Quantitative Analysis of Relationship between GDP and EE - Research Paper Example

Year 2 Research Methods 2008-09 Assignment No. 2 (Quantitative Research) Year Table of Contents Table of Contents 2 INTRODUCTION 3STATISTICAL ANALYSIS AND FINDINGS 4 Relationship between GDP and Education Expenditure (per Capita) 4 Relationship between GDP Class and World Regions 5 Chi-Square Test of Independence 6 Distribution of Total Population Growth 8 Distribution of Energy Consumption per Capita 9 Distribution of Total Population Growth for the World Regions 11 Distribution of Energy Consumption per Capita for the World Regions 12 Analysis of Variance (ANOVA) 14 REFERENCES 18 APPENDIX 19 INTRODUCTION Any country’s level of educational investment reflects the present level of a country’s economic and social well-being. This paper will analyse the relationship between country’s Gross Domestic Product per Capita and Education Expenditure per Capita. Further, it will also discuss the distribution of Total Population Growth (% per annum) and Energy Consumption per Capita (kg oil) for whole world along with distribution in six world regions. STATISTICAL ANALYSIS AND FINDINGS TASK 1 Relationship between GDP and Education Expenditure (per Capita) The average country’s Gross Domestic Product per Capita (US$) is about 7,758 (SD = 9,089). The average country’s Education Expenditure per Capita (US$) is about 393.3 (SD = 492). Figure 1: Scatter plot of GDP per Capita and Education Expenditure per Capita Figure 1 shows the scatter plot of Gross Domestic Product per Capita (US$) and Education Expenditure per Capita (US$). From scatter, it can be seen that almost all the data points lies near about a linear line. This indicate that there is strong positive linear relationship between country’s Gross Domestic Product per Capita (US$) and Education Expenditure per Capita (US$). The GDP per Capita and Education Expenditure per Capita are strongly correlated, r(46) = .967, p < .001. Country’s GDP per Capita significantly predicts Education Expenditure per Capita, β = .967, t(46) = 25.64, p < .001. Country’s GDP per Capita also explains a significant proportion of variance in Education Expenditure per Capita, R2 = .935, F(1, 46) = 657.44, p < .001. The linear regression equation is given by Education Expenditure per Capita = -30.528 + 0.056(GDP per Capita) Relationship between GDP Class and World Regions Figure 2: Clustered Bar Chart of GDP Classes Based on the World Regions GDP can be divided into four classes as low income, low middle income, middle income, and high income. In addition, there are six world regions as Africa, Asia, Europe, North America, Oceania, and South America. Figure 2 shows the GDP classes for all six-world regions. From figure 2, it can be seen that most of the high income GDP class country’s are in Europe and most of the low income GDP class country’s are in Africa and Asia. The countries percentage of low income, low middle income, middle income, and high income GDP in world are 26.3%, 26.3%, 19.3%, and 28.1%, respectively. The countries percentage of low income, low middle income, middle income, and high income GDP in Africa are 54.5%, 36.4%, 9.1%, and 0%, respectively. The countries percentage of low income, low middle income, middle income, and high income GDP in Asia are 46.2%, 15.4%, 23.1%, and 15.4%, respectively. The countries percentage of low income, low middle income, middle income, and high income GDP in Europe are 6.7%, 13.3%, 13.3%, and 66.7%, respectively. The countries percentage of low income, low middle income, middle income, and high income GDP in North America are 14.3%, 42.9%, 14.3%, and 28.6%, respectively. The countries percentage of low income, low middle income, middle income, and high income GDP in Oceania are 0%, 50%, 0%, and 50%, respectively. The countries percentage of low income, low middle income, middle income, and high income GDP in South America are 14.3%, 28.6%, 57.1%, and 0%, respectively. Chi-Square Test of Independence The GDP class is dependent on world region, (15, N = 57) = 34.34, p = .003. In other words, there is strong association between GDP class and world region. The main concern regarding the outcome of Chi-square Dependence test is that all cells have expected count less than 5. Therefore, to overcome this concern GDP classes should be divided in lesser group such as low income and high income and similarly, the world region should be divided in lesser region. By doing this, excepted count will be greater in all cells. TASK 2 Distribution of Total Population Growth The two variables selected for analysis are Total Population Growth (% per annum) and Energy Consumption per Capita (kg oil). Figure 3: Histogram of Total Population Growth (% per Annum) The average total population growth is about 1.5% per annum (SD = 1.3% per annum) with half of the total population growth is below 1.3% per annum. The most common total population growth is about 1.7% per annum. The range of total population growth is 7.9% per annum with -0.2% per annum being minimum and 7.7% per annum being maximum. The distribution of the total population growth is skewed to right (skewness = 1.92) that is also confirmed by histogram (figure 3) and boxplot (figure 4) of the total population growth. Since the distribution is heavily skewed, the best measure of location and dispersion of total population growth is median (1.3% per annum) and Interquartile range (1.8% per annum). Rwanda has total population growth of 7.7% per annum that is much higher compared to other countries total population growth. Figure 4: Boxplot of Total Population Growth (% per Annum) Distribution of Energy Consumption per Capita The average energy consumption per capita is about 2,131 kg oil (SD = 2,822 kg oil) with half of the energy consumption per capita is below 1,174 kg oil. The most common energy consumption per capita is about 17 kg oil. The range of energy consumption per capita is 17,039 kg oil with 17 kg oil being minimum and 17,056 kg oil being maximum. The distribution of the energy consumption per capita is heavily skewed to right (skewness = 3.07) that is also confirmed by histogram (figure 5) and boxplot (figure 6) of the energy consumption per capita. Since the distribution is heavily skewed, the best measure of location and dispersion of energy consumption per capita is median (1,174 kg oil) and Interquartile range (2,824 kg oil). Figure 5: Histogram of Energy Consumption per Capita (kg oil) Figure 6: Boxplot of Energy Consumption per Capita (kg oil) The energy consumption per capita for South Africa and USA is 17,056 and 8,040 kg oil, respectively that is much higher as compared to all other countries energy consumption per capita. Distribution of Total Population Growth for the World Regions The average total population growth for Africa is about 2.77% per annum (SD = 1.85% per annum) with half of the total population growth is below 2.40% per annum (IQR = 1.20% per annum). The range is 6.90% per annum and distribution is skewed to right (skewness = 2.12). Rwanda has total population growth of 7.7% per annum that is much higher as compared to other countries in Africa. The average total population growth for Asia is about 1.97% per annum (SD = 0.98% per annum) with half of the total population growth is below 1.70% per annum (IQR = 1.60% per annum). The range is 3.20% per annum and distribution is approximately normal (skewness = -0.26). The average total population growth for Europe is about 0.46% per annum (SD = 0.84% per annum) with half of the total population growth is below 0.20% per annum (IQR = 0.40% per annum). The range is 3.20% per annum and distribution is skewed to right (skewness = 2.45). Turkey and Bosnia have total population growth of 1.70% and 3.00% per annum that is much higher as compared to other countries in Europe. The average total population growth for North America is about 1.10% per annum (SD = 0.82% per annum) with half of the total population growth is below 0.90% per annum (IQR = 1.20% per annum). The range is 2.40% per annum and distribution is skewed to right (skewness = 1.39). Nicaragua has total population growth of 2.70% per annum that is much higher as compared to other countries in North America. The average total population growth for Oceania is about 1.35% per annum (SD = 0.57% per annum) with half of the total population growth is below 1.10% per annum (IQR = 0.95% per annum). The range is 1.20% per annum and distribution is skewed to right (skewness = 1.85). The average total population growth for South America is about 1.29% per annum (SD = 0.46% per annum) with half of the total population growth is below 0.1.30% per annum (IQR = 1.00% per annum). The range is 1.20% per annum and distribution is approximately normal (skewness = -0.24). Figure 7: Boxplot of Total Population Growth (% per Annum) based on the World Regions Distribution of Energy Consumption per Capita for the World Regions The average energy consumption per capita for Africa is about 1,911 kg oil (SD = 5,067 kg oil) with half of the energy consumption per capita is below 99 kg oil (IQR = 527 kg oil). The range is 17,039 kg oil and distribution is heavily skewed to right (skewness = 3.22). South Africa and Lybia have energy consumption per capita of 17,056 and 2,302 kg oil, respectively that is much higher as compared to other countries in Africa. The average energy consumption per capita for Asia is about 1,660 kg oil (SD = 1,536 kg oil) with half of the energy consumption per capita is below 1,253 kg oil (IQR = 2,780 kg oil). The range is 4,506 kg oil and distribution is approximately normal (skewness = 0.61). The average energy consumption per capita for Europe is about 2,828 kg oil (SD = 1,559 kg oil) with half of the energy consumption per capita is below 2,817 kg oil (IQR = 2,477 kg oil). The range is 5,308 kg oil and distribution is normal (skewness = 0.05). Figure 8: Boxplot of Energy Consumption per Capita (kg oil) based on the World Regions The average energy consumption per capita for North America is about 2,924 kg oil (SD = 3,487 kg oil) with half of the energy consumption per capita is below 1,289 kg oil (IQR = 7,362 kg oil). The range is 7,701 kg oil and distribution is skewed to right (skewness = 1.18). The average energy consumption per capita for Oceania is about 2,645 kg oil (SD = 2,828 kg oil) with half of the energy consumption per capita is below 2,263 kg oil (IQR = 5,207 kg oil). The range is 5,663 kg oil and distribution is approximately normal (skewness = 0.29). The average energy consumption per capita for South America is about 770 kg oil (SD = 406 kg oil) with half of the energy consumption per capita is below 671 kg oil (IQR = 789 kg oil). The range is 1,088 kg oil and distribution is skewed to right (skewness = 0.98). Analysis of Variance (ANOVA) Since there are more than two groups (region), therefore ANOVA test will be performed to compare means of each region for total population growth and energy consumption per capita. ANOVA: Total Population Growth The null and alternate hypotheses are (Each world region has equal mean total population growth) : At least one world region have different mean total population growth. Test of Homogeneity of Variances suggest that variances of total population growth for world regions are not statistically significant. The hypothesis that the each region total population growth means equal is not supported, F (5, 51) = 6.32, p < .001. In other words, total population growth in each region is different (figure 9). Figure 9: Mean plot of Total Population Growth based on the World Regions ANOVA: Energy Consumption per Capita The null and alternate hypotheses are (Each world region has equal mean energy consumption per capita) : At least one world region have different mean energy consumption per capita. Test of Homogeneity of Variances suggest that variances of energy consumption per capita for world regions are not statistically significant The hypothesis that the each region energy consumption per capita means equal is supported, F (5, 51) = 0.71, p = .617. In other words, energy consumption per capita in each region is approximately same (figure 10). Figure 10: Mean plot of Energy Consumption per Capita based on the World Regions Figure 11: World Population Growth by Region (%) (Source: ISEE 2009) The world population is growing at a rate of 1.16% (78 million people) per annum in 2008 or approximately 212,970 people per day (ISEE 2009). Figure 11 shows the world population growth by region (%). The population growth for North America for 1990-2006 is 1.2% that is approximately close to earlier result of 1.1%. The population growth for Europe for 1990-2006 is 0.5% that is same as earlier result of 0.46%. South Africa and Lybia have energy consumption per capita of 2,587.16 and 3,191.34 kg oil, respectively in year 2003 (World Bank). REFERENCES Doane DP & Seward LE 2007. Applied Statistics in Business and Economics. McGraw-Hill/Irwin: New York ISEE 2009. World Population & GDP Growth. Retrieved on April 12, 2009, from http://www.hart-isee.com/index.php?page=world-population-gdp-growth World Bank. Indicators by Countries. Retrieved on April 12, 2009, from http://www.thedti.gov.za/econdb/raportt/zbior11.html APPENDIX Table 1 Descriptive Statistics Mean Std. Deviation N Edu Exp. per Capita 392.3068 492.35903 48 GDP per Capita (US$) 7758.21 9088.927 57 Table 2 Correlations Edu Exp. per Capita GDP per Capita (US$) Edu Exp. per Capita Pearson Correlation 1 .967(**) Sig. (2-tailed) .000 N 48 48 GDP per Capita (US$) Pearson Correlation .967(**) 1 Sig. (2-tailed) .000 N 48 57 ** Correlation is significant at the 0.01 level (2-tailed). Table 3 Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .967(a) .935 .933 127.26738 a Predictors: (Constant), GDP per Capita (US$) Table 4 ANOVA(b) Model Sum of Squares df Mean Square F Sig. 1 Regression 10648557.272 1 10648557.272 657.441 .000(a) Residual 745061.367 46 16196.986 Total 11393618.639 47 a Predictors: (Constant), GDP per Capita (US$) b Dependent Variable: Edu Exp. per Capita Table 5 Coefficients(a) Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) -30.528 24.686 -1.237 .222 GDP per Capita .056 .002 .967 25.641 .000 a Dependent Variable: Edu Exp. per Capita Table 6 Region * GDP Classes Crosstabulation GDP Classes Low Income Low Middle Income Middle Income High Income Total Region Africa Count 6 4 1 0 11 % within Region 54.5% 36.4% 9.1% .0% 100.0% Asia Count 6 2 3 2 13 % within Region 46.2% 15.4% 23.1% 15.4% 100.0% Europe Count 1 2 2 10 15 % within Region 6.7% 13.3% 13.3% 66.7% 100.0% N_America Count 1 3 1 2 7 % within Region 14.3% 42.9% 14.3% 28.6% 100.0% Oceania Count 0 2 0 2 4 % within Region .0% 50.0% .0% 50.0% 100.0% S_America Count 1 2 4 0 7 % within Region 14.3% 28.6% 57.1% .0% 100.0% Total Count 15 15 11 16 57 % within Region 26.3% 26.3% 19.3% 28.1% 100.0% Table 7 Region * GDP Classes Crosstabulation GDP Classes Low Income Low Middle Income Middle Income High Income Total Region Africa Count 6 4 1 0 11 Expected Count 2.9 2.9 2.1 3.1 11.0 Asia Count 6 2 3 2 13 Expected Count 3.4 3.4 2.5 3.6 13.0 Europe Count 1 2 2 10 15 Expected Count 3.9 3.9 2.9 4.2 15.0 N_America Count 1 3 1 2 7 Expected Count 1.8 1.8 1.4 2.0 7.0 Oceania Count 0 2 0 2 4 Expected Count 1.1 1.1 .8 1.1 4.0 S_America Count 1 2 4 0 7 Expected Count 1.8 1.8 1.4 2.0 7.0 Total Count 15 15 11 16 57 Expected Count 15.0 15.0 11.0 16.0 57.0 Table 8 Chi-Square Tests Value df Asymp. Sig. (2-sided) Pearson Chi-Square 34.335(a) 15 .003 Likelihood Ratio 37.287 15 .001 Linear-by-Linear Association 4.473 1 .034 N of Valid Cases 57 a 24 cells (100.0%) have expected count less than 5. The minimum expected count is .77. Table 9 Statistics Total Pop. Growth (% per annum) Energy Consumption per Capita (kg oil) N Valid 57 57 Missing 0 0 Mean 1.4930 2130.95 Median 1.3000 1174.00 Mode 1.70 17(a) Std. Deviation 1.33922 2822.496 Variance 1.794 7966483.944 Skewness 1.917 3.073 Std. Error of Skewness .316 .316 Kurtosis 6.957 13.366 Std. Error of Kurtosis .623 .623 Range 7.90 17039 Minimum -.20 17 Maximum 7.70 17056 Percentiles 25 .4000 341.00 50 1.3000 1174.00 75 2.2000 3165.50 a Multiple modes exist. The smallest value is shown Table 10 Statistics Total Pop. Growth (% per annum) Africa Asia Europe N_America Oceania S_America Count 11 13 15 7 4 7 Mean 2.77 1.97 0.46 1.10 1.35 1.29 Median 2.40 1.70 0.20 0.90 1.10 1.30 Variance 3.44 0.96 0.70 0.68 0.33 0.21 Std. Deviation 1.85 0.98 0.84 0.82 0.57 0.46 Minimum 0.80 0.20 -0.20 0.30 1.00 0.70 Maximum 7.70 3.40 3.00 2.70 2.20 1.90 Range 6.90 3.20 3.20 2.40 1.20 1.20 Interquartile Range 1.20 1.60 0.40 1.20 0.95 1.00 Skewness 2.12 -0.26 2.45 1.39 1.85 -0.24 Kurtosis 5.33 -0.90 6.17 1.94 3.41 -1.01 Percentiles-25 1.80 1.25 0.00 0.40 1.00 0.70 Percentiles-75 3.00 2.85 0.40 1.60 1.95 1.70 Table 11 Statistics Energy Consumption per Capita (kg oil) Africa Asia Europe N_America Oceania S_America Count 11 13 15 7 4 7 Mean 1911.00 1660.46 2828.07 2924.43 2644.50 769.57 Median 99 1253 2817 1289 2262.5 671 Variance 25670793 2359979 2430541 12159050 7995814 165175 Std. Deviation 5066.64 1536.22 1559.02 3486.98 2827.69 406.42 Minimum 17 22 314 339 195 379 Maximum 17056 4528 5622 8040 5858 1467 Range 17039 4506 5308 7701 5663 1088 Interquartile Range 527 2780 2477 7362 5207 789 Skewness 3.22 0.61 0.05 1.18 0.29 0.98 Kurtosis 10.49 -1.08 -0.95 -0.88 -4.31 -0.11 Percentiles-25 33 275 1509 598 232 385 Percentiles-75 560 3055 3986 7960 5439 1174 Table 12 Test of Homogeneity of Variances Levene Statistic df1 df2 Sig. Total Pop. Growth (% per annum) 1.597 5 51 .178 Energy Consumption per Capita (kg oil) 2.220 5 51 .066 Table 13 ANOVA Sum of Squares df Mean Square F Sig. Total Pop. Growth (% per annum) Between Groups 38.433 5 7.687 6.322 .000 Within Groups 62.004 51 1.216 Total 100.437 56 Energy Consumption per Capita (kg oil) Between Groups 29135058.249 5 5827011.650 .713 .617 Within Groups 416988042.593 51 8176236.129 Total 446123100.842 56 Read More