Consider the regression equation  where is a stochastic error term.

a) Explain how estimators of and can be obtained.

b) What algebraic properties do the estimators fulfil?

a) The estimators of the coefficients in a linear regression model can be obtained using the Ordinary Least Squares (OLS) method. In the equation Y=β0+β1X+ϵY = \beta_0 + \beta_1 X + \epsilon, where YY is the dependent variable, XX is the independent variable, β0\beta_0 and β1\beta_1 are the coefficients to be estimated, and ϵ\epsilon is the stochastic error term, the OLS estimators are derived by minimizing the sum of squared residuals (errors), ∑(ϵi2)\sum (\epsilon_i^2). The error term is given by ϵi=Yi−(β0+β1Xi)\epsilon_i = Y_i - (\beta_0 + \beta_1 X_i).

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