Outliers and Influential Points

  • An outlier is an observation that lies outside the overall pattern

    • Outliers in the Y direction will lead to large residuals
  • Influential observations are points that would greatly change the result if removed

  • Points with high leverage have values far from the mean (of X or Y)

High leverage High discrepancy High influence 200 150 100 50 10 200
150 100 50 200 150 100 50 15 20 10 15 20 10 15 20

Transformations to Achieve Linearity


Log Y = Log a Log b + b Log

  • Example

    10,0 • 10 + .008(GDP) Life Life • = 30 + 10 WGDP)


  • Correlation does not prove causation


  • A Lurking Variables is one that is not the explanatory (x) or response (y) variable in the study, but can influence how we interpret the relationship between them

  • What looks like an association between x and y but is a Common Response

    Explanatory X appears related to Y Partial reason for association
Lurking variables Response

  • Confounding

    • The response is at least partially due to a third factor


  • Comparison

    causation x common x response z confounding x z random x

  • Example

    • There is a positive association between the number of drowning and hot dog sales. Is the association between two variables most likely due to causation, cofounding, or common response? Justify your answer.

      • Answer: Common Response

    ( 53 D

  • According to the 19990 census, those states with an above-average number X of people who fail to complete high school tend to have an above average number Y of infant deaths. In other words, there is a positive association between X and Y. The most plausible explanation for this is?

    • Answer: Common Response


  • A drug company is testing a new cream to relieve skin rashes. They try it on 20 people and a placebo on 20 people and find that it works better. Later someone realizes that the new cream was tested on mostly all men and the placebo was tested on mostly all women. Is it possible the difference seen could have been due to confounding? What about common response?


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