Scientists believe that a major cause of global warming is higher levels of carbon dioxide (CO2) in the atmosphere. In the Journal of World-Systems Research (Summer 2003), sociologists examined the impact of a dependence on foreign investment on CO2 emissions in n = 66 developing countries. In particular, the researchers modeled the level of CO2 emissions in a particular year on the basis of foreign investments made 16 years earlier and several other independent variables. The variables and the model results are listed in the following table.

a. Interpret the value of R2.
b. Use the value of R2 to test the null hypothesis,
H0: β1 = β2 = . . . = β7 = 0 at α = .01. Give the appropriate conclusion.
c. Do you advise conducting t-tests on each of the independent variables to test the overall adequacy of the model? Explain.

d. What null hypothesis would you test to determine whether the number of foreign investments made 16 years earlier is a statistically useful predictor of CO2 emissions the current year?
e. Conduct the test mentioned in part d at α = .05. Give the appropriate conclusion.
f. A matrix giving the correlation (r) for each pair of independent variables is shown in the table above. Identify the independent variables that are highly correlated. What problems may result from including these highly correlated variables in the regression model?

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y = In(level of CO2 emissions incurrent year) Estimate t-Value p-Value x1 = In(foreign investments) .79 2.52 <.05 X2 = gross domestic investment .01 -.02 -44 -.03 -1.19 .13 -1.66 -97 >.10 >.10 >.10 trade exports Хз In(GNP) X4 agricultural production >.10 >.10 -.66 X5 X6 = 1 if African country, -1.52 O if not In(level of CO, emissions) .56 3.35 <.001 X7 In(level of CO2 emissions) -.14 .25 Independent Variable X2 .13 Хз 57 .49 X4 X5 -38 -47 -47 Xв .14 -.14 X1 In(foreign įnvestments) gross domestic investment X3 = trade exports .36 .43 -.07 .42 -50 -47 -53 -.06 In(GNP) -.84 agricultural production X6 = 1 if African country, O if not