The World Bank Organisation About the Gross National Income - Essay Example

?Part Analysing Cross-sectional Data Data was collected by the World Bank Organisation about the Gross National Income, expressed in purchasing power parity dollars to adjust for price level differences across countries. The data is not adjusted for inflation. There are values for each year from 2001 -2009 for each country. The numbers are measured in millions of dollars. Source of data: Source: World Bank Organisation. Analysis of the 2008 values only. Summary statistics: Table 1: Summary Statistics of Gross National Income data for the year 2008 for 173 countries of the world. Mean 12668.55 Standard Error 1060.88 Median 7270 Mode 4860 Standard Deviation 13953.7 Sample Variance 1.95E+08 Kurtosis 1.888097 Skewness 1.533519 Range 66920 Minimum 280 Maximum 67200 Sum 2191660 Count 173 Largest(1) 67200 Smallest(1) 280 Range 66920 Frequency table Table 2: Frequency Table of GNI Lower Mid Upper Frequency -2293.85 280 2853.846 1 2853.846 5427.692 8001.538 75 8001.538 10575.38 13149.23 29 13149.23 15723.08 18296.92 21 18296.92 20870.77 23444.62 10 23444.62 26018.46 28592.31 8 28592.31 31166.15 33740 5 33740 36313.85 38887.69 7 38887.69 41461.54 44035.38 9 44035.38 46609.23 49183.08 3 49183.08 51756.92 54330.77 1 54330.77 56904.62 59478.46 2 59478.46 62052.31 64626.15 1 64626.15 67200 69773.85 1 Figure 1: Histogram of Gross National Income Figure 2: Line Graph of Gross National Income Analysis and Conclusions: The data related to Gross National Income for 173 countries is analysed with statistical methods. The methods employed are analysis of summary statistics, analysis of frequency table and histogram and the analysis of line graph of Gross National Income. Summary Statistics: In accordance with the summary statistics demonstrated in Table 1, the following relation can be ascertained: Mean > Median > Mode = 12668 > 7270 > 4860 . This relationship shows that the data is positively skewed. This in turn means that the number of countries with low Gross National Income is higher as compared to those higher Gross National Income. Mean is a measure of the central tendency that is outlier biased. The statistical Median represents centre value of the data. Mode actually represents the majority values in the data. In this case the Median seems more appropriate to be focused as the central tendency as Mean seems to deliver an impression that the GNI of all countries is good whereas the Mode value paints an opposite picture. The Line Graph of Gross National Income asserts the selection of Median as a central tendency as the majority of spikes are almost at same level i.e. around 40,000. The exceptions are quiet evident in the above mentioned graph due to which the Mean cannot be selected as the central tendency. The value of Standard deviation is also high due to these exceptions. The Histogram (Figure 1) of the frequency table (Table 2) shows an asymptotic decay in the frequencies. As a result of which it can be claimed that the data is following Exponential Distribution. This means that as the rate of GNI is proceeding towards higher degree, the number of countries on the scale is diminishing. The frequency table (Table 2) highlights the lower Gross National Income recorded for the majority of countries. Part 2 Correlation and Regression: Data was collected by the Office for National Statistics on the number of visitors(000’s) to London who were here for a holiday and the amount of money they spent (?M). Source of data: Source: Office for National Statistics, International Passenger Survey . Scatter Plot of GMMA vs GMAK is given below: Figure 3: Scatter Plot of GMMA (Visitors to UK) and GMAK (Earnings) GMMA refers to overseas visitors to UK. This is a dependent variable. GMAK means Revenue that the country (? million at current prices) earns as a result of foreign visitors. This is an Independent Variable. The above mentioned scatter plot (Figure 3) shows the increasing trend and a linear relationship between two variables ‘Number of Visitors (GMMA)’ and ‘the respective Earnings form those visitors (GMAK)’. The correlation coefficient = 0.960236 shows a very strong positive relationship between GMMA and GMAK. The R2 = 0.9221, shows a 92% correctness of the prediction done through the formulated model. A linear relationship demonstrated in the scatter plot exhibits strong correlation. This reason is enough for us to fit a regression line at it. The fitted regression line can be given as: y = 0.7394x – 439.88. The method of ‘least squares estimate’ has been used to estimate the parameters of the above mentioned regression line. The model shows that the Earnings are strongly related to the number of visitors. This relationship is in a linear fashion. The negative Intercept of the linear line indicates that if the number of visitors i.e ‘x’ declines to zero (0), the government has to bear the maintenance expenses of the tourist spots. This would be incurred as a loss to the government. The Breakeven point would make the profit zero with some value of x when its multiplication with the coefficient would reveal 439.88. The maximization of the profit can be achieved if the value of the visitors goes above the threshold. According to the R2 value, the model is 92% suitable for predicting the prospective earnings on the basis of the number of visitors. Part 3 Time Series Analysis and Forecasting Data was collected about the number of UK residents going abroad each month from January 2006 to December 2010 and their expenditure whilst they are abroad. The data records the amount of money they spent, measured in ? millions. Source of data: Source: Office for National Statistics, International Passenger Survey Following is the time series plot of the given data: Figure 4: The Time Series Plot of Visits and Expenditure. The data under consideration contains values that are spanned over five years. The duration of their span initiates from the year 2006 and continues up to the year 2010. The data is grouped in four quarters for each year. The characteristics of the data are that it belongs to the United Kingdom. It contains information about people that are going abroad as tourist and their respective expenses. The construction of Time Series Plot has been given preference with respect to this data. The reason for this preference is that the data under consideration is time bound. The above time series plot (Figure 4) clearly demonstrates the trend line. The equation of the trend line is as follows y = -164.09x + 8480.3 The above mentioned realization is showing the seasonal trend in the series. The seasonal trend refers to the fact that every year maximum number of people are going abroad in the third quarter of the year. The time series plot demonstrates that the amount of expenditure has decreased over the years. The reason may be the reduction in the number of people going abroad. Another reason may be that the government might have provided better recreational facilities. Removal of the seasonal pattern is recommended before proceeding with the time-series model. The negative growth rate is evident from the coefficient of x. Table 3: Average Expenditure over the years Years Average Expenditure of 4 Quarters 1 7597.25 2 7787.25 3 7711.25 4 5485 5 5205.75 The average expenditure trend line with R2 = 0.749, indicates the Time Series Trend Line 75% suitable for the prediction of futuristic yearly average value of expenditure. The equation of this trend line can compared with the Time Series Trend Line of the quarterly data. The form of both the equations is almost similar. Figure 5 : Scatter plot of UK tourists’ visits abroad and their expenditures The Scatter plot of UK tourists’ visits abroad and their expenditures strengthens the hypothesis that the expenditure is very strongly and linearly related to the independent variable Visits. Thus the reduction in expenditure seems to be due to the reduced number abroad visitors. The scatter plot shows Coefficient of correlation = 0.9673, which means that there is 96.7% correlation between Visits and Expenditure. Read More