Derivation of the Least Squares Estimator for Beta in Matrix Notation – Proof Nr. 1

In the post that derives the least squares estimator, we make use of the following statement:

\frac{\partial b'X'Xb}{\partial b} =2X'Xb

This post shows how one can prove this statement. Let’s start from the statement that we want to prove:

\frac{\partial \hat{\beta}'X'X\hat{\beta}}{\partial \hat{\beta}}=2 X'X \hat{\beta}'

Continue reading Derivation of the Least Squares Estimator for Beta in Matrix Notation – Proof Nr. 1

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How to set a Seed in Julia?

Julia v0.7 and older

In Julia, you can set a seed to the random number generator using the srand() function. The code example below sets the seed to 1234. Generating a random variable with rand(1) after setting the seed to 1234 will always generate the same number, i.e. it will always return 0.5908446386657102.

Continue reading How to set a Seed in Julia?

Graphically Illustrate Multicollinearity: Venn Diagram

Multicollinearity is a common problem in econometrics. As explained in a previous post, multicollinearity arises when we have too few observations to precisely estimate the effects of two or more highly correlated variables on the dependent variable. This post tries to graphically illustrate the problem of multicollinearity using venn-diagrams. The venn-diagrams below all represent the following regression model Continue reading Graphically Illustrate Multicollinearity: Venn Diagram

The Problem of Multicollinearity

Multicollinearity or collinearity refers to a situation where two or more variables of a regression model are highly correlated. Because of the high correlation, it is difficult to disentangle the pure effect of one single explanatory variables x on the dependent variable y. From a mathematical point of view, multicollinearity only becomes an issue when we face perfect multicollinearity. That is, when we have identical variables in our regression model. Continue reading The Problem of Multicollinearity

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“In God we trust; all others must bring data.” W. Edwards Deming

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