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

# 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 post. Continue 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 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 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. , can affect our estimation in various ways. The exact ways a violation affects our estimates depends on the way we violate . 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 are independent and identically distributed (iid) with an expected value of zero and a constant variance . Formally, Continue reading CLRM – Assumption 4: Independent and Identically Distributed Error Terms

# Proof Gauss Markov Theorem

From a previous posts on the Gauss Markov Theorem and OLS we know that the assumption of unbiasedness must full fill the following condition Continue reading Proof Gauss Markov Theorem

# CLRM – Assumption 3: Explanatory Variables must be exogenous

Assumption 3, exogeneity of explanatory variables requires that the explanatory variables in the model do not explain variation in the error terms, formally we express assumption 3 as Continue reading CLRM – Assumption 3: Explanatory Variables must be exogenous

# CLRM – Assumption 2: Full Rank of Matrix X

Assumption 2 requires the matrix of explanatory variables to have full rank. This means that in case matrix is a matrix the rank of matrix is . Namely,

# 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.