Computing and Others, Econometrics

Linear Regression in R

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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}

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Computing and Others, Econometrics

Construct the OLS estimator as a function in R

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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 →

Computing and Others, Econometrics

Calculate OLS estimator manually in R

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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 →

Econometrics

CLRM – Assumption 5: Normal Distributed Error Terms in Population

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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 →

Econometrics

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

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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 →

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