Final answer:
The Gauss-Markov Theorem involves assumptions for simple linear regression that are necessary for the OLS estimators to be considered the best linear unbiased estimators.
Step-by-step explanation:
The Gauss-Markov Theorem is a statistical principle that applies to the estimates obtained from linear regression models with one independent variable (simple linear regression).
An essential aspect of this theorem is that it establishes the conditions under which the ordinary least squares (OLS) estimator has the lowest variance among all unbiased linear estimators, known as BLUE (Best Linear Unbiased Estimator), provided that certain assumptions are met. These assumptions ensure the validity and efficiency of the ordinary least squares estimations.
Gauss Markov Assumptions
Linear relationship: The regression model should reflect a linear relation between the independent variable (x) and the dependent variable (y).
Independency: The residuals (errors) of the regression should be independent of one another, indicating no autocorrelation.
Normality: For any given value of x, the y-values should be normally distributed around the regression line.
Equal variance (Homoscedasticity): The variance of residuals should be constant for any value of x, implying that the spread of the y-values around the regression line does not depend on x.
When these assumptions are met, the OLS estimators for the slope and intercept provide the best linear and unbiased predictions for the dependent variable, and allow for hypothesis testing and the creation of confidence intervals.