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Economics- Regression Analisys

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3. Rubax, a U.S. manufacturer of athletic shoes, estimates the following linear trend model for shoe sales:
Qt= a + bt + c1D1 + c2D2 + c3D3
Qt= sales of athletic shoes in the tth quarter
t = 1,2,3, ......., 28 (2001(I), 2001(II), ........., 2007(IV) )
D1 = 1 if t is quarter I (winter); 0 otherwise
D2 = 1 if t is quarter II (spring); 0 otherwise
D3 = 1 if t is quarter III (summer); 0 otherwise
The regression analysis produces the following results:
Qt = 184500 + 2,100t + 3280 D1 + 6250 D2 + 7010 D3
(17.90) (6.18) (2.17) (2.82) (4.44)
R2 = 0.9651 F = 159.01
a. Is there sufficient statistical evidence of an upward trend in shoe sales?
b. Do these data indicate a statistically significant seasonal pattern of sales for Rubax shoes? If so, what is the seasonal pattern exhibited by the data?
c. Using the estimated forecast equation, forecast sales of Rubax shoes for 1999(III) and 2000(II).
d. How might you improve this forecast equation?

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Economics in American Firms: Multiple Regression Analysis

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 2006 to July 2011 (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
- 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 2006
- 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 independent variables. Part of his regression results are shown below:

Regression I
R Square 0.825
Observations 67

Coefficients Standard Error Lower 95% Upper 95%
Intercept -4.015 2.766 -9.544 1.514
M1 0.368 0.064 0.240 0.496
Lend 0.005 0.049 -0.093 0.103
Price 0.037 0.009 0.019 0.055
Exchange 0.268 1.175 -2.035 2.571

(a) (3 points) Which variable(s) among the four do you think is (are) an important explanatory variable(s) for Exports? Explain your answer.

(b) (3 points) The economist next computed the sample correlation between Price and Lend, which turns out to be 0.845. 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 0.823
Observations 67

Exchange 0.242 1.135 -1.983 2.467

Regression III

R Square 0.821
Observations 67

Price 0.037 0.004 0.029 0.045

(c) (4 points) 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.

(d) (4 points) What is your estimate of U.S. exports to Singapore in billions of Singapore dollars (using your best model) if M1=102.5, Lend=5.4, Price=126.9, and Exchange=1.26?

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