Section 25 Linear Model: lm implementation
25.3 Assumptions
- \(y\) is related to \(x\) by the simple linear regression model:
\[ \large y_{i} = \beta_0 + \beta_1 x_{i} + \epsilon_{i}, \space i=1,...,n\] \[ \large E(y | X=x_i) = \hat\beta_0 + \hat\beta_1 x_{i} \]
The errors \(\epsilon_1, \epsilon_2, ..., \epsilon_n\) are independent of each other.
The errors \(\epsilon_1, \epsilon_2, ..., \epsilon_n\) have a common variance \(\sigma^2\).
The errors are normally distributed with a mean of 0 and variance \(\sigma^2\), that is:
\[ \large \epsilon \sim N(0,\sigma^2) \]