The following code produces confidence intervals in R using the normal distribution and confidence intervals using the t-distribution.

The code reproduces the figure 1 presented in this post.

Continue reading Confidence Intervals R Code Part 1The following code produces confidence intervals in R using the normal distribution and confidence intervals using the t-distribution.

The code reproduces the figure 1 presented in this post.

Continue reading Confidence Intervals R Code Part 1This blog post explains the difference between confidence intervals that use the t-distribution and confidence intervals that use the Normal distribution. Thereby, the post will not focus on the theoretical/mathematical differences of the two distributions, but rather compare the two types of confidence intervals using simulation studies. Furthermore, in case you are interested in replicating the presented results or simply play around with it yourself, I provide the R code to conduct the simulation exercises and to replicate the figures.

Continue reading What is the difference between using the t-distribution and the Normal distribution when constructing confidence intervals?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.

Continue reading Confidence Intervals in RIn 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.

Continue reading Generate Gamma Distributed Numbers in Julia

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

This post is part of the series on the omitted variable bias and provides a simulation exercise that illustrates how omitting a relevant variable from your regression model biases the coefficients. The R code will be provided at the end. Continue reading Omitted Variable Bias: An Example

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 on the dependent variable . 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

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.

To deal with an omitted variables bias is not easy. However, one can try several things.

First, one can try, Continue reading Omitted Variable Bias: What can we do about it?

Julia presents various ways to carry out multiple regressions. One easy way is to use the *lm()* function of the GLM package. In this post I will present how to use the *lm()* and run OLS on the following model