I’ve heard something frightening from practicing statisticians who frequently use mixed effects models. Sometimes when I ask them whether they produced a [semi]variogram to check the correlation structure they reply “what’s that?” -Frank Harrell

One of the basic assumptions of linear modeling is constant, or homogeneous, variance. What does that mean exactly? Let’s simulate some data that satisfies this condition to illustrate the concept.

Below we create a sorted vector of numbers ranging from 1 to 10 called x, and then create a vector of numbers called y that is a function of x. When we plot x vs y, we get a straight line with an intercept of 1.2 and a slope of 2.1.