## 7.1 Mathematical Model

• The mean of $$Y$$ values at any given $$X$$ is $$\beta_{0} + \beta_{1} X$$
• The variance of $$Y$$ values at any $$X$$ is $$\sigma^2$$ (same for all X)
• This is known as homoscedasticity, or homogeneity of variance.
• $$Y$$ values are normally distributed at any given $$X$$ (need for inference)