5.1 Linear Regression Model

Generally, the regression model is written as

\[ y_{i} = \beta_0 + \beta_1x_{1i} + \beta_2x_{2i} + ... + \beta_qx_{qi} + \epsilon_{i} \]

where

• \(y_{i}\) is the value of the outcome variable for individual \(i\)
• \(\beta_0\) is an intercept parameter, the expected value of \(y_i\) when the predictor variables are all \(0\)
• \(\beta_q\) is a regression parameter indicating the relation between \(x_{qi}\) and the outcome variable, \(y_i\)
• \(\epsilon_{i}\) are errors or disturbances