# Confidence Intervals in R

In this post, I will show how one can easily construct confidence intervals in R. Assume you have a vector of numbers and you want to construct a confidence interval around the mean of this vector. The subsequent R code shows one easy way to calculate the confidence interval around the mean of this vector. The following code loads a function that allows you to pass on the vector and returns the confidence intervals. Per default the function returns the 95% confidence interval. However, the parameter ‘conf_level’ allows you to specify the interval you want. Furthermore, if you do not have many observations, you may want to use Student’s t-distribution instead of the Normal distribution. The Student’s t-distribution has wider tales when the number of observations is low and gives a you more conservative estimates of your confidence interval. In case you want to use Student’s t-distribution you case set the parameter ‘distribution’, i.e. distribution=”normal”.

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# Generate Gamma Distributed Numbers in Julia

In Julia, one can generate random numbers that follow a Gamma distribution by using the Distribution package. Thereby one can use the `rand()` function that draws random numbers and specify the Gamma distribution by using the `Gamma(a,b)` command. The parameters a and b define the shape parameters of the Gamma distribution. This article provides a more generic overview of how to generate random numbers 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

# Omitted Variable Bias

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 third assumption of the assumption of the classical linear regression model. The following series of blog posts explains the omitted variable bias and discusses its consequences.