Now propose a single model with which you can test whether: (a) the relationship between population and CO2 emissions is quadratic; (b) the relationship between income and CO2 emissions is quadratic; (c) the impact of population on CO2 emissions is different in different years; (d) the impact of income on CO2 emissions is different in different years; and (e) the impact of population on CO2 emissions is different at higher than at lower income levels. Please write down your regression equation to test these hypotheses here (do not estimate it yet; Hint: You will have to add quadratic and interaction terms to your regression.)