p.21 Covariance Derivation The covariance between two random variables $X_1$ and $X_2$ is defined as: $$ \text{Cov}(X_1, X_2) = \mathbb{E}\left[(X_1 - \mathbb{E}(X_1))(X_2 - \mathbb{E}(X_2))\right] $$Step 1: Expanding the expression First, expand the product inside the expectation:
Jul 2, 2025
Let’s consider a simple linear regression model: $$ y = \beta_0 + \beta_1 x + \varepsilon $$Where: $y$: outcome variable $x$: predictor $\varepsilon$: error term (disturbance or residual) $\beta_0, \beta_1$: parameters to estimate What OLS Assumes For the OLS (Ordinary Least Squares) estimator to be unbiased, one of the Gauss-Markov assumptions is:
Jun 28, 2025