Expectation & Variance of OLS Estimates

Here α and β are the regression coefficients i.e. the parameters that need to be calculated to understand the relation between Y and X. i has been subscripted along with X and Y to indicate that we are referring to a particular observation, a particular value associated with X and Y. εᵢ is the error term associated with each observation i. Using some mathematical rigour, the OLS (Ordinary Least Squares) estimates for the regression coefficients α and β were derived. Under the OLS <a href="https://www.analyticsvidhya.com/blog/2023/01/a-comprehensive-guide-to-ols-regression-part-1/" rel="noopener ugc nofollow" target="_blank">method</a>, we tried to find a function that minimized the sum of the squares of the difference between the true value of Y and the predicted value of Y. The following estimates were obtained for α and β: <a href="https://medium.com/analytics-vidhya/expectation-variance-of-ols-estimates-9acd2b48a635">Website</a>