Final answer:
The OLS estimator in matrix form is β = (X'X)⁻¹X'Y, aiming to minimize the sum of squared residuals, and its variance is given by VAR(β) = σ²(X'X)⁻¹, where σ² is the variance of the error term.
Step-by-step explanation:
The question asks about the Ordinary Least Squares (OLS) estimator and its variance in matrix form. The OLS estimator is given by the formula β = (X'X)⁻¹X'Y, where β represents the estimated coefficients, X is the matrix of independent variables, and Y is the dependent variable matrix. The prime symbol (') denotes the transpose of a matrix. This estimator minimizes the sum of the squared residuals between the observed values in Y and the values predicted by the model.
The variance of the OLS estimator is VAR(β) = σ²(X'X)⁻¹, where σ² is the variance of the error term U. The variance-covariance matrix of β is estimated by s²(X'X)⁻¹, where s² is the estimated variance of the residuals, which is calculated as the sum of squared residuals divided by the degrees of freedom (n-k, where n is the number of observations and k is the number of independent variables).