Question 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.

Accepted Answer

The coefficient for the dummy variable for male (assuming male = 1 and female = 0) gives the difference in the average income between males and females, and this coefficient is represented by β₁ in the bivariate OLS model. Therefore, the statement is true.

Question 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.

Accepted Answer

The model does not provide enough information to calculate the expected income of a woman whose parents income is $60,000. The value of βS1U1B0 is not given, which is necessary to calculate the expected income based on parental income.

Question 3

We can include a categorical variable (such as region) in a multivariate model in the same way we include a continuous variable.

Accepted Answer

Categorical variables must be encoded (e.g., through one-hot encoding) before they can be included in a multivariate model, unlike continuous variables which can be included directly.

Question 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.

Accepted Answer

The coefficient on the interaction term measures the effect of the interaction between the dummy variable and the continuous variable. Specifically, it measures whether the difference between the two slope coefficients for the two groups indicated by the dummy variable is statistically significant or not. Therefore, the statement is true.

Question 5

When conducting analysis using categorical variables, we include a dummy variable for every category covered by the categorical variable.

Accepted Answer

When using dummy variables to represent a categorical variable with n categories, we typically include n-1 dummy variables to avoid the dummy variable trap, which can cause multicollinearity issues in the analysis.

Question 6

The fitted values from a multivariate regression Y₀= β₀+ β₁X_i+ 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

Accepted Answer

In the multivariate regression equation, the coefficient of the independent variable S1U1B11S1U1B0XS1U1B1iS1U1B0S1U1B1 is βS1U1B11S1U1B0 and the coefficient of the dummy variable is βS1U1B12S1U1B0. This means that holding all other variables constant, a unit increase in S1U1B11S1U1B0XS1U1B1iS1U1B0S1U1B1 leads to an increase of βS1U1B11S1U1B0 in the fitted values, while the dummy variable adds a constant βS1U1B12S1U1B0 to the fitted values. Therefore, the fitted values will be two parallel lines with a slope of βS1U1B11S1U1B0 and separated by βS1U1B12S1U1B0.

Question 7

The fitted values from a multivariate regression Y₀= β₀+ β₁X_i+ β₂Dummy + β₃Dummy*X_i 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

Accepted Answer

The regression equation includes an interaction term (β13Dummy*Xi), which means the slopes of the lines for different values of the dummy variable will be different. The slope for the line when Dummy=0 is β11, and when Dummy=1, the slope is β11 + β13, indicating two lines with different slopes.

Question 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.

Accepted Answer

Categorical variables are converted into dummy variables for inclusion in a regression model, but one category is always omitted to serve as a reference group. This approach avoids the dummy variable trap, which can cause multicollinearity issues in the model.

Question 9

Which of the following is NOT a categorical variable:
A) Race
B) Region
C) Level of Education
D) Car manufacturer

Accepted Answer

The answer of Which of the following is NOT a...

Question 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

Accepted Answer

We can substitute the values into the model to find the expected rate of corruption:

Corruption = 10 - 0.1(50) - 2(1)
Corruption = 10 - 5 - 2
Corruption = 3

However, because the country is a democracy, we must subtract an additional 2 from the corruption score:

Corruption = 3 - 2
Corruption = 1

Therefore, the expected rate of corruption of a democratic country with a per capita GDP of $50,000 is 1.

Question 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

Accepted Answer

For a democratic country, the equation for Corruption becomes:
Corruption = 10 - 0.1 GDP - 2.0(1)
= 8 - 0.1 GDP
Therefore, for an increase of one thousand dollars per capita in GDP, the predicted Corruption will decrease by 0.1.

Question 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.

Accepted Answer

To find the level of experience at which men and women have the same expected income, we need to find the value of Experience that makes the coefficient of the Female variable (which is -5 + Experience) equal to 0. This happens when Experience = 5 years. Therefore, the fitted lines for men and women intersect at 5 years of experience.

Question 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.

Accepted Answer

Jittering data involves adding a small random amount of noise to the data to help distinguish overlapping points in scatterplots. This can be done by adding a small random number to both the independent and dependent variables in the plotted data. Adding noise to the regression model itself (option A or C) is not necessary for jittering data.

Question 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.

Accepted Answer

The coefficient on the dummy variables will differ across models, but the estimated difference of means between men and women will not change. This is because the choice of reference category determines the sign and magnitude of the estimated coefficient for the other category, but the difference between the two categories will be the same regardless of which category is chosen as the reference. The fit of the model may or may not change, depending on other factors such as the inclusion of additional variables. Testing the null hypothesis of no gender effect will also give different results depending on which dummy variable is included in the model.

Question 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 $\beta$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.

Accepted Answer

The t-statistic is the ratio of the estimated coefficient to its standard error, and it measures the magnitude of the estimated coefficient relative to its variability. A t-statistic of 3 indicates that the estimated coefficient is significantly different from zero at the 5% significance level. Therefore, we can conclude that , Parental income, and Male all have significant effects on Income. However, the t-statistic for Male x Parental income is only 0.2, which means we cannot reject the null hypothesis that the coefficient is equal to zero. Therefore, we have no evidence that the effect of parental income differs for men and women.

Question 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).

Accepted Answer

The answer of Explain the reason why we cannot include...

Question 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

Accepted Answer

The answer of Given the following regression results: Income =...

Question 18

Explain the difference between a bivariate and multivariate regression in the contexts of dummy variables.

Accepted Answer

The answer of Explain the difference between a bivariate and...

Question 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?

Accepted Answer

The answer of Given the model College GPA = 2.0...

Question 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).

Accepted Answer

The answer of Explain how to deal with categorical variables...

Quiz 6: Dummy Variables: Smarter Than You Think

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.

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.

We can include a categorical variable (such as region) in a multivariate model in the same way we include a continuous variable.

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.

When conducting analysis using categorical variables, we include a dummy variable for every category covered by the categorical variable.

The fitted values from a multivariate regression Y₀= β₀+ β₁X_i+ β₂Dummy will be

The fitted values from a multivariate regression Y₀= β₀+ β₁X_i+ β₂Dummy + β₃Dummy*X_i will be

When dealing with categorical variables in the context of a multivariate regression, we:

Which of the following is NOT a categorical variable:

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) ?

It is sometimes useful to "jitter" data when viewing a scatterplot involving dummy variables. To jitter data we

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,

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 $\beta$ ₀-hat) . Which of the following conclusions is correct?

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).

Explain the difference between a bivariate and multivariate regression in the contexts of dummy variables.

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).

Quiz 6: Dummy Variables: Smarter Than You Think

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.

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.

We can include a categorical variable (such as region) in a multivariate model in the same way we include a continuous variable.

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.

When conducting analysis using categorical variables, we include a dummy variable for every category covered by the categorical variable.

The fitted values from a multivariate regression Y0 = β0 + β1Xi + β2Dummy will be

The fitted values from a multivariate regression Y0 = β0 + β1Xi + β2Dummy + β3Dummy*Xi will be

When dealing with categorical variables in the context of a multivariate regression, we:

Which of the following is NOT a categorical variable:

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) ?

It is sometimes useful to "jitter" data when viewing a scatterplot involving dummy variables. To jitter data we

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,

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\betaβ 0-hat) . Which of the following conclusions is correct?

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).

Explain the difference between a bivariate and multivariate regression in the contexts of dummy variables.

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).

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.

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.

The fitted values from a multivariate regression Y₀= β₀+ β₁X_i+ β₂Dummy will be

The fitted values from a multivariate regression Y₀= β₀+ β₁X_i+ β₂Dummy + β₃Dummy*X_i will be

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 $\beta$ ₀-hat) . Which of the following conclusions is correct?