Question
7. Coefficient of determination. What percentage of the variation in y is accounted for by x? Is this a strong regression? (1 paragraph)
Country rgdpch2009 grodomsav09 Zimbabwe 142.55 -26.88 Congo, Dem. Rep. 231.29 17.74 Malawi 611.08 17.22 Central African Republic 647.60 2.68 Ethiopia 683.61 4.13 Madagascar 753.19 8.85 Mozambique 759.37 2.23 Guinea 826.54 16.85 Sierra Leone 872.93 2.28 Comoros 915.77 -21.10 Rwanda 1031.23 4.23 Benin 1115.71 10.66 Uganda 1151.70 12.52 Tanzania 1189.05 17.88 Kenya 1206.07 7.81 Nepal 1211.67 8.00 Ghana 1239.17 8.73 Chad 1277.00 5.90 Lesotho 1311.41 -29.13 Cote d`Ivoire 1342.95 19.20 Bangladesh 1397.12 17.25 Haiti 1444.44 -2.29 Gambia, The 1464.73 6.25 Senegal 1492.06 7.97 Mauritania 1573.68 7.35 Zambia 1764.77 25.59 Cambodia 1765.97 18.29 Tajikistan 1872.64 -21.27 Sudan 2188.43 19.41 Nicaragua 2191.73 -2.61 Congo, Republic of 2220.28 45.54 Kyrgyzstan 2298.34 -8.83 Pakistan 2353.25 11.43 Uzbekistan 2384.45 26.04 Moldova 2493.08 -9.43 Papua New Guinea 2746.13 18.07 Philippines 2838.31 15.51 Vietnam 2872.62 27.78 Mongolia 3168.38 43.41 India 3238.55 32.04 Morocco 3294.67 25.07 Swaziland 3439.25 0.22 Honduras 3605.30 0.96 Paraguay 3704.46 10.46 Cape Verde 3780.82 12.01 Bolivia 3793.44 19.79 Syria 4002.14 14.48 Sri Lanka 4034.65 18.03 Indonesia 4075.34 33.76 Guyana 4338.50 2.03 Bhutan 4567.57 63.58 Jordan 4644.48 -6.68 Angola 4754.68 20.82 Namibia 4777.39 13.88 Egypt 4955.67 12.43 Georgia 5051.30 -7.37 Armenia 5368.11 8.20 Algeria 6069.56 45.47 Ecuador 6171.29 21.26 Guatemala 6284.59 3.30 Tunisia 6300.92 23.46 El Salvador 6338.36 -2.38 Ukraine 6404.89 15.38 Dominica 6577.93 2.30 Albania 6643.01 7.44 Turkmenistan 6934.25 41.17 Bosnia and Herzegovina 7115.79 -2.44 Peru 7280.16 26.29 St.Vincent & Grenadines 7372.56 -3.13 Colombia 7529.01 20.48 South Africa 7588.59 18.58 China 7634.28 52.08 Macedonia 7677.74 3.53 Thailand 7794.25 32.37 Tonga 7875.62 -19.25 Brazil 8160.39 16.45 Jamaica 8794.72 2.71 Botswana 8871.53 13.03 Venezuela 9115.39 22.56 Mauritius 9483.62 10.78 Romania 9736.61 23.62 Turkey 9909.50 13.75 Dominican Republic 9911.12 6.82 Panama 10197.56 40.72 Gabon 10283.92 47.29 Bulgaria 10911.88 17.70 Uruguay 11069.14 18.88 Costa Rica 11217.14 20.87 Malaysia 11295.98 36.03 Mexico 11628.87 20.92 Kazakhstan 11730.99 38.67 Argentina 11961.40 26.27 Chile 11999.25 26.81 Grenada 12025.85 -6.64 Latvia 12753.97 18.02 St. Kitts & Nevis 12754.13 6.07 Belarus 12786.74 26.93 Lebanon 12944.58 5.43 St. Lucia 13096.50 3.35 Russia 14631.24 26.09 Croatia 15088.13 23.35 Antigua and Barbuda 15091.07 55.16 Estonia 16264.25 24.74 Poland 16372.87 20.30 Slovak Republic 19125.11 33.39 Portugal 19889.94 12.11 Saudi Arabia 21589.18 37.13 Malta 21632.50 15.08 Czech Republic 21956.91 27.25 Equatorial Guinea 22031.48 72.24 Barbados 22917.24 18.44 Seychelles 23805.29 15.92 Slovenia 24925.14 24.98 Korea, Republic of 25033.62 29.84 Israel 25550.34 18.82 Greece 27284.76 5.56 Spain 27633.98 22.33 Italy 27692.99 18.51 New Zealand 27864.89 19.80 Japan 30007.69 20.67 France 30821.67 17.02 Finland 32161.50 20.78 Germany 32488.16 21.44 Ireland 33348.11 28.65 United Kingdom 33383.26 11.23 Denmark 33908.88 20.86 Belgium 34624.98 22.91 Sweden 35224.61 23.44 Canada 36208.90 19.26 Netherlands 37050.73 25.73 Iceland 37113.41 22.56 Austria 37401.78 25.83 Switzerland 39621.20 30.67 United States 41099.10 11.42 Norway 49945.47 34.68 Macao 51056.60 65.69 Luxembourg 84524.63 49.78 Qatar 159469.10 54.46 Czech Republic 21956.91 27.25 Equatorial Guinea 22031.48 72.24 Barbados 22917.24 18.44 Seychelles 23805.29 15.92 Slovenia 24925.14 24.98 Korea, Republic of 25033.62 29.84 Israel 25550.34 18.82 Greece 27284.76 5.56 Spain 27633.98 22.33 Italy 27692.99 18.51 New Zealand 27864.89 19.80
Explanation / Answer
We found the correlation between the 2 variables: .396
Square it and you will get hte coefficient of determination =.396^2 = .157
So, Coeff of deterination will give the percentage of the variation in y is accounted for by x
The answer is 15.7%
Is this a strong regression?
In short, no. Why? Because the percentage of the variation in y is accounted for by x is 15.7%. The number 15.7% is very small, and therefore, means that the regression equation prediction power is not powerful, it' weak
