Predicting a nation's "average happiness" Consider five statistics for several nations: LSI, the average satisfaction score; GINI, the gini coefficient of income inequality (higher score = greater inequality); CORRUPT, the degree of corruption in government (higher score = less corruption); LIFE, the average life expectancy; and DEMOCRACY, a measure of civil and political liberties (higher score = more political liberties). Data on excel file happiness.xlsx (using R) a. Using numerical and graphical summaries, describe the distribution of each variable. b. Using numerical and graphical summaries, describe the relationship between each other. c. Consider a model using GINI and LIFE. Run the MLR and summarize results. Be sure to check assumptions d. Now consider a model using GINI, LIFE, and DEMOCRACY. Run the MLR and summarize the results. Again make sure to check assumptions. e. Now consider a model using all four explanatory variables. Summarize results and check assumptions.

the table

Country LSI GINI CORRUPT DEMOCRACYLIFE Algeria 5.6 35.3 2.8 1.5 73.77 Argentina 7.1 51.3 2.8 5.5 76.36 Armenia 5 33.8 2.9 3 72.4 Australia 7.8 35.2 8.8 6 81.53 Austria 7.8 29.2 8.7 6 79.36 Azerbaijan 5.3 36.5 2.2 1.5 66.31 Bangladesh 5.3 33.4 1.7 3.5 63.21 Belarus 5.5 29.7 2.6 1 70.34 Belgium 7.3 33 7.4 5.5 79.07 Bolivia 6.5 60.1 2.5 5 66.53 Brazil 7.6 57 3.7 4 71.71 United Kingdom 7.4 36 8.6 5.5 78.54 Bulgaria 4.6 29.2 4 4.5 72.83 Canada 8 32.6 8.4 6 81.16 Chile 6.3 54.9 7.3 5 77.15 Colombia 7.3 58.6 4 3 72.54 Denmark 8.2 24.7 9.5 6 78.13 Dominican Republic7.6 51.6 3 5 73.39 Egypt 5.8 34.4 3.4 1.5 71.85 El Salvador 6.7 52.4 4.2 4.5 72.06 Estonia 5.6 35.8 6.4 5.5 72.56 Finland 8 26.9 9.6 6 78.82 France 7 32.7 7.5 5.5 80.87 Germany 7.3 28.3 8.2 5.5 79.1 Ghana 4.7 40.8 3.5 4.5 59.49 Greece 6.2 34.3 4.3 5 79.52 Honduras 7 53.8 2.6 4 69.37 Hungary 5.7 26.9 5 5.5 73.18 Iceland 7.8 35.9 9.7 6 80.55 India 5.5 36.8 2.9 4.5 69.25 Indonesia 5.7 34.3 2.2 3.5 70.46 Iran 5.6 43 2.9 1 70.86 Ireland 8.1 34.3 7.4 6 78.07 Israel 7.1 39.2 6.3 5 80.61 Italy 6.7 36 5 5.5 80.07 Japan 6.8 24.9 7.3 5.5 82.07 Jordan 5.7 38.8 5.7 3 78.71 Kenya 3.7 42.5 2.1 1.5 56.64 Latvia 5.4 37.67 4.2 5.5 71.88 Lithuania 5.8 36 4.8 5.5 74.67 Mali 3.8 40.1 2.9 4.5 49.94 Mexico 7.7 46.1 3.5 4.5 75.84 Moldova 5.7 33.2 2.9 4 70.5 Morocco 5.8 39.5 3.2 2.5 71.52 Netherlands 7.7 30.9 8.6 6 79.25 New Zealand 7.8 36.2 9.6 6 80.24 Nigeria 4.8 43.7 1.9 3 46.53 Norway 8.1 25.8 8.9 6 79.81 Pakistan 5.2 30.6 2.1 1.5 64.13 Peru 5.9 52 3.5 3.5 70.44 Philippines 5.5 44.5 2.5 4.5 70.8 Poland 6.5 34.5 3.4 5.5 75.41 Portugal 5.9 38.5 6.5 6 78.04 Romania 5.9 31.1 3 5 72.18 Russia 5.9 39.9 2.4 2 65.94 Senegal 4.5 41.3 3.2 3.5 57.08 Slovakia 6.1 25.8 4.3 5.5 75.17 Slovenia 7.1 28.4 6.1 5.5 76.73 South-Africa 5 57.8 4.5 5.5 48.89 South-Korea 6.3 31.6 5 5 78.64 Spain 7.6 34.7 7 5.5 79.92 Sweden 7.9 25 9.2 6 80.74 Switzerland 8 33.7 9.1 6 80.74 Tanzania 2.5 34.6 2.9 3 51.45 Turkey 5.5 43.6 3.5 2.5 73.14 Uganda 4.5 45.7 2.5 1.5 52.34 Ukraine 5.3 28.1 2.6 3 68.06 Uruguay 6.8 44.9 5.9 6 76.14 USA 7.9 40.8 7.6 6 78.14 Uzbekistan 6 36.8 2.2 0.5 71.69 Vietnam 6.1 34.4 2.6 0.5 71.33 Zimbabwe 3.3 50.1 2.6 1.5 44.28