7.6 Prediction: Mean

  • Model = Mathematical equation(s)
  • Underlying a model is always a (joint) distribution
  • Model summarizes (joint) distribution with fewer parameters
    • e.g. intercept/coefficents in linear model
  • Simple model: Mean of the distribution of a variable
ˉy=y1+y2++ynn=nitrust2006in=406686633=6.13


012345678910
trust2006

yi=¯yˆyi±εi

trust2006Anna=3=¯yˆyAnna±εAnna=6.133.13

  • Mean (= model) predicts Anna’s value with a certain error
  • Q: How well does the model (mean = 6.33) predict person’s that have values of 0, of 3 or of 4?
  • Important: We could use this model – this mean – to predict trust values of another group of people
    • First train model (= calculate mean) on this data (training dataset), then use it to predict outcome in other data (validation dataset)
    • Sometime this is called out of sample prediction