Joseph Cambell & Our Lack of Myth essays

Joseph Cambell & Our Lack of Myth essays Are we becoming grandmothers and grandfathers to a legacy of faceless nobodies who will one day populate this post-modern vacuum of human isolation? Do myths have the power to halt this cycle weve been sucked into? Are they a way of rekindling that fascination about life that the future is draining us of? Joseph Campbell would argue in the book The Power of Myth that yes, with a psychological interpretation of myths we can find meaning in our lives, or even more so, the experience of living. Myths are important to the betterment of society because, according to Campbell, they bolster the rituals that define it. Campbell says initiations and rituals are necessary to make one feel like part of a great social order. And what if that great order included everyone, if we were all a part of it? Then would we not all feel like a part of nothing? What good is it to be part of a club if everyone is in it? Campbell would argue that that is the lack of myth speaking. A unified world would be a "club" in the sense that it is a privilege to be a part of it. But with all of us in it as one, we are not all on the same level. Rites serve as a way of "promoting" us and defining our position in society. Without myth it is as though we are all wading aimlessly around in the same bowl of gumbo. When one goes through rituals and initiation rites, he first becomes a part of something bigger, and then also crosses a barrier of maturity. The latter is key. It is a natural desire to want to be accepted, and rituals serve as a segway to reaching that ultimate goal and achieving status. They mark the trans ition between two different roles in the community and lay emphasis on the value of their existence as it continues to progress. He states, ...kids have their own gangs and their own initiations and their own morality, and theyre doing the best they can. But theyre dangerous because their own laws are not those of the city. ...

Sustainable Development in Business Case Study Example | Topics and Well Written Essays - 3500 words

Sustainable Development in Business - Case Study Example (Organisational Sustainability, n.d.) Andrew Mangan, an environmental entrepreneur promoted BPS or by-product synergy programs as a means to achieve the goals of sustainable development. It is a process that helps the companies to discover new ways in order to convert the waste products into saleable commodities. The goal of Mangan is actually twofold - to promote the wider adoption of BPS programs and also to create business out of helping the companies adopt such by-product synergy programs. (Anderson T., and Mackenzie S., n.d.) There has been a lot of research in the field of sustainable technology and design along with the adaptation of business tools, but in most of the instances, the well designed technologies fail to become broadly adopted, not due to the fact that there are flaws in the technology but due to the reason that there is inadequate sustainable method of servicing, distributing, and improving the technology. Any business needs start up capital in order to fund the design of technology and its development along with a self sustaining revenue stream, which would support the growth as well as be meaningful in terms of reducing pollution. The reason behind the development of EnviroFit International business model was to allow for the design, development along with the dissemination of environment friendly technologies all over the world. This model leverages the participation of the local in country stakeholders in order to ease acceptance and the implementation of RetroFit technology. The key components of this model are using donations for the development of technology as well as operating profits from the product sales to growth, support operations, emissions trading, microfinance and also local partnerships. This business model is till in progress and is executing the business plan along with reducing the perceived risks, by making progress against the value setting milestones like raising investment capital, field tests and developing important partners in supply chain; these would increase the credibility of the business model and also its management. This business model would be highly beneficial for those environmental technologies that lack necessary profit margins in order to make them attractive to the traditional for-profit model. This would provide sufficient margins in order to sustain a particular enterprise without continued infusions of donations or capital. This business model would also in effective in reducing the environmental pollution. (Hudnut P., B auer T. and Lorenz N., n.d.) Triple Bottom Line was originated among the investors seeking a way of putting their money in those enterprises that are economically profitable, socially just and environmentally sound. It is the need of the time to model the systems properties or the ecological characteristic of various domains of productivity and also to design the institutions of monetary and financial services, which can optimize the productivity in these domains. The theory and the institutions should base on the concepts of triple bottom line. The concept of

Letter to investor + MACROECONOMIC OUTLOOK (by region) Essay

Letter to investor + MACROECONOMIC OUTLOOK (by region) - Essay Example As compass helps a sailor in sailing to the right direction, our portfolio also helps the invested funds to move towards appropriate path of earning higher returns. Thus we expect that our portfolio is going to excel the benchmark and will beat the benchmark in near future. Our aim is to hit the MSCI benchmark that is our benchmark. We follow the strategy of efficiently allocating invested funds by investing largely in large or medium cap business enterprises. Our key strategy is to direct the funds towards value stocks as the time period of this portfolio is very short, only one year. This short time horizon does not allow us to put our prime focus on growth stocks. However, it does not mean that we never invested in growth stocks. In fact, we have invested in the growth stocks of Information Technology industry as it shows the best opportunity. We attempt to invest in defensive stocks to avoid cyclical economic fluctuations. It will take some time for the global economy to recover fully from the shock of the recent recession. Defensive stocks are able to generate higher returns than others during troubled times. In terms of geographic segmentation of invested funds, we efficiently divided our funds between the USA, Europe and the rest of the world. Since the USA is the largest economy of the world and it is recovering at a very fast pace, majority of funds is invested in the USA. The second largest part of the funds goes to European nations as they are performing better than the other countries of the world after the USA. The rest of the world gets the remaining funds. Again, thank you for investing with us. Sincerely Xxxxx MACROECONOMIC OUTLOOK United States The Unites States is the economic superpower of the world. But the recent economic recession was originated in this country. U.S.A has always been a dominant economic power in the world and it accounts for approximately 21 percent of the world economy. U.S. economic recession was held responsible for the global economic downturn as U.S. economy always influences economies of other countries in a major way. The major factor that has caused this huge economic downturn in U.S.A. was a huge credit crisis. The credit crisis is held responsible for the closure of a number of investment banks across the world. This credit crisis actually originated from the U.S. home loan market. This credit crisis was triggered by busting of a housing market bubble in 2006. The prices of housing started to fall rapidly since 2006 and the market collapsed. The fall continued throughout 2007 and 2008. With the starting of the year of 2008, U.S. sub prime-mortgage market started to encounter several problems, which appeared to be difficult to deal with. These resulted in an application of huge correction in this market, which had great implications for making credits more costly across the world. With the implementation of this correction, a large number of banks of the America, European countries as well a s of Asia had been forced to write down billions of dollars in their holdings. More shocking thing was that a number of well-established and reputed banks like Lehman Brothers had to file for bankruptcy. The bankruptcy of Lehman Brothers is considered to be the biggest ever case of bankruptcy in the history of U.S. Since 2008, more than 80 firms in U.S.A. only have filed for bankruptcy and a large number of firms have appealed to the government for financial

Discussing Causes Of Climate Change An Environmental Sciences Essay

Discussing Causes Of Climate Change An Environmental Sciences Essay Climate has a great influence over our lives. All our normal routine actions are according to the climate we are living in. However the climate has been changing from past few decades, which in turn is changing our living patterns and thus, has made this world a more puzzled place to live in. In this essay the causes of climate change would be discussed, which are divided into two categories, either the climate is changing due to natural reasons or is forced to change by the human activities. Naturally, the climate change is said to occur because of various reasons, mainly because of volcanic eruptions, ocean current, the solar variations, the earths orbital change, and by many other natural reasons, which in turn produces various greenhouse gasses and in the end results into global warming. On the other hand, carbon emission done by humans is the greatest factor leading to global warming and then to climate change. Other activities like, chemicals used in agriculture, deforestation and other uses of energy in households also contribute in the greenhouse effect. Climate can be defined as the long term weather conditions for a region, generally determined by 30 or more years of records. On contrast weather can be defined as the state of the atmosphere at a particular place and time. Moreover, the Green House effect is naturally in which certain atmospheric gases absorbs long wave radiation from the Earths surface which in the end results in heating the earths surface and the atmosphere. Hence global warming can be defined as the increase of Earths average temperature which in then results into climate change. (Glossary: Nasa). The Debate: There is no doubt about the fact that the Earths climate has become warmer over the twentieth century, however, there is still a dispute about whether the temperature increase is due to natural reasons or because of human activities. Two groups of UK scientists have recently investigated both types of effect. Mike Lockwood and colleagues at the Rutherford Appleton Laboratory (RAL) argue that the Suns magnetic field has doubled over the century, and that this natural force of solar system has affected the earths climate (Nature  399:437). On the other hand Simon Tett and colleagues from the UKs Meteorological Office in Reading and RAL argue that while solar forcing may have added to climate change, however, human activities have also been responsible for the temperature changes from many years (Nature  399:569). It has been stated that the Earths average global temperature has increased by 0.6 Kelvin in the past 100 years. Four main processes that can affect the Earths climate hav e been evaluated. Two of these are said to be small aerosol particles from volcanic eruptions and changes in solar luminosity. The other two, sulphate aerosols and greenhouse gases such as carbon dioxide, are due to increasing industrialization, in particular the burning of forests and fossil fuels. Lockwood and colleagues found that the total magnetic flux leaving the Sun has risen by a factor of 1.4 since 1964. Their results could provide support for the theory that changes in the solar wind could contribute to  climate change. The solar wind and the Suns magnetic field are very well linked with each other. According to the theory charged particles in the solar wind would deflect high-energy cosmic rays that would otherwise have ionized the Earths lower atmosphere, leading to the formation of clouds. Since cloud cover determines the amount of solar radiation reflected by the Earth back into space, a more powerful solar wind implies less cloud cover which, in turn, suggests that the Earth would warm up. However, the paper by Tett and colleagues suggests that natural effects alone cannot account for the pattern of temperature change observed over the past 50 years. They used the HadCM2 computer model to predict the Earths global temperature during five overlapping 50-year periods (1906-56, 1916-1966,), and then compared the results with observations. The program models both the oceans and the atmosphere, and also allows for changes in greenhouse emissions, surface albedo (i.e. reflectivity), volcanic aerosols and solar irradiance. They ran the programmers with a number of different solar models, including one that matched the effects highlighted by Lockwood. The results were similar for all cases: it is not possible to distinguish between the contributions of human activity and natural variations to global warming in the first half of the century, but after 1946 increases in the concentration of man-made greenhouse gases and sulphate aerosols was the dominan t effect. (News: Physics World, 1999) Climate Change Human Activities the Cause, Mea Culpa! But Consider 1816, the Year Without Summer! The whole world seems to be getting involved with the facts of Global warming and Climate change. Nobel prizes were awarded to the UNs IPCC (Intergovernmental Panel on Climate Change) and Al Gore several years ago, followed by the Kyoto Protocol Climate Change Conference of 1997, and finally President Obama led leaders of 192 nations in agreement with its principles, promising heavy financial compensations to third world nations. Scientists have calculated that emissions of carbon dioxide by human activities amount to perhaps 30 billion tons per year because of various factors including fossil fuel burning, cement production, gas flaring, industrial operations and breathing etc. They also estimate that volcanic eruptions can on average emit about one-forty-five to two-fifty-five million tons of carbon dioxide into the atmosphere per year. This seems to specify that human activities may release perhaps 100 times the amount of carbon dioxide emitted by volcanoes, thus, this seems to be a realistic base for the universal concern, which is that human activities have a great negative impact on the climate of Earth. However, it seems like that nature itself is trying to make things worse as firstly admitting furor at Copenhagen by world leaders and President Obama in support of Global Warming then along came the coldest winter in recent decades. Then finally when Obamas EPA poised to levy severe pollutant restrictions and harsh financial penalties on American industry, a volcanic eruption in Iceland devastated the air-transport industry by closing down almost all flights over Europe for a week, which led to bankrupting major airlines, with absent bail-outs by governments. The major natural catastrophes: the recent eruption of Icelands Eyjafjallajokull volcano along with many other including Krakatau, earthquakes, tsunamis, hurricanes, or cyclical changing of atmosphere of ocean, should be enough to warn decision-makers about climate change effects. After experiencing the incident of the Iceland volcano eruption, other than man-kind activities in the reference to global warming and climate change seems warranted. The summer of 1816 is considered to be one of the coldest on record which is studied by many weather scientists. The year is known as the Year without a summer. It is also known as the Poverty Year, due to widespread destruction of crops. Severe climate oddity during the summer destroyed crops in Northern Europe, Northeastern United States and Eastern Canada, and average global temperature decrease was sufficient enough to cause many agricultural failures around the world. The most likely cause of the severe climate change seems therefore, to be the volcanic influences because greatly increased volcanic activity causes immense amounts of ash and dust to be blown and trapped high in the atmosphere, which in turn cause increased reflection of solar radiation (instead of absorption at the Earths surface), resulting in globally decreased te mperatures on Earth. Therefore human activities seem minor and insignificant relative to the power of Nature. (Kolom) How do we know that atmospheric build-up of green house gases is due to human activities? Four lines of evidence prove conclusively that the recent buildup of carbon dioxide take place largely from human activities. The nucleus of carbon atoms in carbon dioxide released by burning coal, oil, and natural gas (fossil fuels) vary in their characteristics from the nucleus of carbon atoms in carbon dioxide emitted under natural conditions. Tens of millions of years ago, coal, oil, and natural gas were formed, and the portion of their nucleus, that was once radioactive, has long ago changed to non- radioactive carbon. However the carbon dioxide released from natural sources on the Earths surface holds a measurable radioactive portion. As carbon dioxide has been emitted through fossil fuel combustion, the radioactive fraction of carbon in the atmosphere has decreased. Forty years ago scientists provided the first direct evidence that burning of fossil fuels was causing a buildup of carbon dioxide and thus reducing radioactive carbon in the atmosphere by measuring the decreasing portion of radioactive carbon-14 captured in tree rings, each year between 1800 and 1950. Moreover, scientists began making accurate measurements of the total amount of carbon dioxide in the atmosphere in any countries by late 1950s. Their data show convincingly that the levels of carbon dioxide have increased each year worldwide and these increases are dependable with other estimates of the rise of carbon dioxide emissions due to human activity over this period. In 1980, third evidence was added that the ice buried below the surface of the Greenland and Antarctic ice caps contains bubbles of air trapped when the ice originally formed. These samples of fossil air have been retrieved by drilling deep into the ice. Measurements from the youngest and most shallow segments of the ice cores produced carbon dioxide awareness to those that were measured directly in the atmosphere at the time the ice formed. But the older parts of the cores show that carbon dioxide amounts were about 25% lo wer than today for the ten thousand years previous to the onset of industrialization. The final evidence comes from the geographic pattern of carbon dioxide measured in air. Observations show that there is slightly more carbon dioxide in the northern hemisphere than in the southern hemisphere. The difference arises because most of the human activities that produce carbon dioxide are in the north and it takes about a year for northern hemispheric emissions to circulate through the atmosphere and reach southern latitudes. (Programme, 1997) Discussion: The debate on climate change is as what really caused the climate to vary with time and which affected us adversely. Some say that climate is changed by natural factors like ocean currents or volcanoes while others deny this fact and try to prove the point that human activities have forced the climate to change. I support the second opinion, human activities indeed made the climate to change and result into global warming. The concentration of Carbon dioxide in the atmosphere has increased from 290ppm in 1880 to 352ppm in 1989 which can be concluded as the 20% increase. This increase is almost certainly a result of human activities (Ruddiman,2003). There has been seen a sufficient increase in the emission of Greenhouse gases due to human activities. For example methane has an estimated rate of emission from human activity on the planet which is 375 million tons per year. For carbon dioxide, there is also an estimated rate of emission from human activity which is 7100 million tons per year. The anthropogenic emissions of these two gases are easier to estimate, because we know approximately how much oil, coal, and natural gas humans produce for consumption around the world each year. We also know approximately how much forest is burned and converted to agriculture each year. According to The state of the environment published in 1991 by the Organization for Economic Co-operation and Development, human activities emit about 68 million tones of nitrogen oxides, 99 million tons of sulfur oxides, 177 million tons of carbon monoxide, and 57 million tones of particulates (dust). However, all these numbers are very approximate. On the o ther hand, sulfur oxides have been found to slightly counteract the greenhouse effect caused by other gases. Still, sulfur oxides are very harmful to the environment and are best known for causing acid rain. Carbon monoxide doesnt contribute to the greenhouse effect, but has significant effects on atmospheric chemistry. Dust is generally thought to cool the atmosphere close to Earths surface, but this effect depends on various factors, including the size and color of the dust particles. (Davis, 2004) The Intergovernmental Panel on Climate Change (IPCC) is a scientific body set up by the UN to look at climate change. It says that human activity is the main cause of the changes seen in climate. Recent reports from the  IPCC have concluded that most of the observed increase in globally averaged temperatures since the mid-20th century is  very likely  due to the observed increase in  anthropogenic greenhouse gas  concentrations. From new estimates of the combined anthropogenic  forcing  due to greenhouse gases,  aerosols, and  land surface changes, it is  extremely likely  that human activities have exerted a substantial net warming influence on climate since 1750. (Uk governements digital service: DirectGov) The most important factor for the climate change is the speeding up of greenhouse effect by manmade activities, which is usually known as Global Warming. Basically, the Greenhouse effect is naturally caused by the emissions of gases like nitrous oxide, carbon-dioxide, methane, ozone and water vapor.  However, anthropogenic activities like burning the fossil fuels and deforestation makes the greenhouse effect stronger. Which means more heat is trapped and the Earths climate begins to change unnaturally. The fossil fuels (coal, oil and natural gas) are burned for various human activities mainly used for transportation, manufacturing, heating, cooling, electricity generation etc. this can be summed up after the industrial revolution, in 18th century, and more of the fossil fuels were being burned frequently. Therefore, manmade gases were being emitted into the atmosphere, mostly in the form of carbon dioxide emissions, from the burning activity. These gases speed up the greenhouse effect, forcing the climate to change. Another factor forced the climate to change and resulted into global warming is the act of deforestation.   Deforestation increases the amount of carbon-dioxide in the atmosphere. Also, due to the disappearance of trees, photosynthesis cannot take place which lowers the oxygen level in the atmosphere. Deforestation is rampant today due to the increase in human civilization. The levels of deforestation have increased by about nine percent in recent times. Moreover, the burning of wood also causes it to decay, therefore releasing more carbon-dioxide into the atmosphere, and carbon-dioxide being the main culprit in global warming increases. Another man-made cause of the increase in the Green house effect due to the emission of such gases is the use of any electrical appliances. Even the refrigerator in the house emits gases which contribute to the Greenhouse effect. These gases are known as Chlorofluorocarbons (CFCs) and are used in refrigerators, aerosol cans, and some foaming agents in the packaging industry, fire extinguisher chemicals and cleaners used in the electronic industry. Some processes of the cement manufacturing industries also act as a cause towards the Greenhouse effect.   Population growth also is an indirect contributor and one of the causes of the Greenhouse effect. With the increase in population, the needs and wants of the people increase. Therefore, this increases the manufacturing processes as well as the industry processes. This results in the increase of the release of industrial gases which catalyze the green house effect. The increase in population also results in the increase of agricultural processes. Most man-made machines, like the automobile also contribute to the green house effect. In one of the recent articles global warming has been linked with the recent natural disasters. As almost fourteen million people have been affected by the torrential rains in Pakistan,  making it a more serious humanitarian disaster than the South Asian tsunami and recent earthquakes in Kashmir and Haiti combined. The disaster was driven by a supercharged jet stream that has also caused floods in China and a prolonged heat wave in Russia. Which comes after flash floods in France and Eastern Europe killed more than 30 people over the summer. Jean-Pascal van Ypersele, vice-president of the body set up by the UN to monitor global warming, the Intergovernmental Panel on Climate Change (IPCC), said the dramatic weather patterns are consistent with changes in the climate caused by mankind. These are events which reproduce and intensify in a climate disturbed by greenhouse gas pollution, he said, Extreme events are one of the ways in which climatic changes become dramatically visible. Professor Andrew Watson, a climatologist at the University of East Anglia, which was at the centre of last years climate gate scandal, said the extreme events are fairly consistent with the IPCC reports and what 99 per cent of the scientists believe to be happening. Im quite sure that the increased frequency of these kinds of summers over the last few decades is linked to climate change, he said. (Gray) However , authors such as  Lean and Rind (1996)  believe that, although natural factors may be the reason for most temperature increase before the Industrial Revolution, the most likely cause of climate change since about 1850is the growing concentration of greenhouse gases as the net atmospheric temperature increase, or forcing is largely due to human (anthropogenic) activities .Interestingly, particulate emissions from volcanoes produce a net decrease in global temperatures, due to the reflective properties (albedo) of the sulfate aerosol particles formed in the stratosphere. (Bianchi, 2010) Conclusion: The earths climate is dynamic and always changing through a natural cycle but the anthropogenic activities make this cycle speed up unnaturally that create problems in the atmosphere as either the earth gets oddly warmer or the people have to face natural disasters. However if man has created all these problems, he should also try to make things better by finding practical solutions.

Presentation on Bioplastics :: Environment polypropylene renewable resources

Presentation on Bioplastics Bioplastics, What are they? * Compostable Plastics -or- * Any plastics-made from organisms (or Organism by-products). * Currently, there is much confusion over the definition of bioplastics Mixture of Acids that could be made into bioplastics Making Bioplastics, Etc. Goal of Bioplastic Production * To Save Resources by either reducing the production of standard Polypropylene plastics by replacing it with a less resource-intensive plastic. * Or Save the Environment by making plastics biodegradable * Or, both! Bioplastic degradation speed What are Scientists Doing Now? Several Different Exciting Methods are being tried right now! * Using Soy-based bioplastics * Using Bacteria to make bioplastics * Starch-based Bioplastics * Polylactide Bioplastics * Poly-3-Hydroxybutyrate Current Cost of Bioplastic Comparison Soy-based Bioplastics One of the hottest sections in bioplastics research today. Pure Soy Bioplastic has many undesirable traits. Mixtures of Soy with other substances are currently being attempted. The Soy shown Soy Protein Bacteria-based Bioplastics Steven Pratt of New Zealand (Major New Discovery) Mixture of bacteria can create acids when fermented. The ratio of different acids is based on pH. The bacteria are fed glucose solution and fermented. The acids can be used to make bioplastics Starch-Based * Make up about 50% of the current bioplastic market * Are used in pills that you take * Can be specificially tailored by adding different amounts of plasticizers * This is called â€Å"thermo-plastical starch† Polylactide Bioplastics * Lactic acid is turned into Polylactide by adding a catalyst and heat. * Polylactide bioplastics can be made on existing petroleum plastic equipment * Resembles plastic in properties Poly-3-Hydroxybutyrate * A polyester * Easily biodegradable * Easily processed * Currently very expensive * Current interest is very high * Methylobacterium sp V49 is one bacteria that produces Poly-3-Hydroxybutyrate Challenges Facing Bioplastics * Economically Unfeasible * Biodegradability is a useful and a not-so-useful property

Commercial transactions essay

Therefore, she has no duty of care to Frank and Beeline, while Douglas Pity Ltd, as a professional company has a duty of care to them. Sub Issue 1. 3 and 1. 4: although Black was employed by Brown & Co, it can be reasonably assumed that he wasn't given actual authority to give advice to someone out of his accounting firm, nor was there any implied authority for Black to let him give advice on his employer's behalf. By the way, it was reasonable to expect that Frank and Beeline would act on Black, a professional accountant's advice to sign the purchase contract. Therefore Black has a duty of care o Frank and Beeline, but Brown & Co does not.Issue 2 & Sub Issue 2. 1 and 2. 2: Frank and Beeline cannot sue Marie, but they can make an action against Douglas Pity Ltd. If they can prove that Marie has provided negligent misstatement about the motel business, such as phone call records, they can ask Douglas Pity Ltd to pay part of their losses. They also need to prove that Douglas Pity Ltd h as breached their duty of care to them. Sub Issue 2. 3 and 2. 4: When everything was ready Frank said that they could not sign the contract unless Black gave them advice to sign it. Black, a professional accountant indicated them to do so.Therefore, Brown & Co is not liable for Frank and Bellini's damage, but Black is, because Black has breached his duty of care to Frank and Beeline. CONCLUSION Under the tort of negligence, both Douglas Pity Ltd and Black are liable for Frank and Bellini's losses. Frank and Beeline can sue them and if they can prove that Douglas and Black had given negligent misstatement about profitability of the motel business. For instance, Frank and Beeline need to provide evidence that Black had given unachievable occupancy rate of the motel. However, Frank and Beeline cannot themselves and they were not entirely relying upon Blacks advice.For example, Frank and Beeline didn't enquire Black whether the occupancy rates given by him was practical or not. Overall, the chance of successfully getting remedies from Black is the largest, while there is also a reasonable chance to win the case against Douglas Pity Ltd. Frank and Beeline can expect to recover $ 15000 from Douglas Pity Ltd, $ 25000 from Black, but the remaining part of their loss, approximately $ 35000 are their own liabilities. By the way, it would be very difficult for Frank and Beeline to receive any remedy from Marie and Brown & Co even if they chose to sue them.

What Is the Least Squares Regression Line

A scatterplot is a type of graph that is used to represent paired data. The explanatory variable is plotted along the horizontal axis and the response variable is graphed along the vertical axis. One reason for using this type of graph is to look for relationships between the variables.​​ The most basic pattern to look for in a set of paired data is that of a straight line. Through any two points, we can draw a straight line. If there are more than two points in our scatterplot, most of the time we will no longer be able to draw a line that goes through every point. Instead, we will draw a line that passes through the midst of the points and displays the overall linear trend of the data. As we look at the points in our graph and wish to draw a line through these points, a question arises. Which line should we draw? There is an infinite number of lines that could be drawn. By using our eyes alone, it is clear that each person looking at the scatterplot could produce a slightly different line. This ambiguity is a problem. We want to have a well-defined way for everyone to obtain the same line. The goal is to have a mathematically precise description of which line should be drawn. The least squares regression line is one such line through our data points. Least Squares The name of the least squares line explains what it does. We start with a collection of points with coordinates given by (xi, yi). Any straight line will pass among these points and will either go above or below each of these. We can calculate the distances from these points to the line by choosing a value of x and then subtracting the observed y coordinate that corresponds to this x from the y coordinate of our line. Different lines through the same set of points would give a different set of distances. We want these distances to be as small as we can make them. But there is a problem. Since our distances can be either positive or negative, the sum total of all these distances will cancel each other out. The sum of distances will always equal zero. The solution to this problem is to eliminate all of the negative numbers by squaring the distances between the points and the line. This gives a collection of nonnegative numbers. The goal we had of finding a line of best fit is the same as making the sum of these squared distances as small as possible. Calculus comes to the rescue here. The process of differentiation in calculus makes it possible to minimize the sum of the squared distances from a given line. This explains the phrase â€Å"least squares† in our name for this line. Line of Best Fit Since the least squares line minimizes the squared distances between the line and our points, we can think of this line as the one that best fits our data. This is why the least squares line is also known as the line of best fit. Of all of the possible lines that could be drawn, the least squares line is closest to the set of data as a whole. This may mean that our line will miss hitting any of the points in our set of data. Features of the Least Squares Line There are a few features that every least squares line possesses. The first item of interest deals with the slope of our line. The slope has a connection to the correlation coefficient of our data. In fact, the slope of the line is equal to r(sy/sx). Here s x denotes the standard deviation of the x coordinates and s y the standard deviation of the y coordinates of our data. The sign of the correlation coefficient is directly related to the sign of the slope of our least squares line. Another feature of the least squares line concerns a point that it passes through. While the y intercept of a least squares line may not be interesting from a statistical standpoint, there is one point that is. Every least squares line passes through the middle point of the data. This middle point has an x coordinate that is the mean of the x values and a y coordinate that is the mean of the y values.