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In the context of Introductory Econometric Methods, we often consider the simple linear regression model: Y = α + βX + u where * *Y* is the dependent variable, * *X* is the independent variable, * *α* is the intercept (also denoted as *a*), * *β* is the slope coefficient, and * *u* is the error term. To estimate the parameters *α* and *β*, the most commonly used method is Ordinary Least Squares (OLS). The objective of OLS is to minimize the sum of squared residuals, where residuals are the differences between the observed values and the predicted values of the dependent variable. Let us denote the data as a sample of *n* observations: (Y₁, X₁), (Y₂, X₂), ..., (Yₙ, Xₙ) The estimated regression model becomes: Ŷᵢ = __________ ___ ________ __________ _____ ________ _____ _____ _________.
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