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)
1) In order to analyze salary differences between men and women using a dummy-variable regression model, you would need to collect data on various variables such as years of experience, education level, job classification, and gender.
Here's how you can proceed with the analysis:
1. Collect data: Gather data on salary levels, years of experience, education level, job classification, and gender for a sample of individuals.
2. Code the variables: Assign a numerical value to each category of the gender variable (e.g., 0 for men, 1 for women) to create a dummy variable.
3. Run regression model: Use a dummy-variable regression model to estimate the relationship between salary and the other variables, including the gender dummy variable. The regression model would look like this: Salary = B0 + B1(Experience) + B2(Education) + B3(Job Classification) + B4(Dummy Variable for Gender) + error term.
4. Interpret the results: Analyze the coefficients of the regression model. If the coefficient for the gender dummy variable is statistically significant and positive, it would indicate a salary difference between men and women. A positive coefficient means that women, on average, earn less than men.
5. Account for other factors: It's important to note that the gender dummy variable may not capture all the complexities and nuances related to salary differences. Other factors like discrimination or bias might contribute to salary disparities. Therefore, it's important to consider additional variables or methodologies to further investigate and understand salary differences.
The regression results can be used to understand the extent of salary differences between men and women, and to identify any gender-based pay gaps. This information can then be used to advocate for equal pay and to implement policies or practices that promote fair compensation regardless of gender.
2) To investigate if U.S. consumption for the period 1959-1989 differs from U.S. consumption for the period 1990-2000 using a dummy variable regression model, follow these steps:
1. Collect data: Obtain data on U.S. consumption and GDP for the periods of interest (1959-1989 and 1990-2000).
2. Code the data: Assign a value of 1 to the observations corresponding to the period 1990-2000 and a value of 0 to the observations corresponding to the period 1959-1989. This will create the dummy variable "Dummy 1990".
3. Run regression model: Use a dummy variable regression model to estimate the relationship between consumption, GDP, and the dummy variable. The regression model would look like this: Consumption = B0 + B1(GDP) + B2(Dummy 1990) + error term.
4. Interpret the results: Analyze the coefficients of the regression model. If the coefficient for the "Dummy 1990" variable is statistically significant and positive, it would indicate a difference in consumption between the two periods. A positive coefficient means that consumption in the period 1990-2000 was higher, on average, compared to the period 1959-1989.
The estimated regression equation can be used to quantify the difference in consumption between the two periods and to understand the impact of GDP on consumption. It can also help policymakers and researchers gain insights into the economic trends and patterns during these time periods.
3) To code the data according to the given model, follow these steps:
1. Identify the variables: The model includes GDP, "Dummy 1990," and consumption.
2. Code the data: Assign the values of GDP, "Dummy 1990," and consumption to the corresponding variables for each observation. The data for the year 1999 would be coded as follows:
A. GDP = 9,268.6, "Dummy 1990" = 0, consumption = 6,250,217
B. GDP = 9,268.6, "Dummy 1990" = 1, consumption = 6,250,217
C. GDP = 6,250,217, "Dummy 1990" = 1, consumption = 9,268.6
Make sure to correctly assign the values to each variable to ensure accurate analysis.
4) To investigate if the rate of U.S. consumption for the period 1959-1989 differs from the rate of U.S. consumption for the period 1990-2000 using a differential slope regression model, follow these steps:
1. Collect data: Obtain data on U.S. consumption and GDP for the periods of interest (1959-1989 and 1990-2000).
2. Code the data: Assign a value of 1 to the observations corresponding to the period 1990-2000 and a value of 0 to the observations corresponding to the period 1959-1989. Create the dummy variable "Dummy 1990".
3. Run regression model: Use a differential slope regression model to estimate the relationship between consumption, GDP, and the dummy variable. The regression model would look like this: Consumption = B0 + B1(GDP) + B2(GDP)(Dummy 1990) + error term.
4. Interpret the results: Analyze the coefficients of the regression model. If the coefficient for the interaction term between GDP and the dummy variable ("Dummy 1990") is statistically significant and positive, it would indicate a difference in the slope of the consumption-GDP relationship between the two periods. A positive coefficient means that the rate of consumption growth from GDP was higher for the period 1990-2000 compared to 1959-1989.
The estimated regression equation can be used to quantify the difference in the rate of consumption growth between the two periods and to understand the impact of GDP on consumption. It can provide insights into the economic trends and patterns specific to each period.
5) To code the Penguin Ice Cream data according to the given model, follow these steps:
1. Identify the variables: The model includes profit, sales, and dummy variables for each quarter: D1, D2, and D3.
2. Code the data: Assign the values of profit, sales, D1, D2, and D3 to the corresponding variables for the observation representing the third quarter of 2001. The correct coding would be:
Profit = 33, Sales = 256, D1 = 0, D2 = 0, D3 = 1
Make sure to correctly assign the values to each variable to ensure accurate analysis.
6) To run a regression using the dummy variable regression model in Question 5, follow these steps:
1. Collect data: Use the coded Penguin Ice Cream data from the previous question, including profit, sales, and the dummy variables D1, D2, and D3.
2. Run regression model: Use the dummy variable regression model specified in the question to estimate the relationship between profit, sales, and the dummy variables. The regression model would look like this: Profit = B0 + B1(Sales) + B2(D1) + B3(D2) + B4(D3) + error term.
3. Interpret the results: Analyze the coefficients of the regression model. The estimated regression equation represents the relationship between profit, sales, and the dummy variables. Each coefficient corresponds to the effect on profit when the corresponding variable changes while holding other variables constant.
The correct estimated regression equation in this case would be:
y^ = -1.0754 + 0.0984(Sales) + 0.1882(D1) + 3.0427(D2) + 7.2875(D3)
This means that sales, the dummy variables D1, D2, and D3 have statistically significant effects on profit. The coefficients quantify the magnitude and direction of these effects.
It's important to note that the interpretation of the coefficients may vary depending on the context and specific characteristics of the data.