## 5.3 Example: Linear model (Equation)

• Popular of $$\infty$$ models

• Linear Model = LM = Linear regression model
• Aim
• Relationship: outcome variable und 1+ explanatory variables
$$y_{i} = \underbrace{\color{blue}{\beta_{0}} + \color{orange}{\beta _{1}} \times x_{1i} + \color{orange}{\beta _{2}} \times x_{2i}}_{\text{Modell} = \color{green}{\widehat{y}}_{i} = \text{Predicted values}} + \underbrace{\color{red}{\varepsilon}_{i}}_{\color{red}{Error}} = \color{green}{\widehat{y}}_{i} + \color{red}{\varepsilon}_{i}$$

Name $$trust2006$$
$$y$$
$$\boldsymbol{\color{blue}{\beta_{0}}}$$ $$\boldsymbol{\color{orange}{\beta_{1}}}$$ $$victim2006$$
$$x_{1}$$
$$\boldsymbol{\color{orange}{\beta_{2}}}$$ $$education2006$$
$$x_{2}$$
$$\boldsymbol{\color{red}{\varepsilon}}$$ $$\color{green}{\widehat{y}}$$
Daniel 5 ? ? 1 ? 1 ? ?
Leia 5 ? ? 0 ? 1 ? ?
Harrison 7 ? ? 0 ? 5 ? ?
.. .. .. .. .. .. .. .. ..