Consider the following model of trade between the us and other countries, indexed by i:

log importsi = +1.03 × log gdpi − 1.67 × log distancei + .02 × englishi + ui

where imports is imports from i (in hundreds of billions), gdp is the income of country i (in hundreds of billions), distancei is the distance (in hundreds of miles) between the us and country i, and english is a dummy variable for whether the majority spoken language of i is english.

a. interpret the coefficient on log gdp, log distance and english.

b. china is 7200 miles from the us, has a nominal gdp of 12 trillion (120 hundred billion), and does not primary speak english. estimate us imports from china (remember that to go from log(x) to x you need to exponentiate).

c. suppose that one wanted to test if barriers to trade (distance or linguistic) did not matter for trade flows. i. e., one wanted to test if the coefficients on distance and english were both 0. how would one set this up if the error are homoscedastic?