# Question: An analyst at the United Nations is developing a model

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?

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?

**View Solution:**## Answer to relevant Questions

A firm that operates a large, direct-to-consumer sales force would like to build a system to monitor the progress of new agents. The goal is to identify “superstar agents” as rapidly as possible, offer them incentives, ...1. Test statistic unaffected by collinearity 2. Minimum value of VIF 3. Regression estimate without VIF 4. Effect of collinearity on se (b1) 5. Correlations among variables 6. Scatterplots among variables 7. Percentage of ...The version of the CAPM studied in this chapter specifies a simple regression model as 100 (St – rt) = α + 100 β (Mt – rt) + ε where Mt are the returns on the market, St are the returns on the stock, and rt are the ...Before purchasing videoconferencing equipment, a company tested its current internal computer network. The tests measured how rapidly data moved through its network given the current demand on the network. Eighty files ...These data track monthly performance of stock in Apple Computer since 1990. The data include 264 monthly returns on Apple Computer, as well as returns on the entire stock market, the S&P 500 index, stock in IBM, and Treasury ...Post your question