Statistics 102H: Assumptions

Questions about homework?

• Any questions about managed benifits?
  • Notice, transformations maintain monotonicity
  • Hence, none could fix it
  • graphcally captured by bulging rule
• I'll discuss crime data in class today.

Checking assumptions

• Recall our assumptions:
  • Independence
  • Normality
  • Homoskadasticity
  • (see page 44-46)
• Save residuals
• Use brushing to see how connected to Y
• Make histogram of residuals (show Q-Q plot)

Isolated points

• Trouble or an anoynance?
  • If violation of assumptions it is trouble
  • Otherwise, merely an anoynance. Deal with it!
• deviations in Y direction = trouble (called outlier)
• deviation in X direction = anoynance (called high leverage point)
• BOTH = big trouble! = (called influential outlier)

Cottages

• important points might be leveraged

Housing prices

• Isolated points
• Leverage calculation
• leave-one-out fit (using JMP)
• various transformations
• Tukey calls this pealing the statistical onion

Why use a model?

• By having a model we can
  • Talk about how new data will behave.
  • describe new data using only 3 numbers!
  • know how accurate future predictions will be.
• Prediction intervals in JMP

Homework

• If you didn't look at examples I mentioned last time DO SO!
• Revisiting Display ft.
  • We look two transformation: log(x) and 1/X
  • Make both of these transformations using the formula editor in JMP
  • Now plot Y vs the new variable log(x)
  • Now plot Y vs the new variable 1/x
  • Which fits better?
  • Which graph seems more useful for economics? the orginal graph given in the book, or the ones you just created?
  • Which graph seems more useful for Statistics? In other words, which can you check your assumptions better using?
• You should now have looked at all the examples (except cell phones) upto page 95.
• Re-read introduction to class 2 (p 39 - 52).