Chapter 14: Regression Analysis With a Dichotomous Dependent Variable: Logit Models

Test Bank

Multiple Choice

1. Logistic regression is best suited for dependent variables that are ______.

a. continuous

b. ordinal

c. nominal

d. dichotomous

Learning Objective: 14.1. List the problems that can occur when using ordinary least-squares (OLS) regression to predict the values of a dichotomous dependent variable.

Cognitive Domain: Knowledge

Answer Location: Introduction

Difficulty Level: Easy

2. Applying an OLS regression equation to a binary dependent variable is called a ______.

a. logistic regression model

b. linear probability model

c. ordinary least-squares model

d. probit regression model.

Learning Objective: 14.1. List the problems that can occur when using ordinary least-squares (OLS) regression to predict the values of a dichotomous dependent variable.

Cognitive Domain: Knowledge

Answer Location: Estimating an OLS regression model with a dichotomous dependent variable—the linear probability model

Difficulty Level: Easy

3. Which of the following is NOT a problem that may arise from estimating a binary dependent variable in an OLS regression equation rather than a logistic regression equation ______.

a. increased Type II error rate

b. predicted values of the dependent variable that extend beyond the bounds of 0 or 1

c. the functional form of how the independent variable affects the dependent variable may not be linear

d. the error terms (residuals) are not normally distributed and thus violate the assumption of homoscedasticity

Learning Objective: 14.1. List the problems that can occur when using ordinary least-squares (OLS) regression to predict the values of a dichotomous dependent variable.

Cognitive Domain: Knowledge

Answer Location: Estimating an OLS regression model with a dichotomous dependent variable—the linear probability model

Difficulty Level: Medium

4. The logistic probability distribution uses which distribution?

a. t-distribution

b. logistic probability distribution

c. linear distribution

d. curve-linear distribution

Learning Objective: 14.2. Describe the estimation procedures used to predict a dichotomous dependent variable with the logistic regression model.

Cognitive Domain: Knowledge

Answer Location: Estimating an OLS regression model with a dichotomous dependent variable—the linear probability model

Difficulty Level: Easy

5. In logistic regression, estimating the probability of a binary event occurring is also called the ______.

a. reciprocal of the probability of the dependent variable occurring

b. Bernoulli event of the dependent variable occurring

c. log of the odds of the dependent variable occurring

d. rate of change of the dependent variable occurring

Learning Objective: 14.2. Describe the estimation procedures used to predict a dichotomous dependent variable with the logistic regression model; 14. 4. Interpret both the slope coefficients and the exponential of the slope coefficients from a logistic regression equation.

Cognitive Domain: Knowledge

Answer Location: The logit regression model with one independent variable

Difficulty Level: Medium

6. In the logistic regression model, the constant and regression coefficients are estimated using ______.

a. maximum likelihood estimation

b. least-squares methods

c. proportional odds

d. semi-standardized coefficient

Learning Objective: 14.2. Describe the estimation procedures used to predict a dichotomous dependent variable with the logistic regression model

Cognitive Domain: Knowledge

Answer Location: The logit regression model with one independent variable

Difficulty Level: Easy

7. The odds of an event occurring is ______.

a. the critical value based on the alpha level selected and the number of degrees of freedom

b. the probability of getting the observed results given the fitted regression coefficients

c. the probability of a dependent variable being a particular value

d. the ratio of a probability over its complement

Learning Objective: 14.2. Describe the estimation procedures used to predict a dichotomous dependent variable with the logistic regression model; 14. 4. Interpret both the slope coefficients and the exponential of the slope coefficients from a logistic regression equation.

Cognitive Domain: Knowledge

Answer Location: The logit regression model with one independent variable

Difficulty Level: Medium

8. In contrast to OLS regression, in logistic regression the change in the probability of y with a 1 unit change in the independent variable is ______.

a. linear

b. not constant

c. constant

d. quadratic

Learning Objective: 14.2. Describe the estimation procedures used to predict a dichotomous dependent variable with the logistic regression model; 14. 4. Interpret both the slope coefficients and the exponential of the slope coefficients from a logistic regression equation.

Cognitive Domain: Comprehension

Answer Location: Predicted probabilities in logit models

Difficulty Level: Medium

9. By exponentiating the coefficient for an independent variable in a logistic regression (also called the “antilog”), one will obtain ______.

a. odds multiplier

b. a linear relationship

c. log of the exponentiated odds

d. log of the odds

Learning Objective: 14.4. Interpret both the slope coefficients and the exponential of the slope coefficients from a logistic regression equation. 14. 7. Explain how to interpret slope coefficients from multivariable logistic regression models.

Cognitive Domain: Knowledge

Answer Location: Logistic regression models with two independent variables

Difficulty Level: Easy

10. The odds multiplier reflects the change in the odds of the dependent variable occurring when the dependent variable ______.

a. increases by 1 unit

b. decreases by 1 unit

c. increases by 1%

d. deceases by 1%

Learning Objective: 14.4. Interpret both the slope coefficients and the exponential of the slope coefficients from a logistic regression equation. 14. 7. Explain how to interpret slope coefficients from multivariable logistic regression models.

Cognitive Domain: Comprehension

Answer Location: Logistic regression models with two independent variables

Difficulty Level: Easy

11. To obtain the percent change in the odds of the dependent variable, one must ______.

a. multiply the odds multiplier by 100

b. subtract the odds multiplier from 1, and then multiply the result by 100

c. subtract 1 from the odds multiplier, and then multiply the result by 100

d. multiply the log of the odds by 100

Learning Objective: 14.4. Interpret both the slope coefficients and the exponential of the slope coefficients from a logistic regression equation; 14. 7. Explain how to interpret slope coefficients from multivariable logistic regression models.

Cognitive Domain: Comprehension

Answer Location: The logit regression model with one independent variable

Difficulty Level: Medium

12. The likelihood of a model is ______.

a. the likelihood of obtaining the observed results given the sign and magnitude of the regression coefficients

b. the likelihood that the estimated model is correct

c. the likelihood that the estimated model can be replicated

d. the likelihood that the estimated model is spurious

Learning Objective: 14.2. Describe the estimation procedures used to predict a dichotomous dependent variable with the logistic regression model; 14. 8. Describe how to assess model fit for logistic regression models.

Cognitive Domain: Comprehension

Answer Location: Model goodness-of-fit measures

Difficulty Level: Hard

13. A good logistic model, one wherein the probability of the observed results is high, is one with ______.

a. a high value of -2LL

b. a high value of the odds ratio

c. a small value of -2LL

d. a small value of chi-square

Learning Objective: 14.8. Describe how to assess model fit for logistic regression models.

Cognitive Domain: Comprehension

Answer Location: Model goodness-of-fit measures

Difficulty Level: Medium

14. When testing the improvement in the likelihood functions between a baseline model and a model containing two independent variable, obtaining a chi-square less than the critical value means one would ______.

a. reject the null hypothesis that all independent variables in the model are equal to zero

b. accept the alternative hypothesis that all independent variables in the model are not equal to zero

c. fail to reject the null hypothesis that all independent variables in the model are equal to zero

d. none of the above

Learning Objective: 14.8. Describe how to assess model fit for logistic regression models.

Cognitive Domain: Comprehension

Answer Location: Model goodness-of-fit measures

Difficulty Level: Hard

True/False

15. Logistic regression is used when the dependent variable has binary values.

Learning Objective: 14.1. List the problems that can occur when using ordinary least-squares (OLS) regression to predict the values of a dichotomous dependent variable.

Cognitive Domain: Knowledge

Answer Location: Introduction

Difficulty Level: Easy

16. The OLS model is a nonlinear model while the logit model is linear.

Learning Objective: 14.1. List the problems that can occur when using ordinary least-squares (OLS) regression to predict the values of a dichotomous dependent variable.

Cognitive Domain: Knowledge

Answer Location: Estimating an OLS regression model with a dichotomous dependent variable—the linear probability model

Difficulty Level: Easy

17. The logistic regression coefficient can be transformed into an estimated predicted probability to make it more easily interpreted.

Learning Objective: 14.5. Transform the slope coefficients in a logistic regression model into predicted probabilities of a dependent variable.

Cognitive Domain: Comprehension

Answer Location: Predicted probabilities in logit models

Difficulty Level: Easy

18. The Wald statistic is comparable to the chi-square distribution.

Learning Objective: 14.8. Describe how to assess model fit for logistic regression models.

Cognitive Domain: Comprehension

Answer Location: Significance testing for logistic regression coefficients

Difficulty Level: Medium

19. A perfect fitting model would have a likelihood equal to 1 and -2LL equal to 0.

Learning Objective: 14.8. Describe how to assess model fit for logistic regression models.

Cognitive Domain: Knowledge

Answer Location: Model goodness-of-fit measures

Difficulty Level: Medium

20. Estimating an OLS model on a binary dependent variable will never result in predicted values of the dependent variable that are less than 0 or greater than 1.

Learning Objective: 14.1. List the problems that can occur when using ordinary least-squares (OLS) regression to predict the values of a dichotomous dependent variable.

Cognitive Domain: Knowledge

Answer Location: Estimating an OLS regression model with a dichotomous dependent variable—the linear probability model

Difficulty Level: Medium

21. You obtain a regression coefficient of .132. This is interpreted as the predicted log of the odds of the dependent variable increases by .132 for a unit increase in the independent variable.

Learning Objective: 14.7. Explain how to interpret slope coefficients from multivariable logistic regression models.

Cognitive Domain: Application

Answer Location: The logit regression model with one independent variable

Difficulty Level: Medium

22. Exponentiating the value in question 21 results in a value of 1.14. This is interpreted as a 114% increase in the odds of the dependent variable with a one unit increase in the independent variable.

Learning Objective: 14.5. Transform the slope coefficients in a logistic regression model into predicted probabilities of a dependent variable; 14. 7. Explain how to interpret slope coefficients from multivariable logistic regression models.

Cognitive Domain: Application

Answer Location: The logit regression model with one independent variable

Difficulty Level: Medium

23. The logistic regression model is appropriate for predicting a dependent variable with 3 categories.

Learning Objective: 14.1. List the problems that can occur when using ordinary least-squares (OLS) regression to predict the values of a dichotomous dependent variable.

Cognitive Domain: Knowledge

Answer Location: Introduction

Difficulty Level: Easy

24. While there are disadvantages of using a predicted probability model, one advantage is the ease of interpreting the effect of the independent variable on the dependent variable.

Learning Objective: 14.1. List the problems that can occur when using ordinary least-squares (OLS) regression to predict the values of a dichotomous dependent variable.

Cognitive Domain: Knowledge

Answer Location: Introduction

Difficulty Level: Easy

Essay

25. What are the three main issues of predicting a binary dependent variable in an OLS regression equation? Explain each.

Learning Objective: 14.1. List the problems that can occur when using ordinary least-squares (OLS) regression to predict the values of a dichotomous dependent variable.

Cognitive Domain: Application

Answer Location: Estimating an OLS regression model with a dichotomous dependent variable—the linear probability model

Difficulty Level: Hard