# Linear Regression in R

R presents various ways to carry out linear regressions. The most natural way is to use the lm() function, the R build-in OLS estimator. In this post I will present you how to use lm() and run OLS on the following model

$y = \alpha + \beta_{1} x_{1} + \beta_{2} x_{2} + \beta_{3} x_{3}$

# Construct the OLS estimator as a function in R

This post shows how to manually construct the OLS estimator in R (see this post for the exact mathematical derivation of the OLS estimator). In contrary to a previous post, this post focuses on setting up the OLS estimator as a R function. While the aim of the former post was much more on the construction of the OLS estimator in general, is this post all about constructing a functional form around the estimator. Continue reading Construct the OLS estimator as a function in R

# Calculate OLS estimator manually in R

This post shows how to manually construct the OLS estimator in R (see this post for the exact mathematical derivation of the OLS estimator). The code will go through each single step of the calculation and estimate the coefficients, standard errors and p-values.  In case you are interested the coding an OLS function rather than in the step wise calculation of the estimation itself I recommend you to have a look at this postContinue reading Calculate OLS estimator manually in R

# CLRM – Assumption 5: Normal Distributed Error Terms in Population

Assumption 5 is often listed as a Gauss-Markov assumption and refers to normally distributed error terms $\epsilon$ in the population. Overall, assumption 5 is not a Gauss-Markov assumption in that sense that the OLS estimator will still be the best linear unbiased estimator (BLUE) even if the error terms $\epsilon$ are not normally distributed in the population. Continue reading CLRM – Assumption 5: Normal Distributed Error Terms in Population

# Violation of CLRM – Assumption 4.1: Consequences when the expected value of the error term is non-zero

Violating assumption 4.1 of the OLS assumptions, i.e. $E(\epsilon_i|X) = 0$, can affect our estimation in various ways. The exact ways a violation affects our estimates depends on the way we violate $E(\epsilon_i|X) = 0$. This post looks at different cases and elaborates on the consequences of the violation. We start with a less severe case and then continue discussing a far more sensitive violation of assumption 4.1. Continue reading Violation of CLRM – Assumption 4.1: Consequences when the expected value of the error term is non-zero

# CLRM – Assumption 4: Independent and Identically Distributed Error Terms

Assumption 4 of the four assumption required by the Gauss-Markov theorem states that the error terms of the population $\epsilon_{i}$ are independent and identically distributed (iid) with an expected value of zero and a constant variance $\sigma^{2}$. Formally, Continue reading CLRM – Assumption 4: Independent and Identically Distributed Error Terms

# CLRM – Assumption 2: Full Rank of Matrix X

Assumption 2 requires the matrix of explanatory variables $X$ to have full rank. This means that in case matrix $X$ is a $N \times K$ matrix the rank of matrix $X$ is $K$. Namely, $Rank(X) = K$

# How to Enable Gui Root Login in Debian 8

In this post I am going to explain how to enable GUI root access on Debian 8. Instructions for Debian 9 a similar and can be found here. At this point I should warn you that using the root account is dangerous as you can ruin your whole system.  Try to follow this guide exactly.