearful to the novel’s white, upper-class English audience. This wid espread xenophobia, a fear and hatred of foreigners, was a reaction by Victorian England to the perceived threat of outsiders to white genetic purity. Dracula’s real threat is not in the physical destruction of Western Europe, but in the assimilation, reproduction, and infestation caused by the literal and figurative mixing of his barbarian animal blood with that of the â€Å"superior† English race. The concept of eugenics, the â€Å"qualitative and quantitative improvement of the human genome† (Galton 99), gained widespread popularity during Stoker’s lifetime and became a prevalent theme in the works of many authors aiming to make a social commentary or criticism on the invasion of England by foreign peoples. Adolph Hitler would later adopt eugenic ideals in the intended creation of a â€Å"master race,† one which victimized many of the same groups and relied upon almost identical anti-Semitic imagery as the earlier Victorian proponents (Hauner 15). Race is a key element in the movie Blacula, in which the film’s eponymous villain is an ancient African prince cursed by Count Dracula to walk the earth for eternity in search of human blood. Blacula is literally and metaphorically an updated version of the Transylvanian count, adapted for a primarily

Henry Fords Huge Impact on the World Essay - 696 Words

Henry Ford Can you imagine life without cars? Recent numbers states that each household owns at least two cars. Henry Ford built the automobile; it made it easier for transportation. Henry Ford made a huge impact on the world. Henry Ford was born July 30, 1863, on his family’s farm in Wayne Country. He died April 7, 1947. Ford grew up the oldest of six children on his parent’s farm. Henry Ford had four siblings. They’re names were Jane, Margaret, William, and Robert. Henry Ford mother was Mary Ford, and his father was William Ford. When Henry was twelve, his mother died of childbirth. Henry Ford spent his childhood on his familys farm, located just outside of Detroit, MI. From the time he was a young boy, Ford enjoyed tinkering with†¦show more content†¦In October 1908, he did so, offering the Model T for $950. Henry Ford and his engineers used the first 19 letters of the alphabet to name their automobiles, although some of the cars were never sold to pu blic. Fords affordable Model T irrevocably altered American society. Henry Ford invented the Quadicycle. On June 4, 1896, Henry Ford, at age 32 completed his first successful horseless carriage. Henry Ford asked a friend to build a wall and a door so Henry can build a car. J. Kent Smith showed steel, and Mr. Ford thought it would be good for his car. Henry begins experimenting with home built gasoline internal combustion engines. Ford spent his irregular hours on his efforts to build a gasoline-powered horseless carriage, or automobile. Then, Henry started to think of good for his invention. Ford, driving his own car, beats Winton in an automobile race, attracts investors who form Henry Ford C.O. Ford overtakes Olds, Buick and Cadillac combined to become Number One automaker in U.S., a position it holds for 20 years; Henry Ford becomes company President and majority owner. Ford Motor C.O. founded by Malcolm’s son group, Model A produced in rented Mack Ave. plant. Ford incorporated the Ford Gustafson 3 Motor Company in 1903, Michigan begins Operations as the first moving automobile assembly line in the world. The assembly line slashed the time needed to complete each car from about 12  ½ hours toShow MoreRelatedHenry Ford Started the Car Revolution789 Words   |  3 PagesHenry Ford Who is the person that started the car revolution? Who is the person that introduced us to the world of automobiles? The answer is Henry Ford. Henry Ford was a successful man that created the Ford automobile. Henry Ford’s company is still making great profit in business. Henry Ford wanted to stop World War II by creating tanks, jeeps, and other armed forces but it still didn’t work. Still, Ford’s automobiles were affordable and he became a very rich and a well-known man. Henry has achievedRead MoreResearch Paper Henry Ford1111 Words   |  5 PagesDaniel Rodriguez English 10 Mrs. Toman March 29, 2011 Research Paper: Henry Ford Imagine how life would be if our society did not have cars. Today, our society is dependent on cars for our daily routines. From transporting our food, clothes, and technology to just going to the store across the street, cars are a very important part of our society. In the 19th century, only the wealthy and upper middle class had access to automobiles, and they only used cars for fancy transportationRead MoreHenry Ford s Lasting Legacy1483 Words   |  6 PagesHenry Ford’s Lasting Legacy â€Å"Any customer can have a car painted any colour that he wants so long as it is black.† (Henry Ford). Henry Ford is one of the world’s most renowned leaders for the automobile industry. The son of a farmer, Ford has always been interested in how things worked. He has improved the models of his cars to make manufacturing them faster and more efficient by using assembly lines. He also set a balance between his employees’ wages and hours worked. Ford never stopped innovatingRead MoreThe Work Of Henry Ford Made A Lasting Impact On America Essay1313 Words   |  6 Pagesgrew, people looked for ways to travel more efficiently. The work of Henry Ford made a lasting impact on America in regards to both transportation and manufacturing. Henry Ford was much like other children growing up. Ford was born on July 30, 1863 in Dearborn, Michigan. He was raised on a farm and others could tell he would be extremely successful in his future. In order to learn more about the engines and be more successful, Henry Ford built friendships with the men who ran the full-sized steam enginesRead MoreThe Flivver King: Henry Ford1571 Words   |  7 Pagesï » ¿The Flivver King: A Story of Ford America In the early 1900’s Henry Ford developed the idea of â€Å"a wagon that will run without a horse†.1 This idea and Ford’s success changed America and its people forever. The development of the automobile played a tremendous role in the economy, labor unions and society. Generally, when most people think of Henry Ford they reflect upon his wealth and contributions to the transportation industry as an infinitely positive phenomenon. It is thought that asideRead MoreHenry Fords Impact On Society1744 Words   |  7 Pagesof the last century, Henry Ford can take accountability for creating the American middle class. We can thank him or curse him, but either way, we have to acknowledge the impact Henry Ford had on our society. You might not know that Henry Ford did not start out as a successful producer of automobiles. After building his first car, the Quadricycle. â€Å"In 1899 he formed the Detroit Automobile Company, which quickly failed after only a few vehicles were produced.† (Stanford). Henry and some of his originalRead MoreHenry Ford Paper1781 Words   |  8 Pagesadult life of Henry Ford. Henry ford’s young life, in this paper will consist of his childhood. The paper will then describe all of his education and early jobs. Finally, this paper will conclude with Henry Ford’s adult life and home life (what he did when he wasn’t working), his career’s work and the impact Henry had on American History. This paper should help the reader better understand the life of Henry Ford: Who he was? Who he is? And why he was so vital to our American History. Henry Ford, bornRead MoreHenry Fords Responsibility For Creating The American Middle Class1680 Words   |  7 Pagesperson of the last century, Henry Ford can take responsibility for creating the American middle class. We can thank him or curse him, but either way, we have to acknowledge the impact Henry Ford had on our society. You might not know that Henry Ford did not start out as a successful producer of automobiles. After building his first car, the Quadricycle. In 1899 he formed the Detroit Automobile Company, which quickly failed after only a few vehicles were produced. Henry and some of his original investorsRead MoreAn Overview On An Evolving Era1623 Words   |  7 PagesMadison Pohl Mrs. Christoffersen 11A – Era Research Paper 23 October 2015 An Innovating Era One of the most famous innovative engineers of all time, Henry Ford, once said, â€Å"You can t build a reputation on what you are going to do.† Between 1850 and 1914 the American people happened to be living by this. Everyone tried creating something to profit, not to satisfy American needs, but some Americans built a reputation doing the opposite of that. During the years between 1850 and 1914, Americans wereRead More72F. Mr. Fredrick. Advanced English 9 - 7. February 8,999 Words   |  4 PagesAldous Huxley, he portrayed many of his problems in Brave New World. Huxley wrote a work that not only made the reader look upon Huxley’s time, but also make them look at their own and make a connection to see if the reader had similar problems still occurring. Literary devices such as characterization and allusions were used by Huxley to give the reader an idea of what was occurring in Huxley’s lifetime. Throughout Brave New World Huxley expressed three main problem s: religion, the role of women

The Birthmark Literary Analysis - 1614 Words

The Birthmark by Nathaniel Hawthorne is trying to communicate some important ideas about a variety of themes, he articulates a few weighty themes around this brief argument: the struggle between science and nature. In a story full of successful and almost magical scientific experiments, it is intact nature itself that is more powerful than any creation made by man. As is to be expected, this path to perfection also includes the creation of life and the victory over death. In the birthmark Aylmer does not see, like others who pretended Georgianas hand before him, a singularity that accentuates her immaculate beauty. He sees in that crimson little hand an indication of decay and death. And also of immorality and sin, in tune with the belief†¦show more content†¦For instance, when Aylmer felt miserable, she felt miserable too. Nevertheless, it can be seen that then she demonstrated a total opposite attitude, a strong woman who challenges his husband to go ahead with his experim ents. A girl with no fear at all. Far from being the typical woman in her house, she is educated and intelligent, and she is able to read and understand the intricate experiments that her husband documents in his diaries. With them she understands how his husbands love for her is, and she accepts it, and that Aylmers lofty ideals condemn him to permanent dissatisfaction. She also knows that her husbands attempts to erase the birthmark will not succeed. In spite of this, she voluntarily takes the concoction he offers. The drink finishes with the birthmark, yes, but also with her, who says goodbye to her husband making him know that his search for divine perfection has made him despise the best the earth could offer. Therefore, with all those decisions it can be seen that she has the will to do it and she can make her own decisions. She is completely different from Aylmer. She understood and was aware about what happened to the birthmark, and why she died. Aminadab, the foil character , is the laboratory assistant, but he is purely physical everything that he does for Aylmer is done not out of understanding, he doesnt understand Aylmer science, but he just does all the physical stuff all theShow MoreRelatedThe Birthmark Literary Analysis914 Words   |  4 PagesIn â€Å"The Birthmark†, a short story by Nathanial Hawthorne, the use of the archetypal conflict Nature vs. Science, the character of Damsel in Distress, and the symbol of the Incurable Wound show how easily beauty is overlooked in the endeavor for perfection. The archetypal conflict of Nature vs. Science is shown in Aylmer’s intention to remove the birthmark, nature’s constant reminder of human mortality, from Georgiana’s cheek. Aylmer believed that the birthmark might heighten Georgiana’s beautyRead MoreA Separate Peace, By Nathaniel Hawthorne996 Words   |  4 Pagesnot get to do in depth analysis so as to encounter such in lifestyle. As an example, at this point the planet is at the verge of a war. Humans have completely different views and perceptions of the implications such events would bring around the planet. There has always been an unending struggle of deciding between good and evil. As humans, we have a tendency to do not understand or notice a balance between them so as to achieve a positive outcome. In any work of literary art, here are sides ofRead MoreThe Idea Expression Dichotomy1744 Words   |  7 Pagesplot ‘lovers are in proximity of blood’ is abstract enough to be an idea; While in another case, ‘father had secretly sent his daughter to other while remembering a birthmark on her shoulder. The father’s son had fell in love with his unknown-sister while they accidentally found their proximity of blood by knowing about the birthmark.’ This special arrangement and selection of the story would be close to the bottom of the pyramid, which is the expression.’ The ‘substantial part’ in the UK copyrightRead MoreWilliam Golding s Lord Of The Flies1603 Words   |  7 PagesLiterary devices are techniques often used by authors to portray in-depth analyses of major characters, storylines, and central themes, which take place in a story. These analyses help readers understand a message the author is trying to convey. In the novel Lord of the Flies, William Golding uses different literary devices in order to demonstrate the boys’ struggle against the lack of society and law on the island, as well as the consequences that have transpired due to this loss. This conflictRead MoreSimilar Gothic Elements in the Work of Edgar Allan Poe and Nathaniel Hawthorne2436 Words   |  10 Pages Nathaniel Hawthorne was one of the most valiant and significant writers of fiction before the Civil War. He gained fame for publishing, The Scarlet Letter, and was praised for his literary style. The Scarlet Letter, allowed him to direct atte ntion to issues he valued. Other stories like, â€Å"The Birthmark,† and, â€Å"Rappaccini’s Daughter,† provided a unique view of a how a male dominated society can harm its women. Author Henry James considered him a genius and the most significant writer of hisRead MoreEssay on Analyis of Knowledge of a Possibility by JUllary Putnam2603 Words   |  11 Pagesas define Formal Realism. In Hilary Putnam’s â€Å"Literature Science, and Reflection†, Putnam discusses both the limitations and potentials of knowledge in literature. The criterion for knowledge is rather complex and Putnam addresses literary knowledge in â€Å"both the empirical and conceptual elements† (Putnam 488). On the one hand, there are the conceptual elements of knowledge, those that can be considered â€Å"knowledge of possibility† (Putnam 488) that allow us to think of new possibilitiesRead More Characterization, Identities, and the Supernatural in Otranto2209 Words   |  9 PagesIsabella, to his murderous rage. Morris also points out the recurring set of patterns and coincidences. Theodore escapes from imprisonment not once, not twice, but three times. He appears at the perfect moment to aid Isabella in her escape, and his birthmark is revealed only seconds before Manfreds order to behead him, rescuing him from death and revealing him as the rightful successor to the municipality of Otranto. These perfectly timed appearances emphasize the idea of â€Å"surface† with no â€Å"depth† —Read MoreModern Environmental Degradation And Exploitation3639 Words   |  15 Pagesdegrade the natural splendor and resources of our planet. Since every transformative process bears the scars of revolution, Marx argues that, in emerging from the shackles of capitalism, socialism or the â€Å"first phase† of communism will bear the birthmarks of the previous order. Thus, each worker will be given credit for his contribution. When these changes transform the society and socialism extends throughout the world, humanity will enter the final stage of pure communism characterized by StatelessnessRead MoreEssay The Salem Witchcraft Trials of 16924260 Words   |  18 Pagesdid not participate in the trials, the other girls were joined by other young and mature women in staging public demonstrations of their affliction when in the presence of accused witches. The events in Salem have been used as a theme in many literary works, including the play by Arthur Miller which we are going to read during this unit. They are interesting to anthropologists because they display some of the characteristics of village witchcraft and some of the features of the European witchRead MoreFigurative Language and the Canterbury Tales13472 Words   |  54 Pages1. allegory: a literary work that has a second meaning beneath the surface, often relating to a fixed, corresponding idea or moral principle. 2. alliteration: repetition of initial consonant sounds. It serves to please the ear and bind verses together, to make lines more memorable, and for humorous effect. †¢ Already American vessels had been searched, seized, and sunk. -John F. Kennedy †¢ I should like to hear him fly with the high fields/ And wake to the farm forever fled from the childless

Interest in Public Health Free Essays

The pursuit of a satisfying and meaningful career is my ultimate goal and a master of public health degree is a stepping stone along the path to a future career. For me, it is also a responsibility I owe to myself. My university education exposed me to a number of public health issues. We will write a custom essay sample on Interest in Public Health or any similar topic only for you Order Now While at university, I was affiliated to an anti AIDS club whose increased emphasis was placed on behavioural change to prevent the risk of STDs, HIV/AIDS and unplanned pregnancies. I particularly joined this club so I could make an impact on fellow students and prevent the spread of the virus as I had lost a lot of my close relations to HIV/AIDS. It was from this point that my interest in public health arose. During my fifth year of university education, I proposed to conduct a research on the role of physiotherapy in patients HIV/AIDS patients but could not conduct the named research due to funding difficulties and ethics issues. Nevertheless, I still picked on another public health topic ‘the prevalence of complaints of arm, neck and shoulder among office workers who use computers’ and I earned myself an award as the best graduating student in Research. The findings of the study further prompted me to make a difference and prevent preventable illnesses, thus considered public health research as a career. My work experience as a physiotherapist is within the field of public health and has developed my disease identification, treatment and to a lesser extent preventive skills. I am currently engaged in community (outreach)programmes for HIV/AIDS patients. My role in this activity, is to identify and mobilise patients who are on Anti retro virus drugs who have residual effects (weak limbs) of ARVs and other people in the community who might actually need physiotherapy services. Though this integration of physiotherapy services with HIV/AIDS activities at the hospital is still in its infancy stage, as a department we have achieved an increase of 30% in the number of patients captured in the community and are actually accessing our services. What about the rest of the 70% ? we could still do better. Personally, being the overseer of the physiotherapy aspect of the HIV/AIDS programme I have earned a great deal of insight on issues pertaining to . However, each time we embark on the usual community visits and find cases that could have been prevented, I feel challenged and to some extent motivated to do more than I am already doing because currently our main emphasis is on the curative aspect of disease rather than prevention and primary care . in addition, I as diagnosed with Hyperthyroidism in 2009 and I realise that I am not able to meet the physical demands of my current job and would want to contribute to population health at an administrative level. My participation in the programme confirmed my budding interest in preventive medicine and improved quality of care. I am drawn to public health because of its unbounded solutions to health problems. I am in search of public health skills develop and be able to contribute positively towards the health of the community and society at large. In addition, I feel that my current degree alone, is not offering me adequate career opportunities, in which case gaining a further qualification particularly master of public health, will provide me with new career options and advance my prospects immensely. After I complete the master of public health programme, I will have acquired problem solving skills, locating and using information effectively and analytical thinking skills. In view of this, I intend to join an Non Governmental Organisation dealing in public health issues and possibly work in a rural area as that is where the bulk of the work is to be done. Currently I am studying for a certificate in HIV/AIDS management, I believe the certificate and the master of public health coupled together will help me perform better in my future job role as I would like to be involved in the devising of programmes focused to prevent and provide quality health care especially in HIV/AIDS related projects. How to cite Interest in Public Health, Essay examples

Rhetorical mode free essay sample

Rhetorical modes are methods for effectively communicating through language and writing. Complete the following chart to identify the purpose and structure of the various rhetorical modes used in academic writing. Provide at least two tips for writing each type of rhetorical device. NOTE: You may not copy and paste anything directly from the textbook or a web site. All information included in this assignment must be written in your own words. Rhetorical Mode Purpose – Explain when or why each rhetorical mode is used. Structure – Identify the organizational method that works best with each rhetorical mode. Tips – Provide two tips for writing in each rhetorical mode. Narration Narration is used to tell stories. Narrative writing typically progresses in chronological order. A plot summary can help with organization. Keeping the human senses in mind can help keep details strong. Illustration An essay that clearly demonstrates and supports a point through the use of evidence. We will write a custom essay sample on Rhetorical mode or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page The thesis should be at the beginning, the supporting evidence in the body of the paper. Should use a wide variety of words and phrasing. The evidence should be appropriate to the topics and the audience. Description To make sure your audience is fully immersed in the words on the page by using sensory details. Spatial order, depending on the writer, descriptions could go from top to bottom or left to right. Avoid empty descriptors if possible. Use spatial order to organize your descriptive writing. Classification To break the broad subject down into smaller, more manageable and more specific parts. Organized by breaking it down into subcategories. Choose topics you know well when writing this type of essay. Make sure you break down your topic at least 3 different ways. Process analysis The purpose is to explain how to do something or how something works. In chronological order, step by step instructions on how something is accomplished. Always have someone else read it to make sure it makes sense. Always use strong details and clear examples. Definition The purpose is to simply define something. It is organized by context, the circumstance, conditions, or settings in which something occurs or exists. Clearly define what you’re writing about. Make sure everything is organized. Compare and Contrast The purpose is to highlight the similarities between two or more similar objects while contrasting highlights the differences between two or more objects. It is organized by introduction, body, and conclusion. There should be advantages and disadvantages. Use comparing and contrasting to find likes or differences. Comparisons focus on similarities and contrast focuses on differences. Cause and The purpose is to answer why are things like this? What is the effect, or result, of this? What is the cause of this? Explain how one event leads to another. Make a list of causes and prioritize them according to their significance on the effect. Put causes under main categories and explain them if you find too many interrelated information. Persuasion The purpose is to convince, or persuade, the reader that the opinion, or assertion, or claim of the writer is correct or valid. It is organized by intro, body, and conclusion. Remember to enter their world, provide the reader with compelling evidence. Write a 100- to 150-word paragraph explanation that demonstrates why compare and contrast is the appropriate rhetorical mode for the topic you chose in Week Two. Compare and contrast is the appropriate rhetorical mode for the topic I chose because I have two of the similar objects that will be compared and contrasted and also the differences of the two. I will be comparing and contrasting the two methods of losing weight, which are diet and exercise or diet pills. In the process of me comparing and contrasting the two I will be learning a lot about what I am in the process of doing which makes this project so interesting to me. I am sure there is going to be a lot of similarities and differences.

Eviews Illustrator free essay sample

Windows, Word and Excel are trademarks of Microsoft Corporation. PostScript is a trademark of Adobe Corporation. Professional Organization of English Majors is a trademark of Garrison Keillor. All other product names mentioned in this manual may be trademarks or registered trademarks of their respective companies. Quantitative Micro Software, LLC 4521 Campus Drive, #336, Irvine CA, 92612-2699 Telephone: (949) 856-3368 Fax: (949) 856-2044 web: www. eviews. com First edition: 2007 Second edition: 2009 Editor: Meredith Startz Index: Palmer Publishing Services Chapter 3. Getting the Most from Least Squares Regression is the king of econometric tools. Regression’s job is to find numerical values for theoretical parameters. In the simplest case this means telling us the slope and intercept of a line drawn through two dimensional data. But EViews tells us lots more than just slope and intercept. In this chapter you’ll see how easy it is to get parameter estimates plus a large variety of auxiliary statistics. We begin our exploration of EViews’ regression tool with a quick look back at the NYSE volume data that we first saw in the opening chapter. Then we’ll talk about how to instruct EViews to estimate a regression and how to read the information about each estimated coefficient from the EViews output. In addition to regression coefficients, EViews provides a great deal of summary information about each estimated equation. We’ll walk through these items as well. We take a look at EViews’ features for testing hypotheses about regression coefficients and conclude with a quick look at some of EViews’ most important views of regression results. Regression is a big subject. This chapter focuses on EViews’ most important regression features. We postpone until later chapters various issues, including forecasting (Chapter 8, â€Å"Forecasting†), serial correlation (Chapter 13, â€Å"Serial Correlation—Friend or Foe? †), and heteroskedasticity and nonlinear regression (Chapter 14, â€Å"A Taste of Advanced Estimation†). A First Regression Returning to our earlier examination of trend growth in the volume of stock trades, we start with a scatter diagram of the logarithm of volume plotted against time. EViews has drawn a straight line—a regression line—through the cloud of points plotted with log ( volume ) on the vertical axis and time on the horizontal. The regression line can be written as an algebraic expression: log ( volume t ) = a + bt Using EViews to estimate a regression lets us replace a and b with numbers 62—Chapter 3. Getting the Most from Least Squares based on the data in the workfile. In a bit we’ll see that EViews estimates the regression line to be: log ( volume t ) = – 2. 629649 + 0. 017278t In other words, the intercept a is estimated to be -2. 6 and the slope b is estimated to be 0. 017. Most data points in the scatter plot fall either above or below the regression line. For example, for observation 231 (which happens to be the first quarter of 1938) the actual trading volume was far below the predicted regression line. In other words, the regression line contains errors which aren’t accounted for in the estimated equation. It’s standard to write a regression model to include a term u t to account for these errors. (Econometrics texts sometimes use the Greek letter epsilon, e , rather than u for the error term. ) A complete equation can be written as: log ( volume t ) = a + bt + u t Regression is a statistical procedure. As such, regression analysis takes uncertainty into ? account. Along with an estimated value for each parameter (e. g. , b = 0. 017 ) we get: †¢ Measures of the accuracy of each of the estimated parameters and related information for computing hypothesis tests. †¢ Measures of how well the equation fits the data: How much is explained by the estimated values of a and b and how much remains unexplained. †¢ Diagnostics to check up on whether assumptions underlying the regression model seem satisfied by the data. We’re re-using the data from Chapter 1, â€Å"A Quick Walk Through† to illustrate the features of EViews’ regression procedure. If you want to follow along on the computer, use the workfile â€Å"NYSEVOLUME† as shown. A First Regression—63 EViews allows you to run a regression either by creating an equation object or by typing commands in the command pane. We’ll start with the former approach. Choose the menu command Object/New Object†¦. Pick Equation in the New Object dialog. The empty equation window pops open with space to fill in the variables you want in the regression. Regression equations are easily specified in EViews by a list in which the first variable is the dependent variable—the variable the regression is to explain, followed by a list of explanatory—or independent—variables. Because EViews allows an expression pretty much anywhere a variable is allowed, we can use either variable names or expressions in our regression specification. We want log ( volume ) for our dependent variable and a time trend for our independent variable. Fill out the equation dialog by entering â€Å"log(volume) c @trend†. Hint: EViews tells one item in a list from another by looking for spaces between items. For this reason, spaces generally aren’t allowed inside a single item. If you type: log (volume) c @trend you’ll get an error message. 64—Chapter 3. Getting the Most from Least Squares Exception to the previous hint: When a text string is called for in a command, spaces are allowed inside paired quotes. Reminder: The letter â€Å"C† in a regression specification notifies EViews to estimate an intercept—the parameter we called a above. Hint: Another reminder: @trend is an EViews function to generate a time trend, 0, 1, 2, †¦. Our regression results appear below: The Really Important Regression Results There are 25 pieces of information displayed for this very simple regression. To sort out all the different goodies, we’ll start by showing a couple of ways that the main results might be presented in a scientific paper. Then we’ll discuss the remaining items one number at a time. A favorite scientific convention for reporting the results of a single regression is display the estimated equation inline with standard errors placed below estimated coefficients, looking something like: The Really Important Regression Results—65 log ( volume t ) = – 2. 629649 + 0. 017278 ? t , ser = 0. 967362, R = 0. 852357 ( 0. 89576 ) ( 0. 000334 ) 2 Hint: The dependent variable is also called the left-hand side variable and the independent variables are called the right-hand side variables. That’s because when you write out the regression equation algebraically, as above, convention puts the dependent variable to the left of the equals sign and the independent variabl es to the right. The convention for inline reporting works well for a single equation, but becomes unwieldy when you have more than one equation to report. Results from several related regressions might be displayed in a table, looking something like Table 2. Table 2 (1) Intercept -2. 629649 (0. 089576) 0. 017278 (0. 000334) — (2) -0. 106396 (0. 045666) -0. 000736 (0. 000417) 6. 63E-06 (1. 37E-06) 0. 868273 (0. 022910) 0. 289391 0. 986826 t t 2 log(volume(-1)) ser — 0. 967362 0. 852357 R 2 Column (2)? Don’t worry, we’ll come back to it later. Hint: Good scientific practice is to report only digits that are meaningful when displaying a number. We’ve printed far too many digits in both the inline display and in Table 2 so as to make it easy for you to match up the displayed numbers with the EViews output. From now on we’ll be better behaved. EViews regression output is divided into three panels. The top panel summarizes the input to the regression, the middle panel gives information about each regression coefficient, and the bottom panel provides summary statistics about the whole regression equation. 66—Chapter 3. Getting the Most from Least Squares The most important elements of EViews regression output are the estimated regression coefficients and the statistics associated with each coefficient. We begin by linking up the numbers in the inline display—or equivalently column (1) of Table 2—with the EViews output shown earlier. The names of the independent variables in the regression appear in the first column (labeled â€Å"Variable†) in the EViews output, with the estimated regression coefficients appearing one column over to the right (labeled â€Å"Coefficient†). In econometrics texts, regression coefficients are commonly denoted with a Greek letter such as a or b or, occasionally, with a Roman b . In contrast, EViews presents you with the variable names; for example, â€Å"@TREND† rather than â€Å" b †. The third EViews column, labeled â€Å"Std. Error,† gives the standard error associated with each regression coefficient. In the scientific reporting displays above, we’ve reported the standard error in parentheses directly below the associated coefficient. The standard error is a measure of uncertainty about the true value of the regression coefficient. The standard error of the regression, abbreviated â€Å"ser,† is the estimated standard deviation of the error terms, u t . In the inline display, â€Å"ser=0. 967362† appears to the right of the regression equation proper. EViews labels the ser as â€Å"S. E. of regression,† reporting its value in the left column in the lower summary block. Note that the third column of EViews regression output reports the standard error of the estimated coefficients while the summary block below reports the standard error of the regression. Don’t confuse the two. The final statistic in our scientific display is R . R measures the overall fit of the regression line, in the sense of measuring how close the points are to the estimated regression line 2 in the scatter plot. EViews computes R as the fraction of the variance of the dependent variable explained by the regression. (See the User’s Guide for the precise definition. 2 2 Loosely, R = 1 means the regression fit the data perfectly and R = 0 means the regression is no better than guessing the sample mean. Hint: EViews will report a negative R for a model which fits worse than a model consisting only of the sample mean. 2 2 2 The Pretty Important (But Not So Important As the Last Section’s) Regression Results We’re usually most interested in the regression coefficients and the statistical information provided for each one, so let’s continue along with the middle panel. The Pretty Important (But Not So Important As the Last Section’s) Regression Results—67 -Tests and Stuff All the stuff about individual coefficients is reported in the middle panel, a copy of which we’ve yanked out to examine on its own. The column headed â€Å"t-Statistic† reports, not surprisingly, the t-statistic. Specifically, this is the t-statistic for the hypothesis that the coefficient in the same row equals zero. (It’s computed as the ratio of the estimated coefficient to its standard error: e. g. , 51. 7 = 0. 017  § 0. 00033 . ) Given that there are many potentially interesting hypotheses, why does EViews devote an entire column to testing that specific coefficients equal zero? The hypothesis that a coefficient equals zero is special, because if the coefficient does equal zero then the attached coefficient drops out of the equation. In other words, log ( volume t ) = a + 0 ? t + u t is really the same as log ( volume t ) = a + u t , with the time trend not mattering at all. Foreshadowing hint: EViews automatically computes the test statistic against the hypothesis that a coefficient equals zero. We’ll get to testing other coefficients in a minute, but if you want to leap ahead, look at the equation window menu View/Coefficient Tests†¦. If the t-statistic reported in column four is larger than the critical value you choose for the test, the estimated coefficient is said to be â€Å"statistically significant. † The critical value you pick depends primarily on the risk you’re willing to take of mistakenly rejecting the null hypothesis (the technical term is the â€Å"size† of the test), and secondarily on the degrees of freedom for the test. The larger the risk you’re willing to take, the smaller the critical value, and the more likely you are to find the coefficient â€Å"significant. † Hint: EViews doesn’t compute the degrees of freedom for you. That’s probably because the computation is so easy it’s not worth using scarce screen real estate. Degrees of freedom equals the number of observations (reported in the top panel on the output screen) less the number of parameters estimated (the number of rows in the middle panel). In our example, df = 465 – 2 = 463 . The textbook approach to hypothesis testing proceeds thusly: 1. Pick a size (the probability of mistakenly rejecting), say five percent. 2. Look up the critical value in a t-table for the specified size and degrees of freedom. 68—Chapter 3. Getting the Most from Least Squares . Compare the critical value to the t-statistic reported in column four. Find the variable to be â€Å"significant† if the t-statistic is greater than the critical value. EViews lets you turn the process inside out by using the â€Å"p-value† reported in the right-most column, under the heading â€Å"Prob. † EViews has worked the problem backwards an d figured out what size would give you a critical value that would just match the t-statistic reported in column three. So if you are interested in a five percent test, you can reject if and only if the reported p-value is less than 0. 05. Since the p-value is zero in our example, we’d reject the hypothesis of no trend at any size you’d like. Obviously, that last sentence can’t be literally true. EViews only reports p-values to four decimal places because no one ever cares about smaller probabilities. The p-value isn’t literally 0. 0000, but it’s close enough for all practical purposes. Hint: t-statistics and p-values are different ways of looking at the same issue. A t-statistic of 2 corresponds (approximately) to a p-value of 0. 05. In the old days you’d make the translation by looking at a â€Å"t-table† in the back of a statistics book. EViews just saves you some trouble by giving both t- and p-. Not-really-about-EViews-digression: Saying a coefficient is â€Å"significant† means there is statistical evidence that the coefficient differs from zero. That’s not the same as saying the coefficient is â€Å"large† or that the variable is â€Å"important. † â€Å"Large† and â€Å"important† depend on the substantive issue you’re working on, not on statistics. For example, our estimate is that NYSE volume rises about one and one-half percent each quarter. We’re very sure that the increase differs from zero—a statement about statistical significance, not importance. Consider two different views about what’s â€Å"large. † If you were planning a quarter ahead, it’s hard to imagine that you need to worry about a change as small as one and one-half percent. On the other hand, one and one-half percent per quarter starts to add up over time. The estimated coefficient predicts volume will double each decade, so the estimated increase is certainly large enough to be important for long-run planning. More Practical Advice On Reporting Results Now you know the principles of how to read EViews’ output in order to test whether a coefficient equals zero. Let’s be less coy about common practice. When the p-value is under 0. 05, econometricians say the variable is â€Å"significant† and when it’s above 0. 05 they say it’s â€Å"insignificant. † (Sometimes a variable with a p-value between 0. 10 and 0. 05 is said to be â€Å"weakly significant† and one with a p-value less than 0. 01 is â€Å"strongly significant. †) This practice may or may not be wise, but wise or not it’s what most people do. The Pretty Important (But Not So Important As the Last Section’s) Regression Results—69 We talked above about scientific conventions for reporting results and showed how to report results both inline and in a display table. In both cases standard errors appear in parentheses below the associated coefficient estimates. â€Å"Standard errors in parentheses† is really the first of two-and-a-half reporting conventions used in the statistical literature. The second convention places the t-statistics in the parentheses instead of standard errors. For example, we could have reported the results from EViews inline as log ( volume t ) = – 2. 629649 + 0. 017278 ? t , ser = 0. 967362, R = 0. 852357 ( – 29. 35656 ) ( 51. 70045 ) 2 Both conventions are in wide use. There’s no way for the reader to know which one you’re using—so you have to tell them. Include a comment or footnote: â€Å"Standard errors in parentheses† or â€Å"t-statistics in parentheses. † Fifty percent of economists report standard errors and fifty percent report t-statistics. The remainder report p-values, which is the final convention you’ll want to know about. Where Did This Output Come From Again? The top panel of regression output, shown on the right, summarizes the setting for the regression. The last line, â€Å"Included observations,† is obviously useful. It tells you how much data you have! And the next to last line identifies the sample to remind you which observations you’re using. Hint: EViews automatically excludes all observations in which any variable in the specification is NA (not available). The technical term for this exclusion rule is â€Å"listwise deletion. † 70—Chapter 3. Getting the Most from Least Squares Big (Digression) Hint: Automatic exclusion of NA observations can sometimes have surprising side effects. We’ll use the data abstract at the right as an example. Data are missing from observation 2 for X1 and from observation 3 for X2. A regression of Y on X1 would use observations 1, 3, 4, and 5. A regression of Y on X2 would use observations 1, 2, 4, and 5. A regression of Y on both X1 and X2 would use observations 1, 4, and 5. Notice that the fifth observation on Y is zero, which is perfectly valid, but that the fifth observation on log(Y) is NA. Since the logarithm of zero is undefined EViews inserts NA whenever it’s asked to take the log of zero. A regression of log(Y) on both X1 and X2 would use only observations 1 and 4. The variable, X1(-1), giving the previous period’s values of X1, is missing both the first and third observation. The first value of X1(-1) is NA because the data from the observation before observation 1 doesn’t exist. (There is no observation before the first one, eh? The third observation is NA because it’s the second observation for X1, and that one is NA. So while a regression of Y on X1 would use observations 1, 3, 4, and 5, a regression of Y on X1(-1) would use observations 2, 4, and 5. Moral: When there’s missing data, changing the variables specified in a regression can a lso inadvertently change the sample. What’s the use of the top three lines? It’s nice to know the date and time, but EViews is rather ungainly to use as a wristwatch. More seriously, the top three lines are there so that when you look at the output you can remember what you were doing. Dependent Variable† just reminds you what the regression was explaining— LOG(VOLUME) in this case. â€Å"Method† reminds us which statistical procedure produced the output. EViews has dozens of statistical procedures built-in. The default procedure for estimating the parameters of an equation is â€Å"least squares. † The Pretty Important (But Not So Important As the Last Section’s) Regression Results—71 The third line just reports the date and time EViews estimated the regression. It’s surprising how handy that information can be a couple of months into a project, when you’ve forgotten in what order you were doing things. Since we’re talking about looking at output at a later date, this is a good time to digress on ways to save output for later. You can: †¢ Hit the button to save the equation in the workfile. The equation will appear in the workfile window marked with the icon. Then save the workfile. Hint: Before saving the file, switch to the equation’s label view and write a note to remind yourself why you’re using this equation. †¢ Hit the button. †¢ Spend output to a Rich Text Format (RTF) file, which can then be read directly by most word processors. Select Redirect: in the Print dialog and enter a file name in the Filename: field. As shown, you’ll end up with results stored in the file â€Å"some results. rtf†. †¢ Right-click and choose Select non-empty cells, or hit Ctrl-A— it’s the same thing. Copy and then paste into a word processor. Freeze it If you have output that you want to make sure won’t ever change, even if you change the equation specification, hit . Freezing the equation makes a copy of the current view in the form of a table which is detached from the equation object. (The original equation is unaffected. ) You can then this frozen table so that it will be saved in the workfile. See Chapter 17, â€Å"Odds and Ends. † 72—Chapter 3. Getting the Most from Least Squares Summary Regression Statistics The bottom panel of the regression provides 12 summary statistics about the regression. We’ll go over these statistics briefly, but leave technical details to your favorite econometrics text or the User’s Guide. We’ve already talked about the two most important numbers, â€Å"R-squared† and â€Å"S. E. of regression. † Our regression accounts for 85 percent of the variance in the dependent variable and the estimated standard deviation of the error term is 0. 97. Five other elements, â€Å"Sum squared residuals,† â€Å"Log likelihood,† â€Å"Akaike info criterion,† â€Å"Schwarz criterion,† and â€Å"Hannan-Quinn criter. † are used for making statistical comparisons between two different regressions. This means that they don’t really help us learn anything about the regression we’re working on; rather, these statistics are useful for deciding if one model is better than another. For the record, the sum of squared residuals is used in computing F-tests, the log likelihood is used for computing likelihood ratio tests, and the Akaike and Schwarz criteria are used in Bayesian model comparison. The next two numbers, â€Å"Mean dependent var† and â€Å"S. D. dependent var,† report the sample mean and standard deviation of the left hand side variable. These are the same numbers you’d get by asking for descriptive statistics on the left hand side variables, so long as you were using the sample used in the regression. (Remember: EViews will drop observations from the estimation sample if any of the left-hand side or right-hand side variables are NA— i. e. , missing. ) The standard deviation of the dependent variable is much larger than the standard error of the regression, so our regression has explained most of the variance in og(volume)—which is exactly the story we got from looking at the R-squared. Why use valuable screen space on numbers you could get elsewhere? Primarily as a safety check. A quick glance at the mean of the dependent variable guards against forgetting that you changed the units of measurement or that the sample used is so mehow different from what you were expecting. â€Å"Adjusted R-squared† makes an adjustment to the plain-old R to take account of the num2 ber of right hand side variables in the regression. R measures what fraction of the variation in the left hand side variable is explained by the regression. When you add another 2 right hand side variable to a regression, R always rises. (This is a numerical property of 2 2 least squares. ) The adjusted R , sometimes written R , subtracts a small penalty for each additional variable added. â€Å"F-statistic† and â€Å"Prob(F-statistic)† come as a pair and are used to test the hypothesis that none of the explanatory variables actually explain anything. Put more formally, the â€Å"F-sta2 A Multiple Regression Is Simple Too—73 tistic† computes the standard F-test of the joint hypothesis that all the coefficients, except the intercept, equal zero. Prob(F-statistic)† displays the p-value corresponding to the reported F-statistic. In this example, there is essentially no chance at all that the coefficients of the right-hand side variables all equal zero. Parallel construction notice: The fourth and fifth columns in EViews regression output report the t-statistic and corresponding p-value for the hypothesis th at the individual coefficient in the row equals zero. The F-statistic in the summary area is doing exactly the same test for all the coefficients (except the intercept) together. This example has only one such coefficient, so the t-statistic and the F-statistic test exactly the same hypothesis. Not coincidentally, the reported p-values are identical 2 and the F- is exactly the square of the t-, 2672 = 51. 7 . Our final summary statistic is the â€Å"Durbin-Watson,† the classic test statistic for serial correlation. A Durbin-Watson close to 2. 0 is consistent with no serial correlation, while a number closer to 0 means there probably is serial correlation. The â€Å"DW,† as the statistic is known, of 0. 095 in this example is a very strong indicator of serial correlation. EViews has extensive facilities both for testing for the presence of serial correlation and for correcting regressions when serial correlation exists. We’ll look at the Durbin-Watson, as well as other tests for serial correlation and correction methods, later in the book. (See Chapter 13, â€Å"Serial Correlation—Friend or Foe? †). A Multiple Regression Is Simple Too Traditionally, when teaching about regression, the simple regression is introduced first and then â€Å"multiple regression† is presented as a more advanced and more complicated technique. A simple regression uses an intercept and one explanatory variable on the right to explain the dependent variable. A multiple regression uses one or more explanatory variables. So a simple regression is just a special case of a multiple regression. In learning about a simple regression in this chapter you’ve learned all there is to know about multiple regression too. Well, almost. The main addition with a multiple regression is that there are added right hand-side variables and therefore added rows of coefficients, standard errors, etc. The model we’ve used so far explains the log of NYSE volume as a linear function of time. Let’s add two more variables, time-squared and lagged log(volume), hoping that time and timesquared will improve our ability to match the long-run trend and that lagged values of the dependent variable will help out with the short run. In the last example, we entered the specification in the Equation Estimation dialog. I find it much easier to type the regression command directly into the command pane, although the 74—Chapter 3. Getting the Most from Least Squares method you use is strictly a matter of taste. The regression command is ls followed by the dependent variable, followed by a list of independent variables (using the special symbol â€Å"C† to signal EViews to include an intercept. ) In this case, type: ls log(volume) c @trend @trend^2 log(volume(-1)) and EViews brings up the multiple regression output shown to the right. You already knew some of the numbers in this regression because they appeared in the second column in Table 1 on page 65. When you specify a multiple regression, EViews gives one row in the output for each independent variable. Hint: Most regression specifications include an intercept. Be sure to include â€Å"C† in the list of independent variables unless you’re sure you don’t want an intercept. Hint: Did you notice that EViews reports one fewer observation in this regression than in the last, and that EViews changed the first date in the sample from the first to the second quarter of 1888? This is because the first data we can use for lagged volume, from second quarter 1888, is the (non-lagged) volume value from the first quarter. We can’t compute lagged volume in the first quarter because that would require data from the last quarter of 1887, which is before the beginning of our workfile range. Hypothesis Testing We’ve already seen how to test that a single coefficient equals zero. Just use the reported tstatistic. For example, the t-statistic for lagged log(volume) is 37. 89 with 460 degrees of freedom (464 observations minus 4 estimated coefficients). With EViews it’s nearly as easy to test much more complex hypotheses. Hypothesis Testing—75 Click the button and choose Coefficient Diagnostics/Wald – Coefficient Restrictions†¦ to bring up the dialog shown to the right. In order to whip the Wald Test dialog into shape you need to know three things: †¢ EViews names coefficients C(1), C(2), C(3), etc. numbering them in the order they appear in the regression. As an example, the coefficient on LOG(VOLUME(-1)) is C(4). †¢ You specify a hypothesis as an equation restricting the values of the coefficients in the regression. To test that the coefficient on LOG(VOLUME(-1)) equals zero, specify â€Å"C(4)=0†. †¢ If a hypothesis involves multiple restrictions, you enter multiple coefficient equations separated by commas. Let’s work through some examples, starting with the one we already know the answer to: Is the coefficient on LOG(VOLUME(-1)) significantly different from zero? Hint: We know the results of this test already, because EViews computed the appropriate test statistic for us in its standard regression output. 76—Chapter 3. Getting the Most from Least Squares Complete the Wald Test dialog with C(4)=0. EViews gives the test results as shown to the right. EViews always reports an F-statistic since the F- applies for both single and multiple restrictions. In cases with a single restriction, EViews will also show the t-statistic. Hint: The p-value reported by EViews is computed for a two-tailed test. If you’re interested in a one-tailed test, you’ll have to look up the critical value for yourself. Suppose we wanted to test whether the coefficient on LOG(VOLUME(-1)) equaled one rather than zero. Enter â€Å"c(4)=1† to find the new test statistic. So this hypothesis is also easily rejected. Hypothesis Testing—77 Econometric theory warning: If you’ve studied the advanced topic in econometric theory called the â€Å"unit root problem† you know that standard theory doesn’t apply in this test (although the issue is harmless for this particular set of data). Take this as a reminder that you and EViews are a team, but you’re the brains of the outfit. EViews will obediently do as it’s told. It’s up to you to choose the proper procedure. EViews is happy to test a hypothesis involving multiple coefficients and nonlinear restrictions. To test that the sum of the first two coefficients equals the product of the sines of the second two coefficients (and to emphasize that EViews is perfectly happy to test a hypothesis that is complete nonsense) enter â€Å"c(1)+c(2)=sin(c(3))+sin(c(4))†. Not only is the hypothesis nonsense, apparently it’s not true. 78—Chapter 3. Getting the Most from Least Squares A good example of a hypothesis involving multiple restrictions is the hypothesis that there is no time trend, so the coefficients on 2 both t and t equal zero. Here’s the Wald Test view after entering â€Å"c(2)=0, c(3)=0†. The hypothesis is rejected. Note that EViews correctly reports 2 degrees of freedom for the test statistic. Representing The Representations view, shown at the right, doesn’t tell you anything you don’t already know, but it provides useful reminders of the command used to generate the regression, the interpretation of the coefficient labels C(1), C(2), etc. and the form of the equation written out with the estimated coefficients. Hint: Okay, okay. Maybe you didn’t really need the representations view as a reminder. The real value of this view is that you can copy the equation from this view and then paste it into your word processor, or into an EViews batch program, or even into Excel, where wi th a little judicious editing you can turn the equation into an Excel formula. What’s Left After You’ve Gotten the Most Out of Least Squares Our regression equation does a pretty good job of explaining log(volume), but the explanation isn’t perfect. What remains—the difference between the left-hand side variable and the value predicted by the right-hand side—is called the residual. EViews provides several tools to examine and use the residuals. What’s Left After You’ve Gotten the Most Out of Least Squares—79 Peeking at the Residuals The View Actual, Fitted, Residual provides several different ways to look at the residuals. Usually the best view to look at first is Actual, Fitted, Residual/Actual, Fitted, Residual Graph as illustrated by the graph shown here. Three series are displayed. The residuals are plotted against the left vertical axis and both the actual (log(volume)) and fitted (predicted log(volume)) series are plotted against the vertical axis on the right. As it happens, because our fit is quite good and because we have so many observations, the fitted values nearly cover up the actual values on the graph. But from the residuals it’s easy to see two facts: our model fits better in the later part of the sample than in the earlier years—the residuals become smaller in absolute value—and there are a very small number of data points for which the fit is really terrible. 80—Chapter 3. Getting the Most from Least Squares Points with really big positive or negative residuals are called outliers. In the plot to the right we see a small number of spikes which are much, much larger than the typical residual. We can get a close up on the residuals by choosing Actual, Fitted, Residual/Residual Graph. It might be interesting to look more carefully at specific numbers. Choose Actual, Fitted, Residual/Actual, Fitted, Residual Table for a look that includes numerical values. You can see enormous residuals in the second quarter for 1933. The actual value looks out of line with the surrounding values. Perhaps this was a really unusual quarter on the NYSE, or maybe someone even wrote down the wrong numbers when putting the data together! Grabbing the Residuals Since there is one residual for each observation, you might want to put the residuals in a series for later analysis. Fine. All done. Without you doing anything, EViews stuffs the residuals into the special series each estimation. You can use RESID just like any other series. after Quick Review—81 Resid Hint 1: That was a very slight fib. EViews won’t let you include RESID as a series in an estimation command because the act of estimation changes the values stored in RESID. Resid Hint 2: EViews replaces the values in RESID with new residuals after each estimation. If you want to keep a set, copy them into a new series as in: series rememberresids = resid before estimating anything else. Resid Hint 3: You can store the residuals from an equation in a series with any name you like by using Proc/Make Residual Series†¦ from the equation window. Quick Review To estimate a multiple regression, use the ls command followed first by the dependent variable and then by a list of independent variables. An equation window opens with estimated coefficients, information about the uncertainty attached to each estimate, and a set of summary statistics for the regression as a whole. Various other views make it easy to work with the residuals and to test hypotheses about the estimated coefficients. In later chapters we turn to more advanced uses of least squares. Nonlinear estimation is covered, as are methods of dealing with serial correlation. And, predictably, we’ll spend some time talking about forecasting. 82—Chapter 3. Getting the Most from Least Squares