3.17 Models: 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 \(trust2006\)
\(y\)		 \(\boldsymbol{\color{blue}{\beta_{0}}}\) \(\boldsymbol{\color{orange}{\beta_{1}}}\) \(threat2006\)
\(x_{1}\)		 \(\boldsymbol{\color{orange}{\beta_{2}}}\) \(education2006\)
\(x_{2}\)		 \(\boldsymbol{\color{red}{\varepsilon}}\) \(\color{green}{\widehat{y}}\)
Daniel 5 ? ? 1 ? 1 ? ?
Leia 5 ? ? 0 ? 1 ? ?
Harrison 7 ? ? 0 ? 5 ? ?
.. .. .. .. .. .. .. .. ..