This post is based on a handout that I use for one of my courses, and it relates to the usual linear regression model,
y = Xβ + ε
In our list of standard assumptions about the error term in this linear multiple regression model, we include one that incorporates both homoskedasticity and the absence of autocorrelation. That is, the individual values of the errors are assumed to be generated by a random process whose variance (σ2) is constant, and all possible distinct pairs of these values are uncorrelated. This implies that the full error vector, ε, has a scalar covariance matrix, σ2In.
We refer to this overall situation as one in which the values of the error term follow a “Spherical Distribution”. Let's take a look at the origin of this terminology.