Question

Using this model: propose a single model with which you can test whether: (a) the relationship between population(POP) and CO2 emissions is nonlinear and quadratic; (b) the relationship between income(GNI) and CO2 emissions is nonlinear and quadratic; (c) the impacts of population and income(GNI) on CO2 emissions are different in different years; and (d) the impact of population(POP) on CO2 emissions is different at higher than at lower income levels. What does your model look like? (Hint: You will have to add quadratic and interaction terms to your regression.) t is a dummy variable representing one of two years

Answer 1

Consider the given problem here the regression model is look like.

C = b0 + b1*P + b2*P^2 + a1*Y + a2*Y^2 + d1*D1 + d2*Y*P*D2.

So, here “C” be the “CO2” emission, “P” be the population, “Y” is “GNI”, “D1” be the dummy variable take “0” for year1 and “1” for year2 and “D2” also be a dummy variable takes “1” when income is comparatively high and takes “0” when income is comparatively low.

So, here if “b2” (the coefficient of P^2) is significantly differ from zero, => “P” is nonlinearly related with “C” and their relation is quadratic. Similarly, if “a2” (the coefficient of Y^2) is significantly differ from zero, => “Y” is nonlinearly related with “C” and their relation is quadratic.

Now, “D1” be the dummy variable take “0” for year1 and “1” for year2. So, if “d1” is significantly differ from zero, => the CO2 emission is significantly differ in these two periods and the difference can be captured by the estimated coefficient. Similarly, “D2” also be a dummy variable takes “1” when income is comparatively high and takes “0” when income is comparatively low. So, if “d2” is significantly differ from zero, => “P” the level of population have additional effect on “CO2” emission if level of income is high compare to when level of income is low.