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Correlation

Correlation. Studying the relationship between two variables. Scatter plot. Shows relationship between two variables Dot represents a pair of values from one individual or case. Linear Association. Positive association Y-coordinates increase as X-coordinates increase

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Correlation

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  1. Correlation Studying the relationship between two variables

  2. Scatter plot • Shows relationship between two variables • Dot represents a pair of values from one individual or case

  3. Linear Association • Positive association • Y-coordinates increase as X-coordinates increase • “cloud” slopes up from left to right • Negative association • Y-coordinates decrease as X-coordinates increase • “cloud” slopes down from left to right

  4. Linear Association • Strong association • Dots are tightly clustered around a line • Knowing one variable enables accurate prediction of the other (within data range)

  5. Linear Association • Weak association • Knowing one variable does not give much information about the other • Dots are spread out

  6. Correlation coefficient • Abbreviated as r • Can be any number between -1 and 1 (inclusive) • Numerical measure of strength of association r > 0 : positive association r < 0 : negative association |r| near 1 : strong association |r| near 0 : weak association

  7. Correlation guessing game

  8. Warnings • r measures linear association only • Just because r is near 0 doesn’t mean there’s no pattern

  9. Warnings • r measures linear association only. • Correlations based on rates or averages tend to overstate the strength of association

  10. Taking Averages Strengthens Correlation r= 0.411 r= 0.890

  11. Warnings • r measures linear association only. • Correlations based on rates or averages tend to overstate the strength of association • Association is not the same as causation

  12. Association vs. Causation For the 2011-2012 Carolina Panthers

  13. Association vs. Causation • r = 0.659 : There is a fairly strong positive association between jersey number and weight

  14. Association vs. Causation • r = 0.659 : There is a fairly strong positive association between jersey number and weight • If Cam Newton (#1, 245 lbs) traded jerseys with Byron Bell (#77 340 lbs) what would happen to Newton’s weight?

  15. Association vs. Causation • r = 0.659 : There is a fairly strong positive association between jersey number and weight • If Cam Newton (#1, 245 lbs) traded jerseys with Byron Bell (#77 340 lbs) what would happen to Newton’s weight? Nothing, of course! Changing jersery number doesn’t change player weight.

  16. Attenuation • Q: Two weathermen compute the correlation between daily maximum temperatures for Washington, D.C. and Boston, MA. One weatherman does this for the month of June; the other does it for the whole year. Which weatherman gets the bigger correlation?

  17. Attenuation • Q: Two weathermen compute the correlation between daily maximum temperatures for Washington, D.C. and Boston, MA. One weatherman does this for the month of June; the other does it for the whole year. Which weatherman gets the bigger correlation? • A: The correlation for the whole year is bigger. Focusing on June restricts the range and attenuates (weakens) the correlation.

  18. Attenuation • Q: The National Health and Nutrition Examination Survey studied children ages 6 to 11. From the collected data, it was found that the correlation between height and weight for each age was just about 0.67. For all the children together, would the correlation between height and weight be just about 0.67, somewhat more than 0.67, or somewhat less than 0.67?

  19. Attenuation • Q: The National Health and Nutrition Examination Survey studied children ages 6 to 11. From the collected data, it was found that the correlation between height and weight for each age was just about 0.67. For all the children together, would the correlation between height and weight be just about 0.67, somewhat more than 0.67, or somewhat less than 0.67? • A: Somewhat more than 0.67. When you put all the children together, you expand the range and the data are much more linear.

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