That’s a bit of a mouthful, but note that: “best” = minimal variance of the OLS estimation of the true betas (i.e. Given the assumptions A – E, the OLS estimator is the Best Linear Unbiased Estimator (BLUE). Components of this theorem need further explanation. Like many statistical analyses, ordinary least squares (OLS) regression has underlying assumptions. The following website provides the mathematical proof of the Gauss-Markov Theorem. The fascinating piece is that OLS provides the best linear unbiased estimator (BLUE) of y under a set of classical assumptions. You can find more information on this assumption and its meaning for the OLS estimator here. The independent variables are measured precisely 6. The independent variables are not too strongly collinear 5. For more information about the implications of this theorem on OLS estimates, read my post: The Gauss-Markov Theorem and BLUE OLS Coefficient Estimates. Efficiency of OLS (Ordinary Least Squares) Given the following two assumptions, OLS is the Best Linear Unbiased Estimator (BLUE). The expected value of the errors is always zero 4. Assumptions of OLS regression 1. This means that out of all possible linear unbiased estimators, OLS gives the most precise estimates of and . The data are a random sample of the population 1. The Seven Classical OLS Assumption. Assumptions of Linear Regression. Model is linear in parameters 2. The errors are statistically independent from one another 3. In order for OLS to be BLUE one needs to fulfill assumptions 1 to 4 of the assumptions of the classical linear regression model. 8 2 Linear Regression Models, OLS, Assumptions and Properties 2.2.5 Data generation It is mathematically convenient to assume x i is nonstochastic, like in an agricultural experiment where y i is yield and x i is the fertilizer and water applied. However, the ordinary least squares method is simple, yet powerful enough for many, if not most linear problems.. Unlike the acf plot of lmMod, the correlation values drop below the dashed blue line from lag1 itself. Ideal conditions have to be met in order for OLS to be a good estimate (BLUE, unbiased and efficient) However, assumption 5 is not a Gauss-Markov assumption in that sense that the OLS estimator will still be BLUE even if the assumption is not fulfilled. The first component is the linear component. The First OLS Assumption Following points should be considered when applying MVUE to an estimation problem MVUE is the optimal estimator Finding a MVUE requires full knowledge of PDF (Probability Density Function) of the underlying process. Even if the PDF is known, […] Check 2. runs.test ... (not OLS) is used to compute the estimates, this also implies the Y and the Xs are also normally distributed. The OLS Assumptions. Assumptions of Classical Linear Regression Models (CLRM) Overview of all CLRM Assumptions Assumption 1 LEAST squares linear regression (also known as “least squared errors regression”, “ordinary least squares”, “OLS”, or often just “least squares”), is one of the most basic and most commonly used prediction techniques known to humankind, with applications in fields as diverse as statistics, finance, medicine, economics, and psychology. Why BLUE : We have discussed Minimum Variance Unbiased Estimator (MVUE) in one of the previous articles. However, social scientist are very likely to find stochastic x Gauss-Markov Assumptions, Full Ideal Conditions of OLS The full ideal conditions consist of a collection of assumptions about the true regression model and the data generating process and can be thought of as a description of an ideal data set. So autocorrelation can’t be confirmed. So, the time has come to introduce the OLS assumptions.In this tutorial, we divide them into 5 assumptions. That is, it proves that in case one fulfills the Gauss-Markov assumptions, OLS is BLUE. You should know all of them and consider them before you perform regression analysis.. no other linear estimator has less variance!)