## 5.5 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 model
• 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?