Question 1

When having a choice of which estimator to use with a binary dependent variable,use
A)probit or logit depending on which method is easiest to use in the software package at hand.
B)probit for extreme values of X and the linear probability model for values in between.
C)OLS (linear probability model)since it is easier to interpret.
D)the estimation method which results in estimates closest to your prior expectations.

Accepted Answer

Probit and logit models are both appropriate for binary dependent variables, and the choice between them often depends on convenience or ease of use within a particular software environment. Both models provide similar results, especially for predictions within the range of the data.

Question 2

The binary dependent variable model is an example of a
A)regression model,which has as a regressor,among others,a binary variable.
B)model that cannot be estimated by OLS.
C)limited dependent variable model.
D)model where the left-hand variable is measured in base 2.

Accepted Answer

The binary dependent variable model is a specific type of limited dependent variable model, where the dependent variable can only take on one of two values (typically 0 or 1). This type of model requires the use of specialized estimation techniques, such as probit or logistic regression, and cannot be estimated using ordinary least squares (OLS) regression. Therefore, choices A and B are not correct. Choice D is also incorrect, as the left-hand variable in the binary dependent variable model is not measured in base 2, but rather represents a binary outcome.

Question 3

The logit model derives its name from
A)the logarithmic model.
B)the probit model.
C)the logistic function.
D)the tobit model.

Accepted Answer

The logit model derives its name from the logistic function, which is used to transform the probability of a binary outcome into a continuous variable that can be modeled using regression techniques. The other answer choices are unrelated to the logit model.

Question 4

Nonlinear least squares
A)solves the minimization of the sum of squared predictive mistakes through sophisticated mathematical routines,essentially by trial and error methods.
B)should always be used when you have nonlinear equations.
C)gives you the same results as maximum likelihood estimation.
D)is another name for sophisticated least squares.

Accepted Answer

Nonlinear least squares is a method used to minimize the sum of squared errors between the predicted values and observed values in a nonlinear regression analysis. It does this through sophisticated mathematical routines, which do involve some trial and error methods, but are not limited to them. Therefore, option A is the best choice. Option B is not true since there may be situations where linear least squares may suffice, and option C is not always true. Lastly, option D is not accurate as nonlinear least squares is a specific technique used for nonlinear regression analysis.

Question 5

In the binary dependent variable model,a predicted value of 0.6 means that
A)the most likely value the dependent variable will take on is 60 percent.
B)given the values for the explanatory variables,there is a 60 percent probability that the dependent variable will equal one.
C)the model makes little sense,since the dependent variable can only be 0 or 1.
D)given the values for the explanatory variables,there is a 40 percent probability that the dependent variable will equal one.

Accepted Answer

In a binary dependent variable model, the predicted values are probabilities of the dependent variable being 1, given the values of the explanatory variables. Thus, a predicted value of 0.6 means that there is a 60% probability that the dependent variable will equal 1.

Question 6

(Requires Advanced material)Only one of the following models can be estimated by OLS:
A)Y = AKαLβ + u.
B)Pr(Y = 1  X)= Φ(β0 + β1X)
C)Pr(Y = 1  X)= F(β0 + β1X)=
 .
D)Y = AKα Lβu.

Accepted Answer

The answer of (Requires Advanced material)Only one of the following...

Question 7

In the probit model Pr(Y = 1  X1,X2,... ,Xk)= Φ(β0 + β1X1 + βxX2 + ...+ βkXk),
A)the β's do not have a simple interpretation.
B)the slopes tell you the effect of a unit increase in X on the probability of Y.
C)β0 cannot be negative since probabilities have to lie between 0 and 1.
D)β0 is the probability of observing Y when all X's are 0

Accepted Answer

The answer of In the probit model Pr(Y = 1...

Question 8

The following tools from multiple regression analysis carry over in a meaningful manner to the linear probability model,with the exception of the
A)F-statistic.
B)significance test using the t-statistic.
C)95% confidence interval using ± 1.96 times the standard error.
D)regression R2.

Accepted Answer

The regression R² is not meaningful in the context of a linear probability model because it can be misleading when the dependent variable is binary.

Question 9

(Requires Appendix material)The following are examples of limited dependent variables,with the exception of
A)binary dependent variable.
B)log-log specification.
C)truncated regression model.
D)discrete choice model.

Accepted Answer

Binary dependent variable, truncated regression model, and discrete choice model are all examples of limited dependent variables, whereas log-log specification refers to a method of estimating parameters in a linear regression model and does not relate to limited dependent variables.

Question 10

E(Y  X1,... ,Xk)= Pr(Y = 1  X1,... ,Xk)means that
A)for a binary variable model,the predicted value from the population regression is the probability that Y=1,given X.
B)dividing Y by the X's is the same as the probability of Y being the inverse of the sum of the X's.
C)the exponential of Y is the same as the probability of Y happening.
D)you are pretty certain that Y takes on a value of 1 given the X's.

Accepted Answer

The equation indicates that the population regression predicts the probability of Y being equal to 1 given the values of X1 through Xk in a binary variable model. The predicted value is not a certain value of Y, but rather a probability.

Question 11

(Requires material from Section 11.3 - possibly skipped)For the measure of fit in your regression model with a binary dependent variable,you can meaningfully use the
A)regression R2.
B)size of the regression coefficients.
C)pseudo R2.
D)standard error of the regression.

Accepted Answer

When dealing with a binary dependent variable, the use of regression R2 or standard error of the regression is not meaningful. The size of the regression coefficients can give some indication of the relationship between the independent and dependent variables, but it does not provide a measure of fit. Pseudo R2, on the other hand, is specifically designed for binary dependent variables and provides a measure of the proportion of variation explained by the model. Therefore, C is the best choice for measuring fit in a regression model with a binary dependent variable.

Question 12

The maximum likelihood estimation method produces,in general,all of the following desirable properties with the exception of
A)efficiency.
B)consistency.
C)normally distributed estimators in large samples.
D)unbiasedness in small samples.

Accepted Answer

The maximum likelihood estimation method does not necessarily produce unbiased estimators in small samples, but it does produce asymptotically unbiased estimators (i.e. the bias decreases as sample size increases). Therefore, D is the exception among the desirable properties listed.

Question 13

The logit model can be estimated and yields consistent estimates if you are using
A)OLS estimation.
B)maximum likelihood estimation.
C)differences in means between those individuals with a dependent variable equal to one and those with a dependent variable equal to zero.
D)the linear probability model.

Accepted Answer

The logit model requires maximum likelihood estimation to yield consistent estimates, as it is a form of nonlinear regression. OLS estimation, differences in means, and the linear probability model are not appropriate for estimating the logit model.

Question 14

The major flaw of the linear probability model is that
A)the actuals can only be 0 and 1,but the predicted are almost always different from that.
B)the regression R2 cannot be used as a measure of fit.
C)people do not always make clear-cut decisions.
D)the predicted values can lie above 1 and below 0.

Accepted Answer

The major flaw of the linear probability model is that the predicted values can lie above 1 and below 0. This violates the probability framework, as probabilities cannot be outside the range of 0 to 1.

Question 15

In the expression Pr(deny = 1  P/I Ratio,black)= Φ(-2.26 + 2.74P/I ratio + 0.71black),the effect of increasing the P/I ratio from 0.3 to 0.4 for a white person
A)is 0.274 percentage points.
B)is 6.1 percentage points.
C)should not be interpreted without knowledge of the regression R2.
D)is 2.74 percentage points.

Accepted Answer

The answer of In the expression Pr(deny = 1 ...

Question 16

In the probit model Pr(Y = 1  = Φ(β0 + β1X),Φ
A)is not defined for Φ(0).
B)is the standard normal cumulative distribution function.
C)is set to 1.96.
D)can be computed from the standard normal density function.

Accepted Answer

Φ is the standard normal cumulative distribution function, which is used to calculate the probability of observing a value less than or equal to a specific point in a standard normal distribution. It ranges from 0 to 1 and can be calculated using tables or software. In the probit model, it is used to calculate the probability of the dependent variable taking a value of 1 given the values of the independent variables.

Question 17

The probit model
A)is the same as the logit model.
B)always gives the same fit for the predicted values as the linear probability model for values between 0.1 and 0.9.
C)forces the predicted values to lie between 0 and 1.
D)should not be used since it is too complicated.

Accepted Answer

The probit model forces the predicted values to lie between 0 and 1, similar to the logistic function used in the logit model. It is a commonly used method for binary classification problems, but it may not always give the same fit as the linear probability model. The statement that it should not be used since it is too complicated is not accurate, as it is a valid statistical model in many situations.

Question 18

In the linear probability model,the interpretation of the slope coefficient is
A)the change in odds associated with a unit change in X,holding other regressors constant.
B)not all that meaningful since the dependent variable is either 0 or 1.
C)the change in probability that Y=1 associated with a unit change in X,holding others regressors constant.
D)the response in the dependent variable to a percentage change in the regressor.

Accepted Answer

In the linear probability model, the dependent variable is a binary variable (0 or 1) and the slope coefficient represents the change in probability that the dependent variable is equal to 1 given a unit change in the independent variable, holding other variables constant. Therefore, option C is the correct interpretation of the slope coefficient.

Question 19

The linear probability model is
A)the application of the multiple regression model with a continuous left-hand side variable and a binary variable as at least one of the regressors.
B)an example of probit estimation.
C)another word for logit estimation.
D)the application of the linear multiple regression model to a binary dependent variable.

Accepted Answer

The linear probability model is the application of the linear multiple regression model to a binary dependent variable. It predicts the probability of occurrence of the dependent variable taking the value 1, based on the values of the independent variables.

Question 20

In the expression Pr(Y = 1  = Φ(β0 + β1X),
A)(β0 + β1X)plays the role of z in the cumulative standard normal distribution function.
B)β1 cannot be negative since probabilities have to lie between 0 and 1.
C)β0 cannot be negative since probabilities have to lie between 0 and 1.
D)min (β0 + β1X)> 0 since probabilities have to lie between 0 and 1.

Accepted Answer

The expression Pr(Y = 1 | X = x) is the probability of Y being 1 given the value of X is x. This probability can be written in terms of Φ(β0 + β1X), which is the cumulative standard normal distribution function. In this case, (β0 + β1X) plays the role of z in the cumulative standard normal distribution function.

Quiz 11: Regression With a Binary Dependent Variable

When having a choice of which estimator to use with a binary dependent variable,use

The binary dependent variable model is an example of a

The logit model derives its name from

Nonlinear least squares

In the binary dependent variable model,a predicted value of 0.6 means that

(Requires Advanced material) Only one of the following models can be estimated by OLS:

In the probit model Pr(Y = 1 X1,X2,... ,Xk) = Φ(β0 + β1X1 + βxX2 + ...+ βkXk) ,

The following tools from multiple regression analysis carry over in a meaningful manner to the linear probability model,with the exception of the

(Requires Appendix material) The following are examples of limited dependent variables,with the exception of

E(Y X1,... ,Xk) = Pr(Y = 1 X1,... ,Xk) means that

(Requires material from Section 11.3 - possibly skipped) For the measure of fit in your regression model with a binary dependent variable,you can meaningfully use the

The maximum likelihood estimation method produces,in general,all of the following desirable properties with the exception of

The logit model can be estimated and yields consistent estimates if you are using

The major flaw of the linear probability model is that

In the expression Pr(deny = 1 P/I Ratio,black) = Φ(-2.26 + 2.74P/I ratio + 0.71black) ,the effect of increasing the P/I ratio from 0.3 to 0.4 for a white person

In the probit model Pr(Y = 1 = Φ(β0 + β1X) ,Φ

The probit model

In the linear probability model,the interpretation of the slope coefficient is

The linear probability model is

In the expression Pr(Y = 1 = Φ(β0 + β1X) ,