Slope of Regression Line and Correlation Coefficient

Many times in the study of statistics it is important to make connections between different topics. We will see an example of this, in which the slope of the regression line is directly related to the correlation coefficient.  Since these concepts both involve straight lines, it is only natural to ask the question, How are the correlation coefficient and least square line related?   First, we will look at some background regarding both of these topics. Details Regarding Correlation It is important to remember the details pertaining to the correlation coefficient, which is denoted by r. This statistic is used when we have paired quantitative data. From a scatterplot of this paired data, we can look for trends in the overall distribution of data. Some paired data exhibits a linear or straight line pattern. But in practice, the data never falls exactly along a straight line. Several people looking at the same scatterplot of paired data would disagree on how close it was to showing an overall linear trend. After all, our criteria for this may be somewhat subjective. The scale that we use could also affect our perception of the data. For these reasons and more we need some kind of objective measure to tell how close our paired data is to being linear. The correlation coefficient achieves this for us. A few basic facts about r include: The value of r ranges between any real number from -1 to 1.Values of r close to 0 imply that there is little to no linear relationship between the data.Values of r close to 1 imply that there is a positive linear relationship between the data. This means that as x increases that y also increases.Values of r close to -1 imply that there is a negative linear relationship between the data. This means that as x increases that y decreases. The Slope of the Least Squares Line The last two items in the above list point us toward the slope of the least squares line of best fit. Recall that the slope of a line is a measurement of how many units it goes up or down for every unit we move to the right. Sometimes this is stated as the rise of the line divided by the run, or the change in y values divided by the change in x values. In general, straight lines have slopes that are positive, negative or zero. If we were to examine our least-square regression lines and compare the corresponding values of r, we would notice that every time that our data has a negative correlation coefficient, the slope of the regression line is negative. Similarly, for every time that we have a positive correlation coefficient, the slope of the regression line is positive. It should be evident from this observation that there is definitely a connection between the sign of the correlation coefficient and the slope of the least squares line. It remains to explain why this is true. The Formula for the Slope The reason for the connection between the value of r and the slope of the least squares line has to do with the formula that gives us the slope of this line. For paired data (x,y) we denote the standard deviation of the x data by sx and the standard deviation of the y data by sy. The formula for the slope a of the regression line is: a r(sy/sx) The calculation of a standard deviation involves taking the positive square root of a nonnegative number. As a result, both standard deviations in the formula for the slope must be nonnegative. If we assume that there is some variation in our data, we will be able to disregard the possibility that either of these standard deviations is zero. Therefore the sign of the correlation coefficient will be the same as the sign of the slope of the regression line.

Native Americans And The United States Essay - 2035 Words

It is no secret that many minority groups in America experience challenges that the average American is not subject to, but Native Americans, who live on reservations, experience a unique set of social hardships. Many of these hardships are due to the fact that they live on reservations where resources and esteem are scarce, but in order to preserve cultural identity and sovereignty, many natives believe it is not only their right to live on reservations, but their duty. Likewise, it is a duty of the United States government to provide these people, who have experienced a protracted history of violence and oppression at government’s hands, with the resources they need in order to live fruitful and happy lives. Native Americans are a group of peoples who deserve appreciation and dignity, but also a group who is struggling to survive as a result of the harm our nation has caused them and it is for this reason, we must increase assistance to natives on reservations. Opponents of efforts to increase aid for natives on reservations argue that if natives want a better life, they should move off the reservations and assimilate into American culture. They believe this would eliminate the problems natives face on reservations because natives would be living as normal American citizens. Although this may diminish a select few of the challenges natives face on reservations, it creates a whole new set of issues relating to Native Americans’ rights to sovereignty and the actuality ofShow MoreRelatedThe United States And Native Americans Essay1300 Words   |  6 PagesThe history between Native Americans and Americans is harsh. Native Americans have been pushed off of their land by Americans and put into smaller reservations. The united states have enforced a number of treaties trying to better the relationship but it has oppressed Natives. Recently the united states were plaining to build an oil pipeline that would run through native land and the native Ame ricans did not want the pipeline to be built. So this created more tension between the two. History ofRead MoreNative Americans And The United States Essay1671 Words   |  7 Pagesand early Americans have pushed away Native Americans. Natives were not only thrown into an unknown land, but were also killed in large numbers while changing their culture trying to fit in. The United States was nothing but rude to these people who owned the land centuries before the first Englishman ever stepped foot in America. The United States destroyed these societies to shreds without ever really giving them a good chance to live among the Americans. I believe the United States should haveRead MoreNative Americans And The United States1443 Words   |  6 PagesMany people think that the African-Americans are the most oppressed group of people ever in the United States. 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For thousands of years, Native Americans had roamed around the Americas. There had also been many tribes spread across the West that fought between each other in order to have their land.1 It wasn’t until after reconstruction in the United States, that the white Americans started having ordeals with the Native Americans. The main tribes involvedRead MoreThe Great Impact On Native American Nation And The United States Of America1767 Words   |  8 Pagesdisagreements, disrespect, feuds, or even over the smallest of matters. For example, one of the biggest feuds in American history that just ended recently was between the Hatfield’s and McCoy’s. This just shows you how petty, ignorant, and uncivilized we as a people can become. However, the greatest and most crucial feud of all was between the entire Native American Nation and the United States of America. This war of hate and disrespect towards tribes of people and their culture is uncalled for and has

Compare Contrast Free Essays

In And After The War Young men who are sent to a war learn the reality in a very harsh and brutal way. Both the stories, ‘The Red Convertible’ and ‘The Things They Carried’ portray the life of a young soldier and how he psychologically gets affected from all the things he had seen in the war. Tim O’Brien’s ‘The Things They Carried,’ is more specific on the experiences of a soldier during a war where as Karen Louise Erdrich focuses more on describing the post war traumatic stress in her short story ‘The Red Convertible’. We will write a custom essay sample on Compare Contrast or any similar topic only for you Order Now One thing similar in both the narrations is the Vietnam War and its consequences on the soldiers. From the background of both the authors it’s easy to conclude that Tim O’Brien being a war veteran emphasizes more on the war scenes where as Louise Erdrich focuses mainly on the life inside the reservations, which makes sense as she has a Native American ancestry. In both the stories authors show amp; compare the human emotions of a soldier before and after he gets drafted into a war. In ‘The Things They Carried,’ the story revolves around a twenty two year old First Lieutenant Jimmy Cross, a fresh graduate from New Jersey who is drafted and sent into the Vietnam War. Tim O’Brien does a true justice to the title of the story and emphasizes on the physical strength of the soldiers, and how it gets tear down with all the situations they have been put through. At one point of the story he describes soldiers carrying mementos and objects for good luck superstitiously. For an instance, Dave Jensen one of the soldiers carried a rabbit’s foot and Norman Bowker carried a thumb that had been presented to him as a gift from a soldier of the same platoon, Mitchell Sanders. He also successfully portrays the confused state of mind of a soldier, during the conversation between Henry Dobbins and Mitchell Sanders about the reason behind Sanders cutting off a thumb from a dead corpse of a fifteen or sixteen year old boy. Mitchell tries to make Henry understand that there was a moral behind what he did but Henry walks off speaking sarcastically and unconvinced. In Karen’s ‘The Red Convertible,’ the story is narrated by Lyman Lamartine who is the younger brother of Henry Junior who had just got back from Vietnam after the war was over. The whole story is narrated in a flashback unlike Tim’s ‘The Things They Carried’ where the story moves back and forth in time. For example when the author describes the things that the soldiers carried in the very beginning of the story, he mentions Ted Lavender carrying six or seven ounces of premium dope until he was shot. Karen emphasizes more on the relationship between brothers and compares the state of mind in which they were before and after the war. The younger brother Lyman hadn’t changed much where as the elder brother Henry was completely a different person after he got back from Vietnam. In both the stories authors have successfully shown the life of a young and happy bachelor until he was drafted to the war and then things changed drastically. In ‘The Things They Carried,’ author narrates Lieutenant Jimmy Cross as a romantic young boy who would carry letters from a girl named Martha. He knew there was no such thing as love between them but he would still be hopeful that things might work out his way after the war is over and when he is sent back home. In the later part of the story after one of his soldier dies, he blames himself for what had happened. Though it can be argued that it wasn’t completely his fault but that’s what being in war can do to you. Whereas in ‘The Red Convertible’ author describes the life of the two brothers before and after the war without emphasizing much on what had happened during the war. In the whole story, the red convertible is used as a symbol of Henry and Lyman’s relationship. This is why I think Lyman drives the car into the lake, so he can bury all the memoirs which he had shared with his elder brother Henry. With this act, the author might want to show that Lyman wanted to move on with his life and which is why he drowned the car into the lake after Henry jumped in. After reading both the stories one might say that ‘The Things They Carried,’ emphasizes on the life of a soldier in the war and ‘The Red Convertible’ can be a continuation of the soldier’s life after the war is over and he comes back home. In ‘The Things They Carried’ the reader would observe the emotional stress a soldier goes through during the war. In essence, ‘The Red Convertible’ shows how these emotional stresses can be suicidal later in a soldier’s life. How to cite Compare Contrast, Papers

Emerging and Practical Areas for Runtime Process - MyAssignmenthelp

Question: Discuss about theEmerging and Practical Areas for Runtime Process. Answer: Introduction This paper is a discussion reviewing the article, Business Process Management: 13th International Conference, BPM 2015, Innsbruck, Austria, August 31-September 3, 2015, Proceedings. The main purpose is to assess the undertakings of the 13th International Conference on BPM in 2015. Other articles are also used in supporting the main article in discussion to prove the credibility of the main article. This conference gave an international forum where researchers from all walks met and exchanged their views on the topics in research and also the results of the business process management. The BPM 2015 was presented by the University of Innsbruck in Austria and that happened from August 31st to September 3rd. The rest of the paper gives the account of all what happened during this conference. In this BPM 2015 conference, the researchers present gave over one hundred and twenty submissions. All of the submissions touched on the emerging and empirical areas of BPM. These submissions were rechecked by a procedure including 17 high-ranking Program Committee associates and also 75 PC affiliates. Thirty papers were accepted in total and there were 21 full papers with a 17% acceptance rate. There were also double trade papers with a general recognition rate of 24 percent. The paper aims at giving an examination of the improvement of the empirical exploration in the BPM. The paper also seeks to study the tendencies in the empirical BPM research and all the practices applied by way of an advanced background so as to identify the standing quo and to review the probable future development of the research. During this conference, there were suggestions encouraged. First, an investigation that demonstrates the interdisciplinary landscape of BPM and links with disciplines such as administration and managerial discipline, information systems, date, and information organization, social computing and service-leaning work out. The other research that was encouraged is that which examines the emerging areas of BPM and the application of concepts and methods. The main topics discussed in this paper are: Runtime Process Management The redesign of business processes according to BPM (Conference), Motahari-Nezhad, Recker Weidlich (2015) has a big prospective regarding the lowering of the courses expenditures with throughput periods and also in boosting customers satisfaction. A mere process design enterprise is comprised of a description of the as-is process. The analysis of the as-is situation helps to locate the process flaws and to generate process boosting ideas. In this article, it is said that practitioners typically use a lot of time in the explanation together with the examination of the present situation and the procedure of improving ideas mostly generated in a few workshops by the use of traditional creativity techniques mainly brainstorming. These techniques do not have guidance pertaining the type of process choices that are worth considering and they hardly give an answer for the individual inactivity to look for replacements to ensure that they are not similar with other directions. According to (Rosing, Scheel Scheer,2014), a typical process design business is composition of the description of the current process as brought out by the main article in the review. Process Modelling This refers to the description, diagram and the structural representation that explains the undertakings of a particular organizational unit (BPM (Conference), et al., 2015). Under this topic, model grounded and text based course explanations have their individual certain fortes and which charm to their shareholders. By this, it is unlikely to discover in an association descriptions of similar commercial practices in equal manners. While putting into descriptions that many of such portrayals that may perhaps be used in certain organizations by dozens of people that use different editors, there is likelihood that the risk of these representations turn into lop-sided. To minimize the period and exertion required so as to correct those circumstances, this article, grants a primary tactic to identify by design the discrepancies that arise amid the textual description with the process model. The paper also leverages the normal linguistic dispensation practices to highlight the circumstanc es where the binary procedure representations examine the undertakings in various guidelines. (Vom Schmiedel,2015) also states in process modelling, it is not easy to incorporate both business processes mode as mentioned above. Process Model Discovery I Under this, the process of mining can give a very important information for the improvement of process models and the process management, the business process execution majorly follows some pre-designed process models. These process models as brought out by (BPM Conference, et al. 2015) are mainly a following by many of but not all process executions because business processes many times undergo exceptional circumstances where the detour of to the available process models is important. The businesss needs to recheck the process models according on the previous logged executions so as to guide majority of future workflow executions. The process model enhancement benefits from the techniques from the process of mining and the process analysis. The practice mining methods are put into use to determine procedure representations from the occasion records. Various discovery techniques are suggested so as to attain a procedure model imitating a performance given in the occasion records. The processes that have been discovered may differ considerably in accordance with the chosen method discovered. The main problem with the process model discovery is constructing adequate formal model that reflects the behaviors represented in an event long in the best possible means. As brought out by (Riemann,2015), it is true that businesses should recheck their process models to ensure that they are guided in the future executions. Business Process Models and Analytics Business process models and analytics gives process participants. Related stakeholders and decision makers with insight about the effectiveness and the efficiency of the organizational process. This insight is motivated by the performance considerations. From the compliance viewpoint, (BPM Conference, et al. 2015) states that the intention of procedure analytics is the reduction of the response period of stakeholders to the proceedings could alter the variations in the routine process then to also permit for an additional instant valuation of the implication of the procedure administration choices on procedure metrics. There are many reasons for measuring the various facets of commercial procedures. First is to assess all that has occurred over the past, to comprehend whatever is occurring in the moment, and draft a comprehension of all that might happen in future. (Rosing,2014) also mentions that the analytics process is intended to minimize the stakeholder-time response to any alte rations in the performance process. BPM in Industry With the expansion in the various Workflow Management Systems (WfMSs) organizations undergo difficult decisions when choosing a suitable means on behalf of their Business Process Management (BPM) schemes (BPM Conference, et al., 2015). The major alterations between WfMSs are: the sustained controllable modeling dialects, the integration with outside tools and systems (such as Web-service APIS for business intelligence and monitoring), their robustness, their performance, non-functional requirements and operational costs. There is need to assess the different WfNSs in accordance with the runtime routine of the commercial course implementation through their Workflow apparatus. By making that assessment, it will largely help in empowering the adopters of BPM so that they can map their needs to the existing solutions and so that also the vendors of BPM and their developers can increase their technological giving. The framework for the benchmarking of BPMN particularly the WfMSs makes sur e that the benchmarking process is reliable. The framework also makes sure that it structurally defines and controls the setting in which the routine processes remain conducted plus their outcomes studied. As per (Vom et al., 2015), the businesses need to evaluate various WfNSs based on their runtime performance of their BP. Process Compliance and Deviations The biggest challenge in any business is ensuring it conforms its business undertakings to the rules that have been imposed. This may comprise of many perspectives of the business process that includes data, resources, time, control flow and the interactions of the business stakeholders (BPM Conference, et al.,2015). The process of business compliance cannot be fully arrived at during the design time although it needs to be checked regularly during the process of runtime too. The article has presented a wide-ranging outline for checking the commercial course submission visually. In opposition with other methods, the outline gives support the graphic observing of entirely important course standpoints according to the protracted Compliance Rule Graph linguistic. This doesnt only permit for detection of acquiescence abuses but then again visually pinpoints the grounds too. Lastly, the context helps in assessing the commercial progression obedience and making sure that the business proce ss is running smoothly. (Riemann, 2015) suggests that businesses cannot arrive at the process of business compliance in design time. The correctness concerns of the corporate procedure prototypes have increasingly remained deliberated for over an era. The initial grind was majorly on the syntactical accuracy together with the reliability problems such as the nonexistence of life locks and deadlocks. The obedience of the commercial procedures through the semantic bottlenecks have stayed considered progressively over the ages. Basically, the acquiescence rubrics branch from requirements that are sphere exact for instance the legal regulations and corporate standards. All these must be considered throughout the stages of the procedure development. The approaches that deals by way of the submission of commercial procedures in the event of their execution are taken care of by the compliance monitoring. Emerging and Practical Areas of BPM Technology in a BPM Perspective According to (BPM Conference, et al. 2015), technology in a BPM perspective pertains the vital significance that technology undertakes in then generation of value and also the underpinning of the BPM philosophy by providing a framework that leads an enabling reign of monitoring, traceability and optimization. It also makes sure that businesses develop various scenarios and draft the right adjustments immediately and more effectively thereby making sure that they contribute in competitive advantages. Additionally, technology gives the needed avenue to translate objective choices into rigid plans of actions and allowing the businesses to become more proactive. The aim of BPM is mainly to boost the employee and customer value by efficient, innovative and flexible processes. In such process managed businesses, it is more about the transformation of the business then about technology. It is a misunderstanding to view BPM as a label for new technology. It is purported that technology has a ssisted businesses establish effective business processes. Process Monitoring The business processes are often subjected to unexpected and continuous adjustments. The process employees may start undertaking the process differently so as to cope with the changes in season, workload, regulations and guidelines for instance (BPM Conference,et al., 2015). Detecting the business process early in accordance with the event logs-in other terms called process drift detection, makes it possible for analysts to locate and act upon the adjustments that may in turn impact negatively on the business performance. The earlier methods for the detection of commercial procedure drift are grounded on an examination of a hypothetically bigger piece space and some other circumstances, the operators are required to physically detect the certain structures that come with the gist. Subject to the discovered piece set, the techniques might slip some specific variations. This article has a statistically chastised technique aimed at the detection of the drift. The above article is suppor ted by (Rosing et al., 2014), whereby early detection of business process drift helps them make the right changes so that they are not affected by them. The main idea is to conduct a statistical experiments over the allocation of the runs seen in two successive time spaces. By adapting a sizing space, the method slowdowns a trade-off between the cataloguing accuracy and drift detection interruption. A validation on a real life and synthetic logs indicate that the method precisely detects typical patterns of change and rules up to the extent it is appropriate for wired drift discovery. Conclusion In conclusion, this paper is a review of the article Business process management: 13th International Conference, BPM 2015, Innsbruck, Austria, August 31-September 3, 2015, Proceedings, by BPM (Conference), Motahari-Nezhad, Recker Weidlich. The review is supported by other three articles on the topic BPM to bring out the credibility of the main article. Bibliography BPM (Conference), Motahari-Nezhad, H. R., Recker, J., Weidlich, M. (2015).Business process management: 13th International Conference, BPM 2015, Innsbruck, Austria, August 31-September 3, 2015, Proceedings. https://dx.doi.org/10.1007/978-3-319-23063-4. Riemann, U. (2015). Benefits and Challenges for BPM in the Cloud.International Journal of Organizational and Collective Intelligence (IJOCI).5, 32-61. Rosing, M. V., Scheel, H. V., Scheer, A.-W. (2014).The complete business process handbook: body of knowledge from process modeling to bpm. Volume I Volume I. https://public.eblib.com/choice/publicfullrecord.aspx?p=1888539. Vom Brocke, J., Schmiedel, T. (2015).BPM - Driving Innovation in a Digital World. https://proxy.uqtr.ca/login.cgi?action=loginu=uqtrdb=sciencedirezurl=https://dx.doi.org/10.1007/978-3-319-14430-6.