Least Squares Under Ideal Conditions

Consider the linear regression model https://www.w3.org/1998/Math/MathML">yt=β1Xt1+β1Xt2+⋯+βKXtK+εt⁢                            (t=1,2,⋯ ,T)https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003066958/a1a5d68a-642a-4424-8c7d-f14e7a129864/content/math1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> where y_t is the t-th observation on the dependent variable in the regression, X_ti is the t-th observation on the i-th independent variable (regressor), β_i is the regression coefficient corresponding to the i-th regressor, and ε_t is the t-th observation on the disturbance (error) term. Note that T is the number of observations and K is the number of regressors.