The following is a. model you've estimated Medals. = 31 + ,dgGDPpcg + 33mg. + 545mm + swarm where for country i, e M edalsi is the total number of Olympic medals won since the games began I GDPpcl- is the GDP per capits 0 Big is a dummy variable equal to 1 if i is in the top third of countries in terms of population and 0 otherwise 0 Smolii is a dummy variable equal to 1 if 1? is in the bottom third of countries in terms of population and 0 otherwise o North..- is a dummy variable equal to 1 if the majority of country i lies north of the equator and 0 otherwise You estimate that (a) (Ipts) What is the reference category for this regression? (b) (4pts) What is the difference in the expected number of medals between two countries that are: Parameter Estimate Std. Err. 16 2.46 0.003 0.15 36 2.5 -20 4.52 5 6.18 o A northern country in the bottom third of countries in terms of population and 30,000 in GDP per capita o A southern country with 8 GDP per capits of 15,900 and a population in the middle third of all countries (c) (10pts) Suppose you replace Smlli with M 9:11;. a dummy variable equal to 1 if country 1' is the middle third of countries in terms of population and 0 otherwise. Then: Means.- ==n + "i'gGDPpce + 'mBigg + 'nMed; + emcee; Find 'nz. is. it. and '(5