6.6 Predicting: Linear model (Equation)

• A popular one of out \(\infty\) models

• Linear Model = LM = Linear regression model

• Aim: Model relationship between 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	?	?
..	..	..	..	..	..	..	..	..