The Organization for Economic Cooperation and Development (OECD) tracks various summary statistics of the member economies. The countries lie in Europe, parts of Asia, and North America. Two variables of interest are GDP (gross domestic product per capita, a measure of the overall production in an economy per citizen) and trade balances (measured as a percentage of GDP). Exporting countries tend to have large positive trade balances. Importers have negative balances. These data are from the 2005 report of the OECD.
(a) Describe the association in the scatterplot of GDP on Trade Balance. Does the association in this plot move in the right direction? Does the association appear linear?
(b) Estimate the least squares linear equation for GDP on Trade Balance. Interpret the fitted intercept and slope. Be sure to include their units. Note if either estimate represents a large extrapolation and is consequently not reliable.
(c) Interpret r2 and se associated with the fitted equation. Attach units to these summary statistics as appropriate.
(d) Plot the residuals from this regression. After considering this plot, does se provide an adequate summary of the residual variation?
(e) Which country has the largest values of both variables? Is it the country that you expected?
(f) Locate the United States in the scatterplot and find the residual for the United States. Interpret the value of the residual for the United States.