Study On The Average Number Of Employees Index Finance Essay - Free Essay Example

Sample details Pages: 5 Words: 1374 Downloads: 3 Date added: 2017/06/26 Category Finance Essay Type Research paper Did you like this example? The goal of this article is to study the direction and the intensity of the relationship between the Average Number of Employees Index and the Gross Domestic Product Index. The study is done by analyzing quarterly data from 2007 until 2009 from Romania and by applying statistical and econometrical methods: the graphical method, the regression function, the correlation ratio, the determinant coefficient and the dispersion analysis. The Trimester Evolution of the Average Number of Employees and the Gross Domestic Product Indexes between 2007 and 2009 The Gross Domestic Product (GDP) is the main measurement indicator of the macroeconomic results of a country and the main economic result aggregate in the National Account System. It expresses the gross value of the final goods and services produced within a certain time period by the home and foreign economic agents within the country. It can be computed by two different methods that lead to the same result, with some statistical differences based on the usage of different sources of data. The production method (the value added method) is based on the aggregation of the final product and goods flows obtained by the economic agents. The final usage method (the expense method) starts from adding the elements in which the final economic assets are used (goods and services) evaluated at the market prices, less the value of the imported goods. Table no. 1 GDP Indexes between 2007 and 2009 (% of the corresponding period from the previous year) Year Trimester I Trimester II Trimester III Trimester IV 2007 106.1 106.0 105.9 106.8 2008 108.5 109.6 109.4 103.1 2009 93.8 91.3 92.9 93.5 Source: Monthly Statistical Bulletin no 1/2010, no. 5/2010 Fig. no. 1 The GDP Indexes Evolution between 2007 and 2009 By analyzing figure no.1 a linear growth trend is observed for the GDP indexes between the first trimester of 2007 and the second trimester of 2008, when it reaches a maximum of 109.6%. This is followed by a drop until the second trimester of 2009 when a minimum value of 91.3% is registered, and a growth trend until the fourth trimester of 2009. Table no.2 Average number of employees between 2006 and 2009 (thousands of persons) Year Trimester I Trimester II Trimester III Trimester IV 2006 4567.9 4602 4613.7 4593.4 2007 4675.1 4730.5 4746.3 4731 2008 4781.4 4825.5 4832.2 4785 2009 4764.9 4656.3 4540.3 4416.7 Source: Monthl y Statistical Bulletin no 1/2007, 1/2008, 1/2009, 1/2010 The data from table no.2 was used to compute the average number of employees indexes with a chain base as compared to the same period from the previous year. The information obtained is presented in the below table. Table no.3 The average number of employees indexes between 2007and 2009 (%) Year Trimester I Trimester II Trimester III Trimester IV 2007 102.3 102.8 102.9 103 2008 102.3 102 101.8 101.1 2009 99.7 96.5 94 92.3 From the below figure, a growth trend can be seen for the number of employees index between the first trimester of 2007 and the fourth trimester of 2009. The maximum is reached at 103% after which a linear decline follows until the fourth trimester of 2009, with a minimum value of 92.3%. Figure no.2 The evolution of the average number of employees index between 2007 and 2009 Don’t waste time! Our writers will create an original "Study On The Average Number Of Employees Index Finance Essay" essay for you Create order The correlation analysis between the average number of employees index and the GDP index The independent variable is the average number of employees index which is defined as X and the dependent variable is the GDP denominated as Y. The data to be used in the econometric study are presented in the table below. Table no.4 The average number of employees index and the GDP index between 2007 and 2009 Period I 2007 II 2007 III 2007 IV 2007 I 2008 II 2008 III 2008 IV 2008 I 2009 II 2009 III 2009 IV 2009 The average number of employees index (%) 102.3 102.8 102.9 103 102.3 102 101.8 101.1 99.7 96.5 94 92.3 GDP index (%) 106.1 106 105.9 106.8 108.5 109.6 109.4 103.1 93.8 91.3 92.9 93.5 By studying the figure no 3, it can initially be seen that the relationship between the two variables is linear. This hypothesis will be demonstrated subsequently through econometric methods. The linear regression equation is: (1) Figure no.3 The graphical represen tation of the relationship between the average number of employees index and the GDP index In order to determine the adjustment model parameters, and b, the below normal equations system will be solved through the Kramer method: (2) By analyzing the data from Table no.4 with Excel, submenu Data Analysis, the blow information was obtained: Table no.5 The index value synthesis The adjustment model parameters Correlation ratio Coefficient of determination Fcomputed Ftheory a -63.00394912 0.857644833 0.735554659 27.814998 0.000360739 b 1.651492787 By analyzing the data from the above table it is seen that the correlation ratio is R=0.857644833 that shows that between the average number of employees index and the GDP index there is a direct, strong intensity relationship. The coefficient of determination R2=0.735554659 points out that the independent variable influences the dependent variable in a percentage of 73.55%, which means tha t the average number of employees index variation influences 73.55% of the GDP index variation.The validity testing of the unifactorial linear regression model will be done by using the dispersion analysis also known as ANOVA method. By analyzing the data in from the table no 6 it is noticed that: The regression variance is . The residual variance is . The total variance is . Table no.6 ANOVA table  df SS MS F Significance F Regression 1 414.2122822 414.212282 27.814998 0.000360739 Residual 10 148.9168845 14.8916884   Total 11 563.1291667    This is a simple relationship as there is only one independent variable: k=1. The number of analyzed pairs is n=12.Therefore we can compute the corrected dispersions: (3) (3) (4) (5) Th next step of econometric analysis is testing the validity of the linear model by applying the Fisher-Snedecor test (F Test). The hypotheses used to verify the validity of the linear model are: H0: the linear model is not valid. H1: the linear model is valid. By using the data from the previous table it can be seen that the computed value of the F test is Fcomputed=27.814998. The theoretical value of the F test is Ftheory=0.000360739, which is smaller than 0.05, therefore the H0 hypothesis is rejected and the H1 hypothesis is accepted, which means that the linear model is valid. The hypotheses for testing the correlation ratio are: H0: R=0 (R is not significantly different from zero, so R is not statistically significant) H1: RÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã‚ °Ãƒâ€šÃ‚  0 (R is sign ificantly different from zero, so R is statistically significant). The Fisher-Snedecor test will be applied. The computed test statistic is: (6) . The theoretical value of the F test at the significance level ÃÆ'Ã… ½Ãƒâ€šÃ‚ ±=0.05 is Ftable=4.96. Because FcFtable = the H0 hypothesis is rejected and the H1 hypothesis is accepted. This proves that the correlation ratio is statistically significant. In order to test the regression model variables, the following table will be used. The table was obtained with the Excel program, submenu Data Analysis: Table no.7 The variables value synthesis Coefficients t Stat P-value Lower 95% Upper 95% a= -63.00394910 -2.0095694 0.07222653 -132.8604781 6.852579882 b=1.651492787 5.27399259 0.00036074 0.953775609 2.349209965 The hypotheses for testing the a variable validity are: H0: a=0 (variable a is significantly equal to zero, so a is not statistically significant) H1: a0 (variable a is significantly lower than zero, so a is statistically significant). Because n=12 studied data, n30 we have a small volume sample, and a0, therefore the unilateral left t test will be applied. At a significance level ÃÆ'Ã… ½Ãƒâ€šÃ‚ ±=0.05 , the computed value is tc= -2.0095694 and the theoretical value is t= -0.07222653 which is smaller than -0.05 which means that the H0 hypothesis is rejected and the H1 hypothesis is accepted. This proves that the a variable is statistically significant. The confidence interval is : -132.8604781 a 6.852579882. The hypotheses for testing the b variable are: H0: b=0 (variable b is significantly equal to zero, so b is n ot statistically significant) H1: b0 (variable b is significantly higher than zero, so b is statistically significant). Because n=12 studied data, n30 we have a small volume sample, and b0, therefore the unilateral right t test will be applied. At a significance level ÃÆ'Ã… ½Ãƒâ€šÃ‚ ±=0.05 , the computed value is tc= 5.27399259 and the theoretical value is t= 0.00036074 which is smaller than 0.05 which means that the H0 hypothesis is rejected and the H1 hypothesis is accepted. This proves that the b variable is statistically significant. The confidence interval is : 0.953775609 b 2.349209965. 3. Conclusions Only after following the necessary steps: testing the model validity by using the ANOVA method, testing the significance of the linear regression models variables and establishing the confidence intervals, determining and testing the correlation ratio, the choice and usage of the unifactorial linear regression model is completely proven. By using statisctical and econometrical methods, it was confirmed that there is a very strong linear relationship between the average number of employees index and the GDP index. Therefore, by knowing the value of the average number of employees index at a certain point in time, the GDP index can be predicted.