Country Name 9263.90 ARE 106 Problem Set 1 Please answer each question completel
ID: 3268843 • Letter: C
Question
Country Name
9263.90
ARE 106
Problem Set 1
Please answer each question completely, show your work, and attach your Excel output.
You must submit Problem Set 1 at the beginning of class on Monday, August 14th, 2017 to receive full credit.
(No assignments will be accepted after 2:10 pm Thursday, August 17th, 2017)
Carbon dioxide (CO2) emissions are widely believed to be a driver of global climate change. In this problem set you will use cross-section data to test what drives countries’ “carbon footprints,” that is, their CO2 emissions.
The data set “CO2 by country 2010_Lindsay2017” contains data on a sample of countries’ CO2 emissions, in kilotons; population, in millions; and gross national income (GNI), in millions of US dollars, for the year 2010.
1. Please propose a linear regression model to estimate the effect of population on CO2 emissions, and explain what the parameters and variables in this model are.
2. Now estimate this model in Excel, like we did in class, using ordinary least squares. Report and interpret your estimated parameters here. Specifically, what does each parameter estimate tell us?
3. Propose an economic theory (explanation) to justify adding the income variable to your regression.
4. Write the new linear regression model that includes both population and GNI as explanatory variables.
5. Expand your Excel spreadsheet and use OLS to estimate your multiple regression model. Report and interpret your results. You do not need to interpret the estimate of the intercept.
6. Does the inclusion of GNI in your regression model affect your estimated effect of CO2 emissions with respect to population? Why or why not?
7. Compare the R-squared from the simple and multiple regression. What explains the difference between the two?
Help with the excel on this problem. How to solve and get the answers.
Country Name
CO2(kt) POP(millions) GNI(Millions of US$) United States 5433056.54 309.33 15170300.00 Afghanistan 8236.08 28.40 15998.78 Albania 4283.06 2.86 11807.46 Algeria 123475.22 37.06 160996.42 Angola 30417.77 19.55 73946.34 Argentina 180511.74 40.37 451417.86 Armenia 4220.72 2.96 9718.57 Australia 373080.58 22.03 1096901.32 Austria 66897.08 8.39 393108.52 Bahamas, The 2464.22 0.36 7702.50 Bahrain 24202.20 1.25 23340.38 Bangladesh 56152.77 151.13 124617.10 Barbados 1503.47 0.28 4321.85 Belarus 62221.66 9.49 54058.30 Belgium 108946.57 10.92 493427.31 Belize 421.71 0.31 1258.61 Benin 5188.81 9.51 6508.31 Bermuda 476.71 0.07 7201.48 Bhutan 476.71 0.72 1497.42 Bolivia 15456.41 10.16 18785.53 Botswana 5232.81 1.97 13197.27 Brazil 419754.16 195.21 2104398.02 Bulgaria 44678.73 7.40 47167.59 Burkina Faso 1683.15 15.54 9202.85 Burundi 308.03 9.23 2014.76 Cabo Verde 355.70 0.49 1591.15 Cambodia 4180.38 14.36 10698.07 Cameroon 7234.99 20.62 23358.49 Canada 499137.37 34.01 1582763.45 Central African Republic 264.02 4.35 1981.47 Chad 469.38 11.72 10302.35 Chile 72258.24 17.15 202873.97 China 8286891.95 1337.71 5904605.99 Colombia 75679.55 46.44 275790.73 Congo, Dem. Rep. 3039.94 62.19 20651.16 Congo, Rep. 2027.85 4.11 9024.21 Costa Rica 7770.37 4.67 35553.17 Cote d'Ivoire 5804.86 18.98 23972.20 Croatia 20883.57 4.42 57968.36 Cuba 38364.15 11.28 63388.65 Cyprus 7708.03 1.10 22311.52 Czech Republic 111751.83 10.47 191444.66 Denmark 46303.21 5.55 325079.06 Dominica 135.68 0.07 483.70 Dominican Republic 20964.24 10.02 51355.94 Ecuador 32636.30 15.00 68517.07 Egypt, Arab Rep. 204776.28 78.08 214525.02 El Salvador 6248.57 6.22 20868.00 Equatorial Guinea 4679.09 0.70 9630.16 Estonia 18338.67 1.33 18239.97 Ethiopia 6494.26 87.10 29825.57 Fiji 1290.78 0.86 3043.13 Finland 61843.96 5.36 251109.55 France 361272.84 65.02 2700865.68 Gabon 2574.23 1.56 12869.57 Gambia, The 473.04 1.68 921.90 Germany 745383.76 81.78 3483764.77 Ghana 8998.82 24.26 31641.07 Greece 86717.22 11.15 293454.05 Grenada 260.36 0.10 731.14 Guatemala 11118.34 14.34 40126.71 Guinea 1235.78 10.88 4302.27 Guyana 1701.49 0.79 2272.06 Haiti 2119.53 9.90 6644.82 Honduras 8107.74 7.62 15110.48 Hong Kong SAR, China 36288.63 7.02 233476.93 Hungary 50582.60 10.00 123537.26 Iceland 1961.85 0.32 11112.24 India 2008822.94 1205.62 1690503.86 Indonesia 433989.45 240.68 689283.20 Iraq 114667.09 30.96 140108.12 Ireland 39999.64 4.56 183661.91 Israel 70655.76 7.62 227769.19 Italy 406307.27 59.28 2121166.42 Jamaica 7157.98 2.69 12736.32 Japan 1170715.42 127.45 5643192.13 Jordan 20821.23 6.05 26218.06 Kazakhstan 248728.94 16.32 128676.48 Kenya 12427.46 40.91 39852.51 Korea, Rep. 567567.26 49.41 1095599.47 Kuwait 93695.52 2.99 126113.71 Lao PDR 1873.84 6.40 6713.29 Latvia 7616.36 2.10 24579.69 Lebanon 20403.19 4.34 37501.05 Lesotho 18.34 2.01 2594.04 Liberia 799.41 3.96 1113.30 Lithuania 13560.57 3.10 35969.96 Luxembourg 10828.65 0.51 34073.20 Macao SAR, China 1030.43 0.53 25370.95 Macedonia, FYR 10872.66 2.10 9207.39 Madagascar 2013.18 21.08 8643.30 Malawi 1239.45 15.01 5290.12 Malaysia 216804.04 28.28 239358.02 Maldives 1074.43 0.33 1822.80 Mali 623.39 13.99 9003.28 Marshall Islands 102.68 0.05 198.24 Mauritania 2214.87 3.61 3444.76 Mauritius 4118.04 1.28 9835.24 Mexico 443674.00 117.89 1042119.87 Micronesia, Fed. Sts. 102.68 0.10 305.08 Moldova 4855.11 3.56 6316.18 Mongolia 11510.71 2.71 5640.28 Montenegro 2581.57 0.62 4086.06 Morocco 50608.27 31.64 88304.87 Mozambique 2882.26 23.97 9834.28 Namibia 3175.62 2.18 10766.65 Nepal 3755.01 26.85 16116.35 Netherlands 182077.55 16.62 841677.04 New Zealand 31550.87 4.37 136188.35 Nicaragua 4547.08 5.82 8699.55 Niger 1411.80 15.89 5674.42 Nigeria 78910.17 159.71 349387.81 Norway 57186.87 4.89 425901.89 Oman 57201.53 2.80 50227.83 Pakistan 161395.67 173.15 183913.43 Palau 216.35 0.02 190.20 Panama 9633.21 3.68 30229.00 Papua New Guinea 3135.29 6.86 9262.47 Paraguay 5075.13 6.46 18618.46 Peru 57579.23 29.26 137317.44 Philippines 81590.75 93.44 265929.44 Poland 317254.17 38.18 458863.46 Portugal 52361.09 10.57 230038.36 Romania 78745.16 20.25 162254.86 Russian Federation 1740776.24 142.39 1477812.94 Rwanda 594.05 10.84 5656.02 Samoa 161.35 0.19 622.45 Sao Tome and Principe 99.01 0.18 200.67 Saudi Arabia 464480.56 27.26 533855.47 Senegal 7058.98 12.95 12799.08 Serbia 45962.18 7.29 38478.03 Seychelles 704.06 0.09 926.08 Sierra Leone 689.40 5.75 2606.60 Singapore 13520.23 5.08 235074.91 Slovenia 15328.06 2.05 47507.02 Solomon Islands 201.69 0.53 508.30 South Africa 460124.16 50.90 357979.72 Spain 269674.85 46.58 1411515.96 Sri Lanka 12709.82 20.65 48950.36 St. Kitts and Nevis 249.36 0.05 663.27 St. Lucia 403.37 0.18 1204.73 St. Vincent and the Grenadines 209.02 0.11 668.95 Sudan 14172.96 35.65 60504.61 Suriname 2383.55 0.52 4330.41 Swaziland 1023.09 1.19 3802.06 Sweden 52515.11 9.38 501832.93 Switzerland 38756.52 7.82 616380.88 Tajikistan 2860.26 7.63 5563.45 Tanzania 6846.29 44.97 22626.29 Thailand 295281.51 66.40 305180.57 Timor-Leste 183.35 1.07 3295.00 Togo 1540.14 6.31 2761.61 Tonga 157.68 0.10 373.17 Trinidad and Tobago 50681.61 1.33 19669.16 Tunisia 25878.02 10.55 42169.55 Turkey 298002.42 72.14 723965.76 Turkmenistan 53054.16 5.04 20254.04 Uganda 3784.34 33.99 15713.33 Ukraine 304804.71 45.87 134410.29 United Arab Emirates 167596.57 8.44 285949.29 United Kingdom 493504.86 62.77 2434464.28 Uruguay 6644.60 3.37 37378.59 Uzbekistan 104443.49 28.56 40491.77 Venezuela, RB 201747.34 29.04 387497.39 Vietnam 150229.66 86.93 111512.78 West Bank and Gaza 2365.22 3.81 9512.20 Yemen, Rep. 21851.65 22.76 29984.28 Zambia 2427.55 13.22 18902.38 Zimbabwe 9427.86 13.089263.90
Explanation / Answer
(1)
from the given data we observe that, we consider the variables as X and Y are Population (X) is an indepedent variable and CO2 (Y) is a dependent variable,
then the linear regression model to estimate the effect of population on CO2 emissions is given by
First we enter the data of population(X) and CO2 (Y) on Excel then go to data->data analysis->select Regression-> select the input range of X and Y-> click ok ->then we get,
Null Hypothesis:H0 : There is an effect of CO2 on population in all countries.
Alternative Hypothesis: H1 : There is no effect of CO2 on population in all countries.
(2)
From the above Analysis,the linear Regression equation Y = b0 + b1 X
So from the ordinary least squares or by using the above ANOVA table the estimated parameters are given by
from the above table of Analysis,the intercept = b0 = 6371.419399
and the slope = b1 = 4429.596981
Hence the linear Regression equation is Y = b0 + b1 X => Y = 6371.419399 + 4429.596981 X
From the above ANOVA we observe that the probability value p-value < 5% that is 0.05 hence we Accept the Null hypothesis H0 that is there is an effect of CO2 on population in all countries.
(3)
So we add the new variable Income GNI (X2) in Linear regression equation is given by
Y = b0 + b1 X1 + b2 X2
where X1 = Population and X2 = GNI and Y = CO2
then the Analysis of the given data through Excel is given by
So from the above ANOVA table we observe that the estimated parameters of linear Regression equation are given by
Intercept = b0 = -54203.796
Slope1 = b1 = 3107.6513
Slope2 = b2 = 0.2975358
Hence the linear Regression equation is Y = b0 + b1 X1 + b2 X2 => Y = -54203.796 + 3107.6513 X1 + 0.2975358X2
From the above ANOVA we observe that the probability value p-value < 5% that is = 0.05 hence we Accept the Null hypothesis H0 that is there is an effect of CO2 on population as well as GNI in all countries.
(4)
The linear regression equation of both population (X1) and GNI (X2) are an Explanatory (independent) variables and dependent variable is CO2 (Y) is given by
Y = b0 + b1 X1 + b2 X2
=> Y = -54203.796 + 3107.6513 X1 + 0.2975358X2
------------------------------------------ x ----------------------------------------
SUMMARY OUTPUT Regression Statistics Multiple R 0.798324636 R Square 0.637322224 Adjusted R Square 0.6351505 Standard Error 477331.9984 Observations 169 ANOVA df SS MS F Significance F Regression 1 6.68645E+13 6.69E+13 293.4638 1.277E-38 Residual 167 3.80503E+13 2.28E+11 Total 168 1.04915E+14 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 6371.419399 38087.24183 0.167285 0.867348 -68823.11 81565.953 -68823.1145 81565.9533 Population 4429.596981 258.57523 17.13079 1.28E-38 3919.0994 4940.0945 3919.09942 4940.09454