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)
Transformations to Achieve Linearity
Example
Confounding
- 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
Confounding
- The response is at least partially due to a third factor
Comparison
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
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?
