# Linear Regression

A linear regression is a special case of the classical linear regression models that describes the relationship between two variables by fitting a linear equation to observed data. Thereby, one variable is considered to be the explanatory (or independent) variable, and the other variable is considered to be the dependent variable. For instance, an econometrician might want to relate weight to their calorie consumption using a linear regression model.

# Omitted Variable Bias: Violation of CLRM–Assumption 3: Explanatory Variables must be exogenous

One reason why the omitted variable leads to biased estimates is that omitting a relevant variable violates assumption 3 of the necessary assumptions of the classical regression model that states that all explanatory variables must be exogenous, i.e.

$E(\epsilon_{i}|X)=0$

From this post, we know that omitting a relevant variable from the regression causes the error term and the explanatory variables to be correlated.
Continue reading Omitted Variable Bias: Violation of CLRM–Assumption 3: Explanatory Variables must be exogenous

# Omitted Variable Bias: Conclusion

The following post provides a recap of the previous posts on the omitted variable bias (Introduction, Explanation, In-depth discussion of the bias, Consequences of the omitted variable bias) and concludes with some general advise. In case you haven’t read the previous posts, you might want to start from the beginning in order to fully understand the issues related to the omitted variable bias.

All in all, the omitted variable bias is a severe problem. Neglecting a relevant variable leads to biased and inconsistent estimates. Hence, as a general advice, when you are working with linear regression models, you should pay close attention to potentially omitted variables. In particular, you should ask yourself the following questions: Continue reading Omitted Variable Bias: Conclusion

# Omitted Variable Bias: Consequences

In this post, we will discuss the consequence of the omitted variable bias in a more elaborate way. Particularly, we will show that omitting a variable form the regression model violates an OLS assumption and discuss what will happen if this assumption is violated.

# Omitted Variable Bias: Explaining the Bias

In the previous two posts on the Omitted Variable Bias (Post 1 and Post 2), we discussed the hypothetical case of finding out what determines the price of a car. In the hypothetical example, we assumed, for simplicity, that the price of a car depends only on the age of a car and its milage. In this post, we discuss the effects of the omitted variable bias on single coefficients. In order to do so, suppose that you want to find out what is the effect of miles on the price a car.

# Omitted Variable Bias: Understanding the Bias

The second part of the series on the Omitted Variable Bias intends to increase the readers understanding of the bias. Let’s continue with the example from the Introduction. Let the dependent variable be the price of a car and the explanatory variables be the car’s millage and the car’s age. In our case, both millage and age are important factors to that determine the price of a car. Continue reading Omitted Variable Bias: Understanding the Bias

# Omitted Variable Bias: Introduction

The omitted variable bias is a common and serious problem in regression analysis. Generally, the problem arises if one does not consider all relevant variables in a regression. In this case, one violates the first assumption of the assumption of the classical linear regression model. In the introductory part of this series of posts on the omitted variable bias, you will learn what is exactly the omitted variable bias.

# Mathematical Operations

What are the commands for the most important mathematical operations in Julia and R? The following table translates the most common Julia commands into R language.

# Accessing Vector/Matrix Elements

How to access vector and matrix elements in Julia and R? The following table translates the most common Julia commands into R language.

# Manipulating Vectors and Matrices

How to manipulate vectors and matrices in Julia and R? The following table translates the most common Julia commands into R language.