Report on various features of the data - Essay Example

?Report on various features of the data Introduction Some of the fundamental roles of the government are regulation of the economy and provision of utilities to its citizens. The services require liquidity potentials and this identifies The role of sources of government revenues such as borrowings and tax. Further, some of the sources of revenues are interrelated as they may stimulate one another under their macroeconomic effects in the economy. This paper, based on a data set on United Kingdom government’s borrowing and received taxes, reports the data set’s features to the senior management office. Analysis of borrowings and received tax over the two fiscal years One of the important approaches to understanding the data set is an annual comparison of the data to understand the country’s progress in the period. This involves a comparison of the borrowings over the two fiscal years and a comparison of received tax over the period. The following table summarizes descriptive statists of government borrowings for the two fiscal years. Table 1: Descriptive statistics for the fiscal years ended 2012 and 2013 borrowings Fiscal year ended 2012   Fiscal year ended 2013   Mean 9426.58333 Mean 7411.08333 Standard Error 2231.66604 Standard Error 3249.12642 Median 12910 Median 13078 Mode #N/A Mode #N/A Standard Deviation 7730.71793 Standard Deviation 11255.3041 Sample Variance 59763999.7 Sample Variance 126681870 Kurtosis 1.40046349 Kurtosis 0.73382765 Skewness -1.5053467 Skewness -1.28631268 Range 24102 Range 35145 Minimum -8197 Minimum -17039 Maximum 15905 Maximum 18106 Sum 113119 Sum 88933 Count 12 Count 12 Confidence Level(95.0%) 4911.86383 Confidence Level(95.0%) 7151.27903 From the data, the average borrowings, per month, decreased from the fiscal year ended March 2012 to the fiscal year ended March 2013. This communicates reduced government borrowing and means that the United Kingdom government is gaining stability. This also communicates possible success in reduced budget deficit should the reduced borrowing have been caused by favorable economic environment instead to political decision. The reduced borrowing also offers prospects of reduced foreign debts by reducing further accumulation. The year 2013 had a higher median than its previous year but its higher variance means that the median cannot be a good estimator for the data’s distribution. The difference between mean and median for the yearly borrowings could also be explained by the negative borrowings in the two years and the borrowings were more dispersed in the year ended 2013 that the year ended 2012. The graph bellow compared the annual borrowings and indicates higher borrowings 2012 Graph 1: Comparison of yearly borrowings The nation’s received tax over the two periods can similarly be compared using descriptive statistics that are shown in the table below. Table 2: Descriptive statistics for the fiscal years ended 2012 and 2013 received taxes Fiscal year ended 2012   Fiscal year ended 2013   Mean 12701.91667 Mean 12716.5 Standard Error 1259.548407 Standard Error 1323.836 Median 11077.5 Median 11057.5 Mode #N/A Mode #N/A Standard Deviation 4363.20367 Standard Deviation 4585.903 Sample Variance 19037546.27 Sample Variance 21030504 Kurtosis 5.931301194 Kurtosis 5.685588 Skewness 2.311375522 Skewness 2.248221 Range 15364 Range 16611 Minimum 9578 Minimum 8881 Maximum 24942 Maximum 25492 Sum 152423 Sum 152598 Count 12 Count 12 Confidence Level(95.0%) 2772.24735 Confidence Level(95.0%) 2913.744 The two periods reported an almost similar trend in received tax with means that are almost equal, 12701 and 12716. Medians for the two years similarly close with 11077.5 for the year ended 2012 and 11057.5 for the year 2013. Close similarity in standard deviation, Kurtosis, skewdness, minimum and maximum values and sums of received taxes further indicates similarity in the two periods’ trends and suggest consistency in the economic stability. The following graph shows a comparison of tax received in the two years with a similarity. Graph 2: Tax comparison The following shows scatter graphs for borrowings and tax respectively and these correspond with the values in the line graphs. Graph 3: Scatter graph for borrowings Graph 4: Scatter graph for tax Relationship between borrowings and received tax in the two fiscal years While government-borrowing level identifies its weak economy and reduced borrowing indicates stability towards higher self-reliance, such a development can affect productivity, and employment rates to determine receivable tax. The following table shows an extract from regression analysis of the two data sets. The analysis identifies a correlation coefficient of -0.045, calculated from excel, but the coefficient is not significant because of the high p- value as shown in the table below. The change in received tax is therefore attributable to other economic factors than borrowings. Table 3: Regression analyses extract   Coefficients Standard Error t Stat P-value Intercept 13088.74 1226.556 10.67113 3.66E-10 X Variable 1 -0.04508 0.097782 -0.46104 0.649295 Differences in yearly borrowings and tax receivable data Another important feature of the data is significance of the changes in the two fiscal years and analysis of variance of the two data sets offers the following insights. The following tables shows ANOVA summaries for borrowings and tax received over the two years. Table 4: Analysis of Variance for borrowings ANOVA   df SS MS F Significance F Regression 1 1.77E+08 1.77E+08 3.696864 0.083433 Residual 10 4.8E+08 47996680 Total 11 6.57E+08       The low probability value, 0.083, which is lower than 0.05 means that there was a significant difference in government borrowing over the two years. Table 5: Analysis of Variance for received tax ANOVA   df SS MS F Significance F Regression 1 2.05E+08 2.05E+08 441.8116 1.32E-09 Residual 10 4634963 463496.3 The low p-value also means a significant difference between receivable taxes in the two years. The following table compares the minimum, maximum and first, second, and third quartile values. Table 6: Comparisons BORROWINGS TAX Minimum -17,039 8,881 First quartile 4486 10079.25 Median 12910 11057.5 Third Quartile 14588 13608 Maximum 18,106 25,492 The following plots compares the values for borrowings and tax received Plot 1: Box plot for borrowings and tax Conclusion From the data, the United Kingdom reduced its borrowings from the year 2012 to the year 2013 and increased its received taxes in the same period. Changes in the two variables were however uncorrelated but the yearly changes were significant. It therefore indicates positive economic prospects as the country becomes self reliant and can finance its expenditure from the increased taxes. Tax is however not the cause of the reduced borrowings and this identify economic growth. Read More