Least Squares Regression Normality Assumption
Overview
Normality Assumption
{% \epsilon_i \sim N(0,\sigma^2) %}
and distributed indepedently (I.I.D.)
The density function for each epsilon is
{% P(\epsilon) = \frac{1}{\sqrt{2 \pi} \sigma} exp[\frac{- \epsilon^2}{2 \sigma^2}] %}
then
{% P(y_i | X_i; \beta) = \frac{1}{\sqrt{2 \pi} \sigma} exp[- \frac{y_i - \beta^T X_i}{2 \sigma^2}] %}
{% (y_i | X_i; \beta) \sim N(\beta^T X_i, \sigma^2) %}
Stanford Lecture
