# Robust Standard Errors in STATA

”Robust” standard errors is a technique to obtain unbiased standard errors of OLS coefficients under heteroscedasticity. In contrary to other statistical software, such as R for instance, it is rather simple to calculate robust standard errors in STATA. All you need to is add the option  robust  to you regression command. That is:

# The Gauss Markov Theorem

When studying the classical linear regression model, one necessarily comes across the Gauss-Markov Theorem. The Gauss-Markov Theorem is a central theorem for linear regression models. It states different conditions that, when met, ensure that your estimator has the lowest variance among all unbiased estimators. More formally, Continue reading The Gauss Markov Theorem

# Derivation of the Least Squares Estimator for Beta in Matrix Notation

The following post is going to derive the least squares estimator for $\beta$, which we will denote as $b$. In general start by mathematically formalizing relationships we think are present in the real world and write it down in a formula.

# Relationship between Coefficient of Determination & Squared Pearson Correlation Coefficient

The usual way of interpreting the coefficient of determination $R^{2}$ is to see it as the percentage of the variation of the dependent variable $y$ ($Var(y)$) can be explained by our model. The exact interpretation and derivation of the coefficient of determination $R^{2}$ can be found here.

Another way of interpreting the coefficient of determination $R^{2}$ is to look at it as the Squared Pearson Correlation Coefficient between the observed values $y_{i}$ and the fitted values  Continue reading Relationship between Coefficient of Determination & Squared Pearson Correlation Coefficient

# The Coefficient Of Determination or R2

The coefficient of determination $R^{2}$ shows how much of the variation of the dependent variable $y$ ($Var(y)$) can be explained by our model. Another way of interpreting the coefficient of determination $R^{2}$, which will not be discussed in this post, is to look at it as the squared Pearson correlation coefficient between the observed values $y_{i}$ and the fitted values $\hat{y}_{i}$. Why this is the case exactly can be found in another post.