7.8 Prediction: Linear model (Equation) (2)

$y_{i} = \underbrace{\color{blue}{\beta_{0}} + \color{orange}{\beta _{1}} \times x_{1i} + \color{orange}{\beta _{2}} \times x_{2i}}_{\text{Modell} = \color{green}{\widehat{y}}_{i} = \text{Predicted values}} + \underbrace{\color{red}{\varepsilon}_{i}}_{\color{red}{Error}} = \color{green}{\widehat{y}}_{i} + \color{red}{\varepsilon}_{i}$

• Q: Why is the linear model called “linear” model?

• Important: Variable values (e.g., $y_{i}$ or $x_{1,i}$) vary, parameter values (e.g., $\boldsymbol{\color{blue}{\beta_{0}}}$) constant across rows

• Important: $\color{green}{\widehat{y}_{i}}$ varies across units

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