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# 11 Regression with a Binary Dependent Variable

This chapter, we discusses a special class of regression models that aim to explain a limited dependent variable. In particular, we consider models where the dependent variable is binary. We will see that in such models, the regression function can be interpreted as a conditional probability function of the binary dependent variable.

We review the following concepts:

- the linear probability model
- the Probit model
- the Logit model
- maximum likelihood estimation of nonlinear regression models

Of course, we will also see how to estimate above models using `R` and discuss an application where we examine the question whether there is racial discrimination in the U.S. mortgage market.

The following packages and their dependencies are needed for reproduction of the code chunks presented throughout this chapter on your computer:

`AER`(Christian Kleiber and Zeileis 2020)`stargazer`(Hlavac 2018)

Check whether the following code chunk runs without any errors.

```
library(AER)
library(stargazer)
```

### References

*stargazer: Well-Formatted Regression and Summary Statistics Tables*(version 5.2.2). https://CRAN.R-project.org/package=stargazer.

*AER: Applied Econometrics with R*(version 1.2-9). https://CRAN.R-project.org/package=AER.