Deck 6: Dummy Variables: Smarter Than You Think

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سؤال
In a bivariate OLS model where the dependent variable is income and the dummy variable is male, the coefficient β1 signifies the difference in the average income between males and females.
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سؤال
Given the model Income = β0 + β1Parental income + β2Male
where Male is a dummy variable, β0=30,000, β1=0.1, and β2=10,000, the expected income of a woman whose parents income is $60,000 is equal to $52,000.
سؤال
We can include a categorical variable (such as region) in a multivariate model in the same way we include a continuous variable.
سؤال
The coefficient on the interaction of a dummy variable and a continuous variable indicates whether slope associated with the continuous variable is different for the group indicated by the dummy variable.
سؤال
When conducting analysis using categorical variables, we include a dummy variable for every category covered by the categorical variable.
سؤال
The fitted values from a multivariate regression Y0 = β0 + β1Xi + β2Dummy will be

A) Two parallel lines with a slope of β2 and separated by β1.
B) Two parallel lines with a slope of β1 and separated by B2.
C) Two lines with differing slopes separated by β1
D) Two lines with differing slopes separated by β2
سؤال
The fitted values from a multivariate regression Y0 = β0 + β1Xi + β2Dummy + β3Dummy*Xi will be

A) Two parallel lines with a slope of B2 and separated by β1.
B) Two parallel lines with a slope of β1 and separated by β2.
C) Two lines with slopes of β1 and β1+ β3 separated by β2.
D) Two lines with slopes of β1and β1+ β3
سؤال
When dealing with categorical variables in the context of a multivariate regression, we:

A) Include the categorical variable directly into the model and interpret the results
B) Change the categorical variable into a dummy variable (per category) and include all of the dummy variables in the regression.
C) Change the categorical variable into a dummy variable (per category) and include all but one of the dummy variables in the regression.
D) Interact the categorical variable with a continuous variable.
سؤال
Which of the following is NOT a categorical variable:

A) Race
B) Region
C) Level of Education
D) Car manufacturer
سؤال
We are analyzing the effects of regime type on corruption rates with the following model: Corruption = 10 - 0.1 GDP (per capita) - 2.0 Democracy
Where Corruption is an index of corruption, GDP (per capita) is measured in thousands of dollars, and Democracy is a dummy variable that is equal to one if a country is a democracy and 0 otherwise. What is the expected rate of corruption of a democratic country with a per capita GDP of $50,000?

A) Not enough information to come up with an answer
B) 8.5
C) 13.0
D) - 4992
سؤال
We are analyzing the effects of regime type on corruption rates with the following model: Corruption = 10 - 0.1 GDP (per capita) - 2.0 Democracy
Where Corruption is an index of corruption, GDP (per capita) is measured in thousands of dollars, and Democracy is a dummy variable that is equal to one if a country is a democracy and 0 otherwise. Suppose we want to know the estimated effect on corruption of an extra thousand dollars per capita for a democratic country. Our estimate implies the change in predicted corruption will be

A) 0.1 higher
B) 0.1 lower
C) 2.1 higher
D) 2.1 lower
سؤال
Given the model Income = 40 + 1.5Experience - 5Female + 1Experience x Female, at what level of experience will the expected income of men and women be the same (in other words, at what level of experience will the fitted lines for men and women intersect)?

A) At 10 years of experience
B) At 2.5 years of experience
C) At 5 years of experience
D) Not enough information.
سؤال
It is sometimes useful to "jitter" data when viewing a scatterplot involving dummy variables. To jitter data we

A) Add a small random number to both the independent and dependent variable before running the regression.
B) Add a small random number to both the independent and dependent variable to the plotted data.
C) Add a small random number to both the independent and dependent variable before running the regression and to the plotted data.
D) None of the above.
سؤال
Suppose we are interested in the effect of gender on income and estimate a model that includes a dummy variable for men. If we instead estimate a model that includes a dummy variable for women,

A) The coefficient on the dummy variables will be exactly the same.
B) The coefficient on the dummy variables will differ across models, but the estimated difference of means between men and women will not change.
C) The fit of the model will change.
D) We will get different answers when testing a null hypothesis that there is no gender effect.
سؤال
Consider the following regression results: Income = 30 + 0.2Parental income + 5 Male + 0.001 Male x Parental income and the t-statistics are 3, 3, 3 and 0.2 for the four estimated coefficients (starting with β\beta 0-hat). Which of the following conclusions is correct?

A) Men are not estimated to have greater income than women.
B) The fitted value for a man whose parents had 0 income is 30.
C) We have no evidence that the effect of parental income differs for men and women.
D) The effect of parental income on women is larger than for men.
سؤال
Explain the reason why we cannot include all of the dummy variables that are part of a given category, and instead need to leave one out (which serves as the reference point).
سؤال
Given the following regression results: Income = 20,000 + 2,000Years of Experience + 10,000 Male + 1,000Male x Years of experience calculate the following:
a. The expected income of a man with 3 years of work experience
b. The expected income of a woman with 3 years of work experience
c. The expected income of a man with no work experience
سؤال
Explain the difference between a bivariate and multivariate regression in the contexts of dummy variables.
سؤال
Given the model College GPA = 2.0 + 0.01Parental income + 0.05 Hours studied per week +0.2 Private high school
where Parental income is measured in thousands of U.S. dollars and Private high school is a dummy variable, answer the following
a. The expected college GPA of someone who went to private high school, studies for 20 hours a week, and whose parents income is 60,000.
b. The expected college GPA of someone who did not go to private high school, studies for 5 hours a week, and whose parents income is 100,000.
c. What is the expected increase in college GPA due to 2 additional hours of studying (holding everything else constant).
d. What is the expected increase in college GPA associated with having attended a private school rather than a public school?
سؤال
Explain how to deal with categorical variables when it comes to running regression analysis, and how to interpret the results. Frame your answer in the context of explaining income (the dependent variable) as a function of region (a categorical independent variable).
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ملء الشاشة (f)
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Deck 6: Dummy Variables: Smarter Than You Think
1
In a bivariate OLS model where the dependent variable is income and the dummy variable is male, the coefficient β1 signifies the difference in the average income between males and females.
True
2
Given the model Income = β0 + β1Parental income + β2Male
where Male is a dummy variable, β0=30,000, β1=0.1, and β2=10,000, the expected income of a woman whose parents income is $60,000 is equal to $52,000.
False
3
We can include a categorical variable (such as region) in a multivariate model in the same way we include a continuous variable.
False
4
The coefficient on the interaction of a dummy variable and a continuous variable indicates whether slope associated with the continuous variable is different for the group indicated by the dummy variable.
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5
When conducting analysis using categorical variables, we include a dummy variable for every category covered by the categorical variable.
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6
The fitted values from a multivariate regression Y0 = β0 + β1Xi + β2Dummy will be

A) Two parallel lines with a slope of β2 and separated by β1.
B) Two parallel lines with a slope of β1 and separated by B2.
C) Two lines with differing slopes separated by β1
D) Two lines with differing slopes separated by β2
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7
The fitted values from a multivariate regression Y0 = β0 + β1Xi + β2Dummy + β3Dummy*Xi will be

A) Two parallel lines with a slope of B2 and separated by β1.
B) Two parallel lines with a slope of β1 and separated by β2.
C) Two lines with slopes of β1 and β1+ β3 separated by β2.
D) Two lines with slopes of β1and β1+ β3
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8
When dealing with categorical variables in the context of a multivariate regression, we:

A) Include the categorical variable directly into the model and interpret the results
B) Change the categorical variable into a dummy variable (per category) and include all of the dummy variables in the regression.
C) Change the categorical variable into a dummy variable (per category) and include all but one of the dummy variables in the regression.
D) Interact the categorical variable with a continuous variable.
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9
Which of the following is NOT a categorical variable:

A) Race
B) Region
C) Level of Education
D) Car manufacturer
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10
We are analyzing the effects of regime type on corruption rates with the following model: Corruption = 10 - 0.1 GDP (per capita) - 2.0 Democracy
Where Corruption is an index of corruption, GDP (per capita) is measured in thousands of dollars, and Democracy is a dummy variable that is equal to one if a country is a democracy and 0 otherwise. What is the expected rate of corruption of a democratic country with a per capita GDP of $50,000?

A) Not enough information to come up with an answer
B) 8.5
C) 13.0
D) - 4992
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11
We are analyzing the effects of regime type on corruption rates with the following model: Corruption = 10 - 0.1 GDP (per capita) - 2.0 Democracy
Where Corruption is an index of corruption, GDP (per capita) is measured in thousands of dollars, and Democracy is a dummy variable that is equal to one if a country is a democracy and 0 otherwise. Suppose we want to know the estimated effect on corruption of an extra thousand dollars per capita for a democratic country. Our estimate implies the change in predicted corruption will be

A) 0.1 higher
B) 0.1 lower
C) 2.1 higher
D) 2.1 lower
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12
Given the model Income = 40 + 1.5Experience - 5Female + 1Experience x Female, at what level of experience will the expected income of men and women be the same (in other words, at what level of experience will the fitted lines for men and women intersect)?

A) At 10 years of experience
B) At 2.5 years of experience
C) At 5 years of experience
D) Not enough information.
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13
It is sometimes useful to "jitter" data when viewing a scatterplot involving dummy variables. To jitter data we

A) Add a small random number to both the independent and dependent variable before running the regression.
B) Add a small random number to both the independent and dependent variable to the plotted data.
C) Add a small random number to both the independent and dependent variable before running the regression and to the plotted data.
D) None of the above.
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14
Suppose we are interested in the effect of gender on income and estimate a model that includes a dummy variable for men. If we instead estimate a model that includes a dummy variable for women,

A) The coefficient on the dummy variables will be exactly the same.
B) The coefficient on the dummy variables will differ across models, but the estimated difference of means between men and women will not change.
C) The fit of the model will change.
D) We will get different answers when testing a null hypothesis that there is no gender effect.
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15
Consider the following regression results: Income = 30 + 0.2Parental income + 5 Male + 0.001 Male x Parental income and the t-statistics are 3, 3, 3 and 0.2 for the four estimated coefficients (starting with β\beta 0-hat). Which of the following conclusions is correct?

A) Men are not estimated to have greater income than women.
B) The fitted value for a man whose parents had 0 income is 30.
C) We have no evidence that the effect of parental income differs for men and women.
D) The effect of parental income on women is larger than for men.
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16
Explain the reason why we cannot include all of the dummy variables that are part of a given category, and instead need to leave one out (which serves as the reference point).
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17
Given the following regression results: Income = 20,000 + 2,000Years of Experience + 10,000 Male + 1,000Male x Years of experience calculate the following:
a. The expected income of a man with 3 years of work experience
b. The expected income of a woman with 3 years of work experience
c. The expected income of a man with no work experience
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18
Explain the difference between a bivariate and multivariate regression in the contexts of dummy variables.
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19
Given the model College GPA = 2.0 + 0.01Parental income + 0.05 Hours studied per week +0.2 Private high school
where Parental income is measured in thousands of U.S. dollars and Private high school is a dummy variable, answer the following
a. The expected college GPA of someone who went to private high school, studies for 20 hours a week, and whose parents income is 60,000.
b. The expected college GPA of someone who did not go to private high school, studies for 5 hours a week, and whose parents income is 100,000.
c. What is the expected increase in college GPA due to 2 additional hours of studying (holding everything else constant).
d. What is the expected increase in college GPA associated with having attended a private school rather than a public school?
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20
Explain how to deal with categorical variables when it comes to running regression analysis, and how to interpret the results. Frame your answer in the context of explaining income (the dependent variable) as a function of region (a categorical independent variable).
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