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6 Regression Models with Multiple Regressors

In what follows we introduce linear regression models that use more than just one explanatory variable and discuss important key concepts in multiple regression. As we broaden our scope beyond the relationship of only two variables (the dependent variable and a single regressor) some potential new issues arise such as multicollinearity and omitted variable bias (OVB). In particular, this chapter deals with omitted variables and its implication for causal interpretation of OLS-estimated coefficients.

Naturally, we will discuss estimation of multiple regression models using R. We will also illustrate the importance of thoughtful usage of multiple regression models via simulation studies that demonstrate the consequences of using highly correlated regressors or misspecified models.

The packages AER (Kleiber & Zeileis, 2017) and MASS (Ripley, 2018) are needed for reproducing the code presented in this chapter. Make sure that the following code chunk executes without any errors.

library(AER)
library(MASS)

References

Kleiber, C., & Zeileis, A. (2017). AER: Applied Econometrics with R (Version 1.2-5). Retrieved from https://CRAN.R-project.org/package=AER

Ripley, B. (2018). MASS: Support Functions and Datasets for Venables and Ripley’s MASS (Version 7.3-51.1). Retrieved from https://CRAN.R-project.org/package=MASS