Stat 112: Model, parameters and Lurking variables

• Administrivia:

• Statistics: scatter diagram of Y vs X
• probability: histograms of future observations given X
• Both describe X relating to Y
• Model details
  • describes the population
  • Average Y = beta₀ + beta₁ x
  • Actual Y = beta₀ + beta₁ x + noise
  • Noise = normal, with SD = sigma
  • Three greek letters (parameters):
    • beta₀ = intercept
    • beta₁ = slope
    • sigma = noise

  • Called "Simple Linear Regression Model"

• Estimating parameters from data
  • Fit by least squares: Y = b₀ + b₁ X
  • b₀ estimates beta₀
  • b₁ estimates beta₁
  • JMP will compute standard errors for you
  • good guess for slope: b₁ +/- 2 * SE

• Look at insurance data (or see handout)
• Model is different than causation.
  • X ---> Y could generate model
  • Y ---> X could generate model (draw smoking = Y, cancer = X)
  • Z ---> X and Z ---> Y could generate model
  • In all above, the model might hold
  • But causation is only in the first case

• proving causation requires a controled experiment
• proving the model requires data (easy to do with observation)

• If we have good residuals, and a good linear fit do we have causation?
  • NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO!
  • Why: Lurking variables
  • X causes Y is possible
  • Y causes X is possible
  • Z causes X and Y is posible (Z is lurking variable)
  • Infant death rates and breast feeding: lurking variable

Last modified: Tue Feb 1 09:54:30 EST 2000