4.9 Summary of notation and terminology

  • $x_i$ is observation $i$ on variable $x$.
  • $y_i=\beta_0+\beta_1x_i+\varepsilon_i$ is the simple linear model with intercept $\beta_0$ and slope $\beta_1$. The error is denoted by $\varepsilon_i$.
  • $y_i=\hat{\beta}_0+\hat{\beta}_1 x_i+e_i$ is the estimated regression model with intercept $\hat{\beta}_0$ and slope $\hat{\beta}_1$. The estimated error or residual is denoted by $e_i$.
  • $\hat{y}_i=\hat{\beta}_0+\hat{\beta}_1 x_i$ is the fitted or estimated regression line; $\hat{y}_i$ is the fitted value corresponding to observation $y_i$.