c) Generate a new variable that is In(GDP), i.e., the natural log of GDP. Run the regression of InGDP on population for the whole sample. What does the unconditional relationship between them suggest? Interpret your output, making reference to the coefficient on your independent variable, the constant, the standard errors and test statistic / confidence intervals, and the R2. d) Now include time as an x variable, proxying it using the year of observation. What happens to the relationship between InGDP and population? Interpret your output again and explain the change. e) Replicate the same regression (InGDP on population and year) for the low, middle, and high income subsamples separately. How does the relationship in each case change compared to the overall relationship? f) :"Partial out" InGDP and population for the whole sample by first regressing each separately on year, predicting residuals from those regressions (using the predict vornome, resid command), and then running the regression of residual Ys on residual Xs. How does this regression relate to the regression in part e? g) Use the xtset command to define your data as a panel of countries with yearly observations, and then use the I1. time series operator to calculate per capita growth, or the % change in GDP per capita for each country in a given year (i.e., the difference between the current and previous year divided by the previous year). Run the regression of GDP growth against both population and time for the whole sample, and for the three low-middle-high income subsamples. Interpret your results to explain how the relationship between population, economic growth, and time varies within the sample. h) Run two separate regressions of GDP per capita against population, one for the year 1980 and one for the year 2010. Interpret your output for both, and then plot a graph for each subsample showing both the scatter plot of GDPpc against population with a linear fit curve, to be submitted with your write up. You will need to use the state graph commands scatter, Ifit, and twoway (to combine the two graphs into one). What can you conclude about the relationship between GDP per capita and population in 1980 vs in 2010? Do these results make sense in light of part ? Find an additional data source that you can merge into the GDP data we have been using for at least one country. Examples could include: the annual temperature data for the planet from NASA GISS's website, the presence of certain industries or resources, or whether the countries are democracies or not. Merge the data source into your data set, make a summary stats table, and run at least one regression and generate one scatter plot figure providing evidence of an additional factor associated with GDP. Interpret it. Bonus points will be given for interesting questions or data. j Interpret all the regressions we've been running from the point of view of the Gauss Markov assumptions (which you hopefully didn't forget about while interpreting your results above..). Which have been violated, when? What has that led to? Make explicit reference to both the problems of identification and inference in your