An extension of the Solow growth model that includes human capital in addition to physical capital, suggests that investment in human capital (education) will increase the wealth of a nation (per capita income). To test this hypothesis, you collect data for 104 countries and perform the following regression: RelPersInc = 0.046 - 5.869 x gpop +0.738 x S + 0.055 × Educ, R² = 0.775, SER = 0.1377 K (0.079) (2.238) (0.294) (0.010) where RelPersinc is GDP per worker relative to the United States, gpop is the average population growth rate, 1980 to 1990, S is the average investment share of GDP from 1960 to 1990, and Educ is the average educational attainment in years for 1985. Numbers in parentheses are for heteroskedasticity-robust standard errors. Hint: Type your answers in three decimal places. a) An increase in the investment share of 0.1 results in an increase of GDP per worker relative to the United States by [a1]. For every additional year of average educational attainment, the increase is [a2]. To test for equality of the coefficients between the OECD and other countries, you introduce a binary variable (DOECD), which takes on the value of one for the OECD countries and is zero otherwise. To conduct the test for equality of the coefficients, you estimate the following regression: RelPersInc = -0.068 - 0.063 x gpop + 0.719 x S + 0.044 x Educ, (0.072) (2.271) (0.365) (0.012) +0.381 X DOECD -8.038 x (DOECD x gpop) - 0.430 × (DOECD × S) (0.184) (5.366) (0.768) +0.003 x (DOECD x Educ), R² = 0.845, SER = 0.116 (0.018) Write down the two regression functions, one for the OECD countries, the other for the non-OECD countries. b) The regression for the non-OECD countries is RelPersInc = [b1] - [b2] x gpop + [b3]x S + [b4] × Educ. c) For the OECD countries we get RelPersInc = + [c1] [c2] x gpop + [c3] SK + [c4] × Educ.