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 male (β₁) measures the difference in average income between males and females. 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

We are not given a value for βS1U1B1, which is necessary to calculate the expected income for a woman with parental income of $60,000.

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 converted into a form that can be provided to the model, typically through one-hot encoding or dummy variables, 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 captures the change in the slope of the continuous variable for the group indicated by the dummy variable.

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

Accepted Answer

The fitted values from a multivariate regression with a dummy variable will result in two parallel lines if the dummy variable only shifts the intercept and not the slope. The slope of both lines will be determined by β1 (β₁ in the notation provided), and the separation between the two lines will be determined by the coefficient of the dummy variable, β2 (B₂ in the notation provided), which affects the intercept.

Question 7

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

Accepted Answer

The model 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, it's β11 + β13, indicating two lines with different slopes based on the presence of the Dummy variable.

Question 8

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

Accepted Answer

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

Question 9

Which of the following is NOT a categorical variable:

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?

Accepted Answer

Plugging in the given values, we get: Corruption = 10 - 0.1 (50)- 2.0 (1) Simplifying the equation, we get: Corruption = 10 - 5 + 2 = 7 Therefore, the expected rate of corruption of a democratic country with a per capita GDP of $50,000 is 7.

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

Accepted Answer

The coefficient for GDP (per capita) is -0.1, so an extra thousand dollars per capita would result in a decrease in corruption by 0.1(1,000) = 100. However, since the country is democratic, the Democracy variable is equal to 1, which means that the coefficient for Democracy (-2.0) also applies. Therefore, the predicted change in corruption would be a decrease of 100 + (-2.0) = -102. This implies a decrease in predicted corruption, so the answer is B: 0.1 lower.

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)?

Accepted Answer

To find the level of experience at which the expected income of men and women will be the same, we set the coefficients of Female and Experience x Female to zero, and solve for Experience. That is,

1.5 + Experience = 0

Experience x (-5 + Female) = 0

The first equation tells us that Experience = -1.5. However, this is not a valid solution because it falls outside the range of plausible values for experience (presumably it cannot be negative).

Therefore, we consider the second equation separately:

(-5 + Female) = 0
Female = 5

Substituting Female = 5 into the first equation, we get:

1.5 + Experience - 25 = 0
Experience = 23.5/1.5

Experience = 15.67

Thus, the expected income of men and women will be the same when Experience = 15.67, which is closest to 5 years (choice C).

Question 13

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

Accepted Answer

Jittering involves adding a small amount of random noise to the data points to spread them out horizontally, making it easier to see patterns that might otherwise be obscured. Adding noise to the regression equation (A) would not help in visualizing the data, and adding noise to both the regression and plotted data (C) would be redundant and potentially misleading. Therefore, adding noise only to the plotted data (B) is the best option.

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,

Accepted Answer

The coefficient on the dummy variables will differ across models since the reference category changes, but the estimated difference of means between men and women will still be captured by the coefficients on the dummy variables. This means that the effect of gender on income will still be estimated, but the interpretation of the coefficients will change. The fit of the model may or may not change, depending on the data and the specific model specifications. We will not get different answers when testing a null hypothesis that there is no gender effect, since the null hypothesis will be the same in both models.

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?

Accepted Answer

The t-statistics for the coefficients for S1U1B1 S1U1B0 and the interaction term with Male are all 3, indicating that they are statistically significant. However, the t-statistic for the coefficient for Male is only 0.2, indicating that it is not statistically significant. Therefore, we cannot conclude that men have greater income than women. The coefficient for S1U1B0 indicates that for a person whose parents had 0 income, their estimated income would be 30. The lack of significance in the interaction term suggests that the effect of parental income does not differ for men and women. Therefore, the correct conclusion is C. We cannot make a comparison of the effect of parental income between men and women, so option D is incorrect.

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?