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Based on the definition of the linear regression model in its matrix form, i.e., y=Xβ+ε, the...

Based on the definition of the linear regression model in its matrix form, i.e., y=Xβ+ε, the assumption that ε~N(0,σ2I), and the general formula for the point estimators for the parameters of the model (b=XTX-1XTy); show:

  1. how to derivate the formula for the point estimators for the parameters of the models by means of the Least Square Estimation (LSE). [Hint: you must minimize ete]
  2. that the LSE estimator, i.e., b=XTX-1XTy, is unbiased. [Hint: E[b]=β]
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