Category Archives: Econometrics

Econometrics, Mathematical Proofs, Statistics

The Gauss Markov Theorem

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When studying the classical linear regression model, one necessarily comes across the Gauss-Markov Theorem. The Gauss-Markov Theorem is a central theorem for linear regression models. It states different conditions that, when met, ensure that your estimator has the lowest variance among all unbiased estimators. More formally, Continue reading The Gauss Markov Theorem →

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Econometrics, Statistics

Relationship between Coefficient of Determination & Squared Pearson Correlation Coefficient

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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 →

Econometrics, Statistics

The Coefficient Of Determination or R2

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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.

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Econometrics, Macroeconomics, Statistics

Balance Statistic

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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.

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Econometrics, Mathematical Proofs, Statistics

Proof of Unbiasedness of Sample Variance Estimator

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Proof of Unbiasness of Sample Variance Estimator

(As I received some remarks about the unnecessary length of this proof, I provide shorter version here)

In different application of statistics or econometrics but also in many other examples it is necessary to estimate the variance of a sample. The estimator of the variance, see equation (1) is normally common knowledge and most people simple apply it without any further concern. The question which arose for me was why do we actually divide by n-1 and not simply by n? In the following lines we are going to see the proof that the sample variance estimator is indeed unbiased.

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