Linear regression with categorical predictors in Mathematica

Chapter 15 of The Art of Computer Systems Performance Analysis [1] covers linear regression with categorical predictors.

If all the variables are categorical, Jain recommends a factorial design instead instead of linear regression with categorical predictors. Jain also notes that the factorial designs will yield more precise results with less variance than regression with categorical predictors.

We'll use the following sample data for results:

First, we'll create the dataset in mathematica:

data = {
  {"unix", 64, 26.4},
  {"unix", 64, 26.4},
  {"unix", 64, 26.4},
  {"unix", 64, 26.2},
  {"unix", 234, 33.8},
  {"unix", 590, 41.6},
  {"unix", 846, 50.},
  {"unix", 1060, 48.4},
  {"unix", 1082, 49.},
  {"unix", 1088, 42.},
  {"unix", 1088, 41.8},
  {"unix", 1088, 41.8},
  {"unix", 1088, 42.},
  {"argus", 92, 32.8},
  {"argus", 92, 34.2},
  {"argus", 92, 32.4},
  {"argus", 92, 34.4},
  {"argus", 348, 41.4},
  {"argus", 604, 51.2},
  {"argus", 860, 76.},
  {"argus", 1074, 80.8},
  {"argus", 1074, 79.8},
  {"argus", 1088, 58.6},
  {"argus", 1088, 57.6},
  {"argus", 1088, 59.8},
  {"argus", 1088, 57.4}
}

Computing the linear model only requires declaring nominal variables:

lm = LinearModelFit[data, {type, bytes}, {type, bytes}, NominalVariables -> type]

(* Fitted Model [21.8124 + 0.0252066 bytes
       + 14.9266 DiscreteIndicator[type, argus, {argus, unix}] *)

The shared setup cost for both Unix and Argus is 21.8124 ms. Argus has an additional setup cost of 14.9266 ms. In other words, the total setup cost for Unix is 21.81 ms and the total setup cost for Argus is 36.74 ms. The per-byte processing time for both systems is 0.025 ms.

Jain ends the section by noting that this model is only valid if both the Unix and Argus systems use the same code path. Otherwise, two separate, simple linear regression models, one for Unix and one for Argus would be more realistic.