Question 1

In the regression equation = b₀ + b₁x + b₂d, a dummy variable d affects the slope of the line.

Accepted Answer

False

Question 2

A dummy variable is also referred to as a(n) ________ variable.

Accepted Answer

indicator

Question 3

For the model y = β₀+ β₁x + β₂d + β₃xd + ε, the dummy variable d causes only a shift in intercept.

Accepted Answer

The model includes an interaction term between the dummy variable $d$ and another variable $x$ (represented by $xd$), which means $d$ can affect both the intercept and the slope of the relationship between $y$ and $x$, not just cause a shift in the intercept.

Question 4

If the number of dummy variables representing a qualitative variable equals the number of categories of this variable, one deals with the problem of perfect multicollinearity.

Accepted Answer

This is true. When the number of dummy variables equals the number of categories, there is no redundant information and perfect multicollinearity is avoided.

Question 5

For the model y = β₀+ β₁x + β₂d + β₃xd+ε, in which d is a dummy variable, we cannot perform the F test for the joint significance of the dummy variable d and the interaction variable xd.

Accepted Answer

The F test can be used to test the joint significance of the dummy variable $d$ and the interaction term $xd$ by comparing a model including these terms against a restricted model without them, to see if they significantly improve the model's explanatory power.

Question 6

For the model y = β₀+ β₁x + β₂d + β₃xd + ε, in which d is a dummy variable, we can perform standard t tests for the individual significance of x, d, and xd.

Accepted Answer

Since the model includes all variables of interest (x, d, and xd) and the use of a dummy variable allows for the estimation of different intercepts between the two groups, it is possible to perform standard t tests for the individual significance of each variable.

Question 7

For the logit model, the predicted values of the response variables can always be interpreted as probabilities.

Accepted Answer

In the logit model, the predicted values are transformed probabilities that represent the log odds of the event happening. These log odds can be converted to probabilities using the logistic function, allowing for interpretation of the predicted values as probabilities.

Question 8

A binary choice model is also referred to as a discrete choice model.

Accepted Answer

The statement is true. A binary choice model is a type of discrete choice model that involves a choice between two alternatives.

Question 9

Regression models that use a binary variable as the response variable are called binary choice models.

Accepted Answer

Binary choice models are regression models that use a binary variable as the response variable, where the binary variable can only take on two values (usually 0 and 1) representing a binary choice or decision. Examples include logistic regression and probit regression models.

Question 10

A model y = β₀ + β₁x + ε, in which y is a binary variable, is called a linear probability model.

Accepted Answer

The model is called a linear probability model because it predicts the probability of a binary outcome (y) using a linear combination of variables.

Question 11

Using a ________ we can determine if a particular dummy variable is statistically significant.

Accepted Answer

The answer of Using a ________ we can determine if...

Question 12

The logit model can be estimated with standard ordinary least squares.

Accepted Answer

The logit model is a type of logistic regression that involves modeling the probability of a binary outcome. It cannot be estimated with standard OLS, which is designed for continuous dependent variables. Instead, specialized software such as Stata, R, or SAS is needed to estimate the logit model using maximum likelihood estimation.

Question 13

A dummy variable is a variable that takes on the values of 0 and 1.

Accepted Answer

A dummy variable, also known as an indicator variable, takes on a value of 0 or 1 to represent the absence or presence of a particular characteristic or attribute.

Question 14

Consider the regression model y = β₀+ β₁x + β₂d + β₃xd + ε. If the dummy variable d changes from 0 to 1, the estimated changes in the intercept and the slope are b₀+ b₂ and b₂, respectively.

Accepted Answer

The correct estimated changes in the intercept and the slope when the dummy variable d changes from 0 to 1 are $ \beta_{12} $ and $ \beta_{13} $, respectively. The intercept changes by $ \beta_{12} $ and the slope of x changes by $ \beta_{13} $, not $ \beta_{10} + \beta_{12} $ and $ \beta_{12} $, as initially stated.

Question 15

A dummy variable is also called an interaction variable.

Accepted Answer

A dummy variable is not the same as an interaction variable. A dummy variable is a binary variable that takes on the values 0 or 1 to indicate the absence or presence of a particular categorical characteristic, while an interaction variable is created by multiplying two or more variables together to explore how their effects may interact or affect each other.

Question 16

Including as many dummy variables as there are categories is referred to as the dummy variable ________.

Accepted Answer

The answer of Including as many dummy variables as there...

Question 17

For the linear probability model y = β₀ + β₁x + ε, the predictions made by = b₀ + b₁x can be always interpreted as probabilities.

Accepted Answer

The answer of For the linear probability model y =...

Question 18

Gender is an example of ________ variable.

Accepted Answer

The answer of Gender is an example of ________ variable.
...

Question 19

The number of dummy variables representing a qualitative variable should be one less than the number of categories of the variable.

Accepted Answer

This is because using N-1 dummy variables (where N is the number of categories) avoids the issue of multicollinearity in the model, ensuring that the dummy variables are independent of each other.

Question 20

Variables employed in a regression model can be quantitative or qualitative.

Accepted Answer

This is true. Quantitative variables are numerical and can take on any value, while qualitative variables are categorical and usually represented by words or phrases. Both types of variables can be used in regression models.

Quiz 17: Regression Models With Dummy Variables

In the regression equation = b0 + b1x + b2d, a dummy variable d affects the slope of the line.