Regression Theory Methods and Applications †MyAssignmenthelp.com

Question: Discuss about the Regression Theory Methods and Applications. Answer: Introduction This report shows the relationship between the GDP and the port traffic. To estimate the relation, a regression analysis is conducted to determine the slope coefficient. With the help of a regression equation, it can be determined that to what extent the traffic changes depending upon the increase and decrease in GDP. The report also includes that to what extent traffic will be affected by a 2% increase in GDP. Regression analysis has been performed in order to solve the same. A GDP of a country will adversely affect its port traffic data. An increase in GDP will increase the traffic in the country. It is very important for the government to get its facts clear about GDP in order to determine traffic growth management. A proper method is used to conduct the research and to find out the relationship between GDP and port traffic. Following variables are selected to perform a regression analysis. X: it is an independent variable. As per the data, GDP is taken as an X variable. Y: it is an dependent variable and the given traffic data is considered to be Y because it depends upon the changes in GDP A method of regression analysis is used in order to find the relationship between GDP and port traffic data. A general regression equation is Y=A+Bx (Seber Lee, 2012). Y is the dependent variable, which is to be predicted. A stands for alpha or constant. The value of Y is equal to A, when X is equal to zero. B means beta is the coefficient of X or the slope of regression line. X is the independent variable, on which value of Y depends (Sen Srivastava, 2012). In context to world The relation between GDP and traffic data of the world is identified by using regression analysis. A regression equation is formed on the basis of which results are derived. A general regression equation is Y=A+Bx (Seber Lee, 2012). The below data relates to the GDP of overall world from 2005-2015 including several countries. Although the data for port traffic is given from 1996-2016 but for comparison, traffic data has been taken for the same period as of GDP. Data: Overall World Year GDP Traffic (dependent-Y) 2005 4,68,46,562.58 37,15,31,066.03 2006 5,38,56,933.86 32,30,84,816.18 2007 6,22,87,613.36 32,17,21,995.55 2008 7,16,94,770.04 27,25,28,200.00 2009 5,58,36,300.10 25,70,76,764.50 2010 6,78,44,395.31 29,33,00,431.75 2011 8,13,13,055.71 29,70,19,863.00 2012 8,20,74,909.57 31,74,33,197.00 2013 8,44,04,438.30 32,26,20,177.50 2014 8,43,96,763.46 39,83,11,678.00 2015 7,33,62,771.37 40,21,86,242.00 Calculation of regression equation SUMMARY OUTPUT Regression Statistics Multiple R 0.125528054 R Square 0.015757292 Adjusted R Square -0.093603009 Standard Error 49856404.43 Observations 11 ANOVA df SS MS F Significance F Regression 1 3.58149E+14 3.58149E+14 0.144086037 0.713053944 Residual 9 2.23709E+16 2.48566E+15 Total 10 2.27291E+16 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 293844084.2 83871194.23 3.503516158 0.006686437 104114261.8 483573906.6 104114261.8 483573906.6 X Variable 1 0.451002953 1.188142245 0.379586665 0.713053944 -2.236761531 3.138767436 -2.236761531 3.138767436 Regression Equation Y= A+Bx Y=293844084.20+0.45*X Y (dependent variable) Traffic 0.90% 2.900% X (independent) GDP B Slope or beta A Intercept From the given data, a regression equation is formed by using the formula. In this, Y is traffic data which is dependent and X is GDP data which is independent. The relationship between these two is identified using regression analysis. The calculation performed above shows that to what extent traffic data changes as GDP increases or decreases. The equation formed is: Y=293844084.20+0.45*X A= 293844084.20 B=0.45 For example, if the value of GDP (X) is 10,00,00,000 then, what will be the value of traffic data (y). The regression equation for this will be: Y=293844084.20+0.45*10,00,00,000 and the value of Y can be computed. Now addressing the question which is if the GDP increase by 2%, will the traffic data increase or decrease. The answer to this is calculated above and it seems that there is a positive relationship between GDP and port traffic. If value of X increase by 2% then the value of Y will also increase by 2.90%. This implies that rise in the overall GDP of world will lead to an increase in the port traffic. In context to UAE A linear regression is also performed to find out the relation between GDP and port traffic of UAE particular. The below data is exclusively related to the country GDP and traffic. Data: UAE only Year GDP Traffic (dependent-Y) 2005 1,17,287.13 1,34,33,352.38 2006 1,45,587.47 1,29,38,693.75 2007 1,78,630.36 1,44,59,505.50 2008 2,39,212.53 1,39,39,740.00 2009 1,92,000.00 1,38,74,367.00 2010 2,14,000.00 1,45,98,299.00 2011 3,02,000.00 1,58,51,696.00 2012 3,49,000.00 1,76,00,000.00 2013 3,79,000.00 1,76,00,000.00 2014 3,75,000.00 2,08,66,050.50 2015 2,65,000.00 2,15,92,000.00 Calculation of regression equation SUMMARY OUTPUT Regression Statistics Multiple R 0.73927209 R Square 0.546523223 Adjusted R Square 0.496136914 Standard Error 2118818.21 Observations 11 ANOVA df SS MS F Significance F Regression 1 4.86949E+13 4.86949E+13 10.84666129 0.0093272 Residual 9 4.04045E+13 4.48939E+12 Total 10 8.90994E+13 Coefficients Standard Error t Stat P-value Lower 95% Lower 95.0% Upper 95.0% Intercept 10012052.43 1946762.51 5.142924408 0.000608898 5608169.682 5608169.682 14415935.18 X Variable 1 24.16683158 7.337898095 3.293426982 0.0093272 7.567352876 7.567352876 40.76631028 Regression Equation Regression Equation Y= A+Bx Y=10012052.43+24.17*X Y Traffic 48% 50.340 % X GDP B Slope or beta The above calculation is done on the basis of the data given for a particular country which is UAE. Regression equation formed by using formula is: Y=10012052.43+24.17*X A= 10012052.43 B= 24.17 As it is already discussed that putting the value of X (GDP) in the equation will give the value of Y (traffic). So solving the question in context of UAE, if GDP rises by 2% then the port traffic will be 50.340%. Increase in GDP is equal to the 2% of beta. Analysing the relation on the national basis also shows that port traffic is directly and positively related with GDP. Conclusion The report concludes the fluctuations in GDP will have its effects on port traffic of a country. Increase or decrease in traffic is dependent upon the rise or fall in the GDP growth. Both have a positive relationship which is identified by using regression formula. References Seber, G. A., Lee, A. J. (2012).Linear regression analysis(Vol. 936). John Wiley Sons. Sen, A., Srivastava, M. (2012).Regression analysis: theory, methods, and applications. Springer Science Business Media.