An analyst at the United Nations is developing a model that describes GDP (gross domestic product per capita, a measure of the overall production in an economy per citizen) among developed countries. She is using national data for 29 countries from the 2005 report of the Organization for Economic Cooperation and Development (OECD). She started with the equation (estimated by least squares):

Estimated per capita GDP = $26,714 +$1.441 Trade Balance

The trade balance is measured as a percentage of GDP. Exporting countries tend to have large positive trade balances. Importers have negative balances. This equation explains only 37% of the variation in per capita GDP, so she added a second explanatory variable, the number of kilograms of municipal waste per person.

(a) Examine scatterplots of the response versus the two explanatory variables as well as the scatterplot between the explanatory variables. Do you notice any unusual features in the data? Do the relevant plots appear straight enough for multiple regression?

(b) Do you think, before fitting the multiple regression, that the partial slope for trade balance will be the same as in the equation shown? Explain.

(c) Fit the multiple regression that expands the one-predictor equation by adding the second explanatory variable to the model. Summarize the estimates obtained for the fitted model.

(d) Does the estimated model appear to meet the conditions for the use of the MRM?

(e) Draw the path diagram for this estimated model. Use it to explain why the estimated slope for the trade balance has become smaller than in the simple regression shown.

(f) Give a confidence interval, to presentation precision, for the slope of the municipal waste variable. Does this interval imply that countries can increase their GDP by encouraging residents to produce more municipal waste?

Nation	GDP (per cap)	Trade Bal (%GDP)	Muni Waste (kg/person)
Australia	30500	-2.9	690
Austria	35800	4.8	560
Belgium	33800	2.9	440
Canada	30700	3.9	380
Czech Republic	10500	-0.3	280
Denmark	44700	5.1	670
Finland	35600	5.6	450
France	32900	0.3	540
Germany	33200	4.9	640
Greece	18600	-8.6	430
Hungary	9900	-3	460
Iceland	41800	-5.9	730
Ireland	44700	15.6	760
Italy	28800	0.8	520
Japan	36500	1.6	410
Korea	14100	4.4	390
Mexico	6500	-1.6	320
Netherlands	35500	5.4	600
New Zealand	23700	0.2	400
Norway	54500	14.2	700
Poland	6300	-1.8	260
Portugal	16000	-7.7	450
Slovak Republic	7600	-2.7	300
Spain	24400	-3.6	650
Sweden	38500	8	470
Switzerland	47900	7.1	660
Turkey	4200	-5.8	360
United Kingdom	35500	-3.3	610
United States	39700	-4.5	740