We have a data file that contains data from the 2005 World Factbook relating to gross domestic product

(GDP) per capita in US$ thousands (gdp) and the percentage of the population that are internet users (intpct) for 213 countries. Here, GDP is based on purchasing power parities to account for between-country differences in price levels. This problem investigates whether there is a linear association between these two variables. In particular, how effective is it to use gdp to predict intpct using simple linear regression.

You can read the data into R as follows:

mydata=read.csv("http://www.datadescant.com/stat104/internet.csv")

a) Using R, find the least squares line for the data.

b) Interpret the estimates of the slope and the y-intercept in the context of the problem.

c) Predict the percentage of internet users if GDP per capita is US$20,000.

d) Draw a scatterplot with intpct on the vertical axis and gdp on the horizontal axis, and add the least squares line to the plot.

e) Based on the scatterplot, do you think it is appropriate to use this simple linear regression model in this problem or is the model potentially misleading (and if so, how)?

f) Comment on the following residual diagnostic graph produced in R:

begin{verbatim}

> mydata=read.csv("http://www.datadescant.com/stat104/internet.csv")

> fit=lm(mydata$intpct~mydata$gdp)

> plot(fit,which=1)

end{verbatim}

g) Now fit the model using log(intpct) instead of pct. Does this appear to be a better model? Why?

Countr+V1:X153y gdp intpct Afghanistan 1 3.4 Albania 7.4 43.4 Algeria 7.4 13.4 Andorra 46.7 79.1 Angola 8.7 4.5 Anguilla 12.2 24.5 AntiguaandBarbuda 16.5 74 Argentina 14.7 32.8 Armenia 5.8 7 Aruba 21.8 22.6 Australia 41.3 72.6 Bahamas,The 28.6 37 Bahrain 40.4 34.5 Bangladesh 1.7 0.4 Barbados 21.7 65.6 Belarus 13.4 27.6 Belgium 37.9 77.8 Belize 8.4 11.2 Benin 1.6 2.1 Bermuda 69.9 78.6 Bhutan 5 7.1 Bolivia 4.8 10.9 BosniaandHerzegovina 6.6 30.8 Botswana 13.1 5.8 Brazil 10.9 37.4 BritishVirginIslands 38.5 15.8 Brunei 50.3 78.4 Bulgaria 12.8 47.9 BurkinaFaso 1.2 1.1 Burma 1.1 0.2 Burundi 0.3 1.5 Cambodia 2 0.5 Cameroon 2.3 3.8 Canada 39.6 79.2 CapeVerde 3.7 29.1 CaymanIslands 43.8 44.8 CentralAfricanRepublic 0.7 0.5 Chad 1.8 1.6 Chile 15.5 41.5 China 7.4 29.1 Colombia 9.8 50.4 Comoros 1 3.1 Congo,DemocraticRepublicofthe 0.3 0.4 Congo,Republicofthe 4.2 5.8 CookIslands 9.1 53.9 CostaRica 11.4 32.4 CotedIvoire 1.8 4.5 Croatia 17.5 49.8 Cuba 9.9 14.5 Cyprus 21 38.7 CzechRepublic 25.6 65.6 Denmark 36.7 85.9 Djibouti 2.8 3.4 Dominica 10.5 38.4 DominicanRepublic 8.6 27.1 Ecuador 8 22.3 Egypt 6.2 24.5 ElSalvador 7.3 12.3 EquatorialGuinea 37.9 2.2 Eritrea 0.7 3.4 Estonia 19 75.7 Ethiopia 1 0.5 FalklandIslands(IslasMalvinas) 35.4 92.4 FaroeIslands 32.8 76.1 Fiji 4.3 12.9 Finland 35.3 83.5 France 33.3 69.3 FrenchPolynesia 18 40.7 Gabon 14.6 6.3 Gambia,The 1.9 7.2 Georgia 4.8 28.3 Germany 35.9 79.9 Ghana 1.6 5.2 Gibraltar 43 69.8 Greece 30.2 46.2 Greenland 36.5 62.4 Grenada 10.5 23.1 Guatemala 5.2 16.5 Guernsey 44.6 74.2 Guinea 1 0.9 Guinea-Bissau 1.1 2.3 Guyana 6.8 25.5 Haiti 1.2 10.3 Honduras 4.2 9 HongKong 45.6 68.4 Hungary 19 61.9 Iceland 36.7 97 India 3.4 5.2 Indonesia 4.3 8.1 Iran 11.2 10.5 Iraq 3.6 1.1 Ireland 37.6 65.1 Israel 29.5 60.6 Italy 30.7 47.9 Jamaica 8.4 55.1 Japan 34.2 78.4 Jersey 57 31.3 Jordan 5.3 25.2 Kazakhstan 12.8 34.1 Kenya 1.6 9.7 Kiribati 6.2 7.7 Korea,South 30.2 80.8 Kuwait 51.7 42.4 Kyrgyzstan 2.2 39.3 Laos 2.4 4.6 Latvia 14.3 68.2 Lebanon 14.2 24.1 Lesotho 1.7 4 Liberia 0.5 0.5 Libya 13.8 5.4 Lithuania 15.9 55.6 Luxembourg 81.8 84.3 Macau 33 47.2 Macedonia 9.4 50.9 Madagascar 1 1.5 Malawi 0.9 4.5 Malaysia 14.7 53.4 Maldives 4.6 21.9 Mali 1.2 1.8 Malta 26.9 58.9 MarshallIslands 2.5 3.3 Mauritania 2.1 2.3 Mauritius 13.5 22.2 Mexico 13.8 27.3 Micronesia,FederatedStatesof 2.2 15.9 Moldova 2.5 30.9 Monaco 30 75.3 Mongolia 3.3 10.5 Montenegro 9.9 42.3 Montserrat 3.4 23.3 Morocco 4.9 41.3 Mozambique 1 2.7 Namibia 6.9 5.9 Nepal 1.2 2 Netherlands 40.5 88.3 NewCaledonia 15 33.2 NewZealand 28 79.2 Nicaragua 2.9 3.5 Niger 0.7 0.7 Nigeria 2.4 28.3 Niue 5.8 83.9 Norway 59.1 94.4 Oman 25.8 48.4 Pakistan 2.4 10.9 Panama 12.7 27.7 PapuaNewGuinea 2.5 2 Paraguay 4.9 17.1 Peru 9.2 31.3 Philippines 3.5 8.1 Poland 18.8 58.4 Portugal 23 48 PuertoRico 16.3 25.1 Romania 11.5 35.5 Russia 15.9 29.4 Rwanda 1.1 4 SaintHelena,Ascension,andTristandaCunha 2.5 11.7 SaintKittsandNevis 14.4 33.8 SaintLucia 11.1 88.5 SaintVincentandtheGrenadines 10.6 73.2 Samoa 5.2 4.7 SanMarino 36.2 53.4 SaoTomeandPrincipe 1.8 14.9 SaudiArabia 24.2 37.4 Senegal 1.9 14.4 Serbia 11 56.2 Seychelles 21.6 35.9 SierraLeone 0.9 0.3 Singapore 57.2 68.2 Slovakia 22.2 74.2 Slovenia 28.4 64.9 SolomonIslands 2.8 1.7 Somalia 0.6 1.1 SouthAfrica 10.7 9 Spain 29.5 60.1 SriLanka 4.9 8.3 Sudan 2.2 9.3 Suriname 9.9 33.1 Swaziland 4.5 6.6 Sweden 39 92.4 Switzerland 42.9 80.5 Syria 4.8 19.8 Taiwan 35.8 70 Tajikistan 2 9.2 Tanzania 1.5 1.6 Thailand 8.7 26.2 Timor-Leste 2.6 0.2 Togo 0.9 5.3 Tokelau 1 57.8 Tonga 6.3 7.9 TrinidadandTobago 22.1 48.3 Tunisia 9.5 32.9 Turkey 12.3 34.6 Turkmenistan 7.4 1.6 Tuvalu 1.6 39.8 Uganda 1.2 9.2 Ukraine 6.7 17.2 UnitedArabEmirates 40.2 67 UnitedKingdom 35.1 82 UnitedStates 47.4 78.2 Uruguay 14.3 42.5 Uzbekistan 3.1 16.7 Vanuatu 5.5 7.6 Venezuela 12.6 32.3 Vietnam 3.1 25.8 VirginIslands 14.5 27.4 WallisandFutuna 3.8 8.4 WestBank 2.9 53.7 Yemen 2.6 9.7 Zambia 1.5 5.9 Zimbabwe 0.4 11.8