What is an indirect proof?

In economics, especially in theoretical economics, it is often necessary to formally prove your statements. Meaning to show your statements are correct in a logical way. One possible way of showing that your statements are correct is by providing an indirect proof. The following couple of lines try to explain the concept of indirect proof in a simple way.

Derivation of the Least Squares Estimator for Beta in Matrix Notation

The following post is going to derive the least squares estimator for $\beta$, which we will denote as $b$. In general start by mathematically formalizing relationships we think are present in the real world and write it down in a formula.

Relationship between Coefficient of Determination & Squared Pearson Correlation Coefficient

The usual way of interpreting the coefficient of determination $R^{2}$ is to see it as the percentage of the variation of the dependent variable $y$ ($Var(y)$) can be explained by our model. The exact interpretation and derivation of the coefficient of determination $R^{2}$ can be found here.

Another way of interpreting the coefficient of determination $R^{2}$ is to look at it as the Squared Pearson Correlation Coefficient between the observed values $y_{i}$ and the fitted values  Continue reading Relationship between Coefficient of Determination & Squared Pearson Correlation Coefficient

The Coefficient Of Determination or R2

The coefficient of determination $R^{2}$ shows how much of the variation of the dependent variable $y$ ($Var(y)$) can be explained by our model. Another way of interpreting the coefficient of determination $R^{2}$, which will not be discussed in this post, is to look at it as the squared Pearson correlation coefficient between the observed values $y_{i}$ and the fitted values $\hat{y}_{i}$. Why this is the case exactly can be found in another post.

Balance Statistic

The following article tries to explain the Balance Statistic sometimes referred to as Saldo or Saldo Statistic. It is used as a quantification method for qualitative survey question. The benefit of applying the Balance Statistic arises when the survey is repeated over time as it tracks changes in respondents answers in a comprehensible way. The Balance Statistic is common in Business Tendency Surveys.

The Reach of the Continetal Blockade – The Case of Toulouse

Introduction:

Finding a definition of globalization feels like finding a description for a phenomenon that can only be defined by itself. A definition for globalization is like a fraction that tries to approach π. In the same way the approximation gets closer and closer to the true value of π, but never reaches it Continue reading The Reach of the Continetal Blockade – The Case of Toulouse

Stochastic Independence versus Stochastic Dependence

Stochastic Independence versus Stochastic Dependence

In order to fully understand the Bayesian rule it is important to be familiar with some concepts of standard probability theory. Assume we have two events, let’s call them A and B. The probability that event A occurs is P(A) and the probability that event B occurs is P(B). If event A and event B are independent from each other, the probability that both events are occurring at the same time, also known as the joint probability $P(A\cap B)$.