Question: In recent years, many American firms have intensified their efforts to market their products in the Pacific Rim. A consortium of U.S. firms that produce raw materials used in Singapore is interested in predicting the level of exports from the U.S. to Singapore, as well as understanding the relationship between U.S. exports to Singapore and certain variables affecting the economy of that country. The consortium hired an economist to perform an analysis.

The economist obtained monthly data on five economic variables for the period January 1994 to July 1999 (a total of 67 months) from the Monetary Authority of Singapore. These variables are as follows:

Exports: U.S. exports to Singapore in billions of Singapore dollars,

(the dependent variable)

M1: money supply figures in billions of Singapore dollars

Lend: minimum Singapore bank lending rate in percentage

Price: index of local prices where the base year is 1994

Exchange: exchange rate of Singapore dollars per U.S. dollar

Part I .

The economist performed a multiple regression analysis with Exports as the dependent variable and the four economic variables M1, Lend, Price, and Exchange as the explanatory variables. Part of his regression results are shown below:

Regression I

1. Calculate a 95% confidence interval for the true coefficient of the variable Exchange. Which variable(s) among the four do you think is(are) an important explanatory variable(s) for Exports? Explain your answer.
2. The economist next computed the sample correlation between Price and Lend, which turns out to be 0.745. What problems, if any, can you identify in Regression I based on this information? How would you modify the model to avoid these problems?
   Part II
   The economist tried two other regression runs with Exports as the dependent variable. In one model, he used three independent variables: M1, Price, and Exchange. In the other model, he used only two independent variables: M1 and Price. Part of his regression results are shown below:
   
   Regression II

   	R Square	0.825
   	Adjusted R Square	0.817
   	Observations	67
   		Coefficients	Standard Error
   	Intercept	-3.995	2.736
   	M1	0.364	0.041
   	Price	0.037	0.004
   	Exchange	0.242	1.135

   
   Regression III

   	R Square	0.825
   	Adjusted R Square	0.819
   	Observations	67
   		Coefficients	Standard Error
   	Intercept	-3.423	0.541
   	M1	0.361	0.039
   	Price	0.037	0.004

3. In your opinion, which of the three regression models (I, II, III) is the best overall? Support your answer with any statistical reasoning that you feel is appropriate.
4. What is your estimate of U.S. exports to Singapore in billions of Singapore dollars (using your best model) if M1=9.5, Lend=12.7, Price=155, and Exchange=1.5?

Price: $2.99

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