# Regression analysis

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1) Salary levels are determined by a number of important factors such as the years of experience, education level, job classification, etc. Other factors that contribute to salary levels might be due to gender or racial discrimination. Discuss how a dummy-variable regression model can be used to analyze salary differences between men and women. Suggest how the regression results can be used.
2)
Year Consumption GDP
1959 318127 507.4
1960 332293 527.4
1961 342653 545.7
1962 363761 586.5
1963 383135 618.7
1964 411735 664.4
1965 444288 720.1
1966 481769 789.3
1967 508694 834.1
1968 558727 911.5
1969 605516 985.3
1970 648948 1,039.7
1971 702414 1,128.6
1972 770724 1,240.4
1973 852512 1,385.5
1974 932378 1,501.0
1975 1030342 1,635.2
1976 1149774 1,823.9
1977 1278414 2,031.4
1978 1430394 2,295.9
1979 1596257 2,566.4
1980 1762904 2,795.6
1981 1944151 3,131.3
1982 2079306 3,259.2
1983 2286430 3,534.9
1984 2498404 3,932.7
1985 2712585 4,213.0
1986 2895167 4,452.9
1987 3105337 4,742.5
1988 3356583 5,108.3
1989 3596666 5,489.1
1990 3831501 5,803.2
1991 3971236 5,986.2
1992 4209653 6,318.9
1993 4454704 6,642.3
1994 4716394 7,054.3
1995 4968988 7,400.5
1996 5237499 7,813.2
1997 5529283 8,318.4
1998 5856036 8,781.5
1999 6250217 9,268.6
2000 6728413 9,872.9
1. 1. Use the BEA consumption and GDP data file to code the data according to the following model:

y^ = B0� + B1(GDP) + B2(Dummy 1990),
where Dummy 1990 = 1 if 1990 � 2000
0 otherwise

The data for consumption, GDP, and the dummy variable, respectively, in the year 1999 are:

A. 6,250,217 9,268.6 0
B. 6,250,217 9,268.6 1
C. 9,268.6 1 6,250,217

2. 2. Use the BEA consumption and GDP data to run a dummy variable regression model to investigate if U.S. consumption for the period 1959 � 1989 differs from U.S. consumption for the period 1990 � 2000. ��Use the following differential intercept dummy variable model

y^ = B0� + B1(GDP) + B2(Dummy 1990),
where Dummy 1990 = 1 if 1990 � 2000, �0 otherwise

The estimated regression equation is:

A. y^ = 690.4 + 2253.3288 (GDP) + 779.9 (Dummy 1990)
B. y^ = �55900.1 - 663.3028 (GDP) - 103839.3 (Dummy 1990).
C. y^ = -55900.1 + 663.3028 (GDP) + 103839.3 (Dummy 1990).

3. 3. Use the BEA consumption and GDP data to code the data according to the following model:

y^ = B0� + B1(GDP) + B2(GDP)(Dummy 1990),
Where Dummy 1990 = 1 if 1990 � 2000,� 0 otherwise

The data for consumption, GDP, and the dummy variable, respectively, in the year 1999 are

A. 6,250,217 6,250,217 9,268.6
B. 6,250,217 9,268.6 1
C. 6,250,217 9,268.6 9,268.6

4. 4. Use the BEA consumption and GDP data to run a dummy variable regression model to investigate if the rate of U.S. consumption for the period 1959 � 1989 differs from the rate U.S. consumption for the period 1990 � 2000. Use a differential slope regression model as presented below�

y^ = B0� + B1(GDP) + B2(GDP)(Dummy 1990),
where Dummy 1990 = 1 if 1990 � 2000, 0 otherwise

The estimated regression equation is:

A. y^ = -43234.762 + 656.5583 (GDP) + 19.3396 (Dummy 1990)
B. y^ = �43234.762 - 656.5583 (GDP) + 19.3396 (Dummy 1990)
C. y^ = -43234.762 + 675.8979186 (GDP) - 19.3396 (Dummy 1990)

5. Code the Penguin Ice Cream data according to the following model with quarter 4 as the base period.
Time Profit Sales
1998 Q1 12 121
Q2 17 152
Q3 24 182
Q4 10 115
1999 Q1 13 128
Q2 18 174
Q3 26 222
Q4 12 125
2000 Q1 15 179
Q2 24 234
Q3 31 246
Q4 15 162
2001 Q1 15 167
Q2 27 234
Q3 33 256
Q4 14 160

y^ = B0� + B1(sales) + B1(D1) + B2(D2) + B3(D3),

where �������������D1 = 1 if Quarter 1, 0 otherwise

D2 = 1 if Quarter 2, 0 otherwise

D3 = 1 if Quarter 3, 0 otherwise

The data for the third quarter of 2001 for Penguin�s Profit, Sales, Quarter 1, Quarter 2, and Quarter 3, respectively, are:

A. 33 26 0 0 0
B. 33 26 1 0 0
C. 33 256 0 0 1

6. Run a regression using the dummy variable regression model in Question 5, above.

The estimated regression equation is:

A. y^ = -1.0754� + 0.0984(Sales) + 0.1882(D1) + 3.0427(D2) + 7.2875(D4)
B. y^ = �-1.0754� + 0.0984(Sales) + 0.1882(D1) + 3.0427(D2) + 7.2875(D3)
C. y^ = 2.3982� + 2.0354(Sales) + 0.5552(D1) + 4.0157(D2) - 6.1875(D3)

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