3.18 Models: Example: Linear model (Visualization)

  • Trusti = b0 + b1Threati + b1Educationi + \(\epsilon\)i (Wikipedia)
  • Plane generated through equation above is not model of the data
    • Admissible model must be consistent with all the data points
    • Plane cannot be model, unless it exactly fits all the data points
    • The error term, \(\epsilon\)i, must be included in the model, so that it is consistent with all data points
  • Statistical inference:
    • Assume some probability distributions for the \(\epsilon\)i, e.g. i.i.d. Normal, with zero mean
    • Model has 3 parameters: b0, b1, b2

Notes

  • Lessons
    • Underlying any model (mean, LM etc.) is a (join) distribution