3.19 Models: Estimation

• Estimation = Fitting the model to the data (by adapting the parameters)
• 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?