Stored in Countries, perform a natural logarithmic transformation on per capita GDP and develop a regression model by using per capita GDP, natural logarithm of per capita GDP, and population growth as independent variables.

a. State the regression equation.

b. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. c. Perform residual analysis.

d. Compute the coefficient of determination, \(r^{2}\), and the adjusted \(r^{2}\).

e. What conclusions can you draw based on the results of (a) through (d)?