6.9 Prediction: Linear model (Estimation)

  • Estimation = Fitting the model to the data (by adapting/finding the parameters)
    • e.g. easy in case of the mean (analytical) but more difficult e.g. for linear (or other) model(s)
  • Modellparameter: \(\color{orange}{\beta_{0}}\), \(\color{orange}{\beta_{1}}\) and \(\color{orange}{\beta_{2}}\)
  • Ordinary Least Squares (OLS)
    • Least squares methods (Astronomy)
    • Choose \(\color{orange}{\beta_{0}}\), \(\color{orange}{\beta_{1}}\) and \(\color{orange}{\beta_{2}}\) so that the sum of the squared errors \(\color{red}{\varepsilon}_{i}\) is minimized (See graph!)
    • Q: Why do we square the errors?