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Multiple regression analysis - Local bank

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EXHIBIT 1: A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0=female, 1=male) and job type (0=clerical, 1=technical). The following tables summarizes the regression results:

df SS MS F
Regression SS 3 1004346.771 334782.257 5.96
Unexplained SS 26 1461134.596 56197.48445

Coefficients Standard Error t Stat P-Value
Constant 784.92 322.25 2.44 0.02
Service 9.19 3.20 2.87 0.01
Gender 222.78 89.00 2.50 0.02
Job -28.21 89.61 -0.31 0.76

(A) Referencing Exhibit 1, the adjusted multiple coefficient of determination is (3 points):
(a) 5.93%
(b) 59.3 %
(c) 40.7 %
(d) 33.9%
(e) None of the above ________________

(B) Referencing Exhibit 1, based on hypothesis tests for the individual regression coefficients at a 5% significance level (2 points),
(a) All the regression coefficients are not equal to zero,
(b) "Job" is the only significant independent variable in the model
(c) Only "Service" and "Gender" are significantly related to monthly salary
(d) "Service" is the only significant variable in the model
(e) None of the variables are significant ________________

(C) Referencing Exhibit 1, which of the variables are dummy variables in the model (2 points)?
(a) Salary
(b) Service
(c) Service and gender
(d) Gender and job
(e) Service, gender and job ________________

(D) Referencing Exhibit 1, the results for the variable "Gender" show (2 points)
(a) Males average $222.78 more than females in monthly salary
(b) Females average $222.78 more than males in monthly salary
(c) Gender is not related to monthly salary
(d) Gender and months of service are correlated ________________

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This solution interprets a multiple regression analysis by answering and explaining 4 multiple choice questions.

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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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