7.11 Prediction: Linear model (Prediction)

\(y_{Leia} = \color{blue}{5.56} + \color{orange}{-0.66} \times x_{1Leia} + \color{orange}{0.12} \times x_{2Leia} + \color{red}{\varepsilon}_{Leia}\)

\(5 = \color{blue}{5.56} + \color{orange}{-0.66} \times 0 + \color{orange}{0.12} \times 1 + \color{red}{-0.69} = \color{green}{5.69} + \color{red}{-0.69}\)

Name	\(trust2006\)	\(\boldsymbol{\color{blue}{\beta_{0}}}\)	\(\boldsymbol{\color{orange}{\beta_{1}}}\)	\(victim2006\)	\(\boldsymbol{\color{orange}{\beta_{2}}}\)	\(education2006\)	\(\boldsymbol{\color{red}{\varepsilon}}\)	\(\color{green}{\widehat{y}}\)
Daniel	5	5.56	-0.66	1	0.12	1	-0.02	5.02
Leia	5	5.56	-0.66	0	0.12	1	-0.69	5.69
Harrison	7	5.56	-0.66	0	0.12	5	0.81	6.19
..	..	..	..	..	..	..	..	..

• Important note on “prediction”
  • We can predict outcome values of units that are part of the sample on which the model is based
  • Objective of machine learning (ML) is to predict outcome values of units that were NOT part of the sample on which the model is based (trained)