Summary points

In lecture 2, we

• Defined a linear model

• Defined a simple linear regression

\[y_i= \alpha + \beta x_i + \epsilon_i \quad \quad \mathrm{for} \, i=1, \dots, n\]

• \(\alpha + \beta x_i\) is the deterministic part of the model,

• \(\epsilon_i\) is the random part and \(\beta x_i\) is the part where the explanatory variable is incorporated.

• \(\alpha\) and \(\beta\) are model parameters to be estimated.