Qnt 561 wk6
Qnt 561 wk6
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Date Created: 11/14/15
Week 6 Team D Discussion Regression Analysis QNT561 November 28 2011 Jonathan Edelman Week 6 Team D Discussion Regression Analysis The following paper summarizes the review and discussion process undertaken by Team D examining four articles that each detailed one or more applications of regression analysis Comparison Methods of Multiple Linear Regressions in Fish Landing Multiple linear regression MLR is used to analyze the relationship between a single response variable dependent variable and two or more controlled variables independent variables The main objective of the paper 39Comparison Methods of Multiple Linear Regressions in Fish Landing39 written by Ghani lntan and Sabri 2011 is to make comparisons between independent variables and marine sh landing Data is taken from Fisheries Annually Statistics of Department of Fisheries Malaysia focusing on the marine sh landing in Terengganu during the 40 year period of 1968 until 2007 Many researchers have conducted research about sh leveraging MLR In 2009 researchers Ahmad and Mamat conducted MLR research to identify the key factors correlated with a youth39s interest in becoming a sherman MLR revealed that the three factors most strongly correlated with respondents interest in a shing career were training programs pro t and marketing Ghani lntan and Sabri 2011 chose to leverage MLR for their research given the presence of more than two controlled variables In their research marine sh landing Y was the response variable and shermen X1 shing boats X2 and shing gear licensed X3 were controlled variables Evaluating every possible regression can be burdensome To make the process less cumbersome stepwisetype procedures have been developed Three methods categorized as stepwisetype procedures are forward selection backward elimination and stepwise regression The forward selection method aims to add controlled variables one at a time into the MLR equation based on the speci ed AlphatoEnter The backward elimination is similar but instead starts with an MLR equation containing all of the variables and removes one at a time based on the speci ed AlphatoRemove The stepwise regression method is a mixture of forward selection and backward elimination These three methods were applied in the study to compare the strength of correlation for the methods involved to sh landing and were analyzed using Minitab 15 and Statistical Package for the Social Sciences 170 SPSS 170 Interpretation of the MLR analysis was also done using Minitab 15 and SPSS 170 software Controlled variables selected by each method of MLR analysis were concluded as follows Table V Methods Controled Variables Selected Forward selection Fishermen and Fishing gears licensed Backward elimination Fishermen and Fishing gears licensed Stepwise regression Fishermen and Fishing gears licensed Table V shows that the result of each the MLR methods was X1 and X3 being most strongly correlated to variances in marine sh landing The researchers also performed residual analysis The three methods are the same therefore residual analysis is used which helps to know whether the mean of the three methods is the same The following hypothesis H0 and alternative hypothesis H 1 were developed and tested H0 The means of all the methods are equal H1 The means of all the methods are not equal Table VI ANOVA table Sum of Squares df Mean Square F ISig l Between Groups 0001 2 0001 0000 1000 Within Groups 1135E11 117 9699432101 Total 1135E11 119 Table VI shows an ANOVA table using SPSS which showed that the signi cant level 1000 is higher than an alpha of 005 meaning that the researchers failed to reject the null hypothesis which states that the means of the three methods are equal This signi es that all methods have the same result and can be used in this study Pollution Assessment in River Water A 2011 study by researchers Agarwal and Saxena studied the amount of pollution present in the water of two rivers surrounded by several cities with thriving industries The authors attempt to nd a correlation between the levels of untreated waste emitted by industries and the corresponding amounts of pollution present in the water in the form of biological oxygen demand BOD and chemical oxygen demand COD The authors develop a regression equation to de ne the levels of pollution and predict later pollution levels based on changes in untreated chemical emissions Based on the data presented in the study Agarwal and Saxena made excellent and correct use of the regression analysis equation to de ne the correlation between resulting BOD and COD levels in the water and the water alkalinity The data from their measurements was put into tables and introduced in scatter plots The equations were developed using the least squares method The study and resultant equation were simple and straightforward and may bene t decision makers in the Moradabad area of India better equipping them to make decisions regarding how much untreated waste a company can emit without exceeding the allowable level of pollution in the Moradabadarea rivers Agarwal and Saxena should expand the study to determine if there are factors other than industrial waste that are polluting the rivers Additionally the study could examine river pollution levels as an independent variable seeking to identify what conditions or lifeforms may be affected as a result of river pollution levels For instance the study might seek to treat crops damage as a dependent variable and water pollution levels as an independent variable Another example would be treating health levels of the population as a dependent variable The level of correlation between river pollution levels and these dependent variables should also be studied Racial Discrimination within the DEA Segar v Civiletti is a class action lawsuit brought against the United States Drug Enforcement Administration DEA in 1981 alleging racial discrimination against AfricanAmerican special agents of the DEA in violation of Title VII of the Civil Rights Act of 1964 In this case the plaintiffs relied heavily on regression analysis to quantify their claims that the DEA was engaging in racially discriminatory practices against AfricanAmericans in a recruitment and hiring b initial grade assignments c type of appointment d type of work performed e training f discipline g supervisory evaluations h awards and promotions and i salary United States District Court District of Columbia 1981 The plaintiffs found that as ofJanuary 1 1975 AfricanAmerican DEA employees earned a mean salary of 17637 while white employees earned a mean salary of 20604 This knowledge prompted regression analysis that treated salary as a dependent variable and examined the correlation between salary level and four independent variables 1 years of federal experience 2 years of nonfederal experience 3 level of educational attainment and 4 race Using data observations for DEA employees hired before and after 1972 and a calculated race coef cient accounting for differences in education and experience that was the amount AfricanAmerican agents were paid less than white agents the following results were obtained pic In the above summarized results the tratio are a measure of the statistical signi cance of the study there is less than 1 in 1000 chance that the discrepancies in salary can be explained by chance The same regression analysis was conducted only for agents hired after 1972 since Title VII is applicable to the DEA only for post 1972 discrimination This second iteration produced the following results pic In every year except 1975 there was less than a 1 in 20 chance that salary discrepancies could be explained by chance the results are statistically signi cant at the 05 level for 19761978 The defendants the DEA predictably attempted to attack the validity of the regression analysis conducted by the plaintiffs One method that the defendants used to question validity was to calculate quotR2quot values or coef cients of multiple determination Lind Marchal and Wathen 2008 state that the quotR2quot value is a measure of quotthe percent of variation in the dependent variable Y explained by the set of independent variables X1 X2 X3 p 521 Because the quotR2quot values in this study ranged from only 021 to 052 the defendants argued that 1 years of federal experience 2 years of nonfederal experience 3 level of educational attainment and 4 race were not strongly correlated to salary levels and speculated that in ation and DEA promotion standards were better correlated to variance in salary levels United States District Court District of Columbia 1981 However the United States District Court District of Columbia 1981 found quotthe R2 values of the analyses are not so low as to adversely affect the veracity of Plaintiffs39 studiesquot para n Ultimately the court ruled in favor of the plaintiffs regarding their claims of discrimination in a salary b grade at entry c work assignment d supervisory evaluation e discipline and f promotion Determinants of Serum PCBs in Adolescents and Adults Regression tree analysis is a nonparametric testing method which uses various predictors to determine an outcome In the article quotDeterminants of Serum PCBs in Adolescents and Adults Regression Tree Analysis and Linear Regression Analysisquot the authors detailed their use of regression tree analysis to determine what predictors most strongly affected the concentration of polychlorinated biphenyl PCB in humans in a speci c Belgian region Govarts Hond Schoeters and Bruckers 2010 discussed the tested independent variables stating quotPotential predictor variables were collected via a selfadministered questionnaire assessing information on lifestyle food intake use of tobacco and alcohol residence history health education hobbies and occupationquot para 2 The authors compared testing methods and results from nonparametric multiple regression models and linear regression models The tests were developed using various biomarkers based on physical characteristics and environmental in uences of subjects ranging in age from 14 to 15 years of age and from 50 to 65 years of age Govarts et al 2010 Based on literature research and data collected from the questionnaires 84 variables were chosen to introduce into a regression tree and a multiple linear regression analysis Govarts et al 2010 The regression tree was developed using dependent variables divided and subdivided based on correlation of inputs Linear regression models were developed for testing the adolescent group and adult group independently Linear regression covariates were tested using a ten percent level of signi cance and were tted with and without outliers to determine the level of in uence for both Test results concluded using the regression tree the body mass index predictor contributed to nearly half the signi cance of PCB levels in adolescents and blood fat content was the major predictor for adults Comparison of the regression tree method and multiple linear regression methods concluded the same predictors were signi cant for both methods The study concluded linear regression methods parametric methods may create skewed data when normality consistency and randomness are not completely satis ed thus nonparametric methods should be used Govarts et al 2010 Conclusion This paper summarized the review and discussion process undertaken by Team D examining four articles that each detailed one or more applications of regression analysis References Agarwal A amp Saxena M 2011 Assessment of pollution by Physicochemical Water Parameters Using Regression Analysis A Case Study of Gagan River at Moradabad lndia Advances In Applied Science Research 22 185189 Ghani lntan M M amp Sabri A 2011 Comparison Methods of Multiple Linear Regressions in Fish Landing Australian Journal of Basic and Applied Sciences 51 2330 Govarts E Hond E amp Schoeters G 2010 Spring Determinants of serum PCBs in adolescents and adults Regression tree analysis and linear regression analysis Human and Ecological Risk Assessment 165 Lind DA Marchal WG amp Wathen SA2008 Statistical techniques in business and economics 13th ed Boston McGrawHilllrwin Segar v Civiletti 508 F Supp 690 Dist Court Dist of Columbia 1981
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