From data for 101 countries on per capita income in dollars (X) and life expectancy in years (Y) in the early 1970s, Sen and Srivastava obtained the following regression results:

 Ŷ_i = −2.40 + 9.39 ln X_i − 3.36 [D_i (ln X_i − 7)]

se = (4.73)   (0.859)         (2.42)                        R² = 0.752

where D_i = 1 if ln X_i > 7, and D_i = 0 otherwise. When ln Xi = 7, X = $1,097 (approximately).

a. What might be the reason(s) for introducing the income variable in the log form?

b. How would you interpret the coefficient 9.39 of ln X_i ?

c. What might be the reason for introducing the regressor D_i (ln X_i − 7)? How do you explain this regressor verbally? And how do you interpret the coefficient −3.36 of this regressor 

d. Assuming per capita income of $1,097 as the dividing line between poorer and richer countries, how would you derive the regression for countries whose per capita is less than $1,097 and the regression for countries whose per capita income is greater than $1,097?