ABSTRACT
Statistical models describe the systematic behavior as well as the random variation in a precise manner. In this chapter we introduce the normal distribution as a tool to describe random variation.
So far we have focused on the average or expected behavior of the observations. In linear regression, we looked at the expected value of y for a given value of x, and in the one-way ANOVA setting, we modeled the expected value for an observation from group j. The average behavior is described by the systematic (or fixed) part of a model. However, we have also emphasized that there is variation around these expected values — not all y’s have the same value even though they have the same corresponding value of x (linear regression), and not all observations within a group are identical (one-way ANOVA) — and that we need to take this random variation into account.
