1. Chapter 7 Scatterplots, association, and correlation math2200

2. Scatterplot Since 1937, the Gallup Poll asked likely U.S. voters whether they would vote for a qualified woman for president if their preferred political party nominated one. A scatterplot of percentage saying they would vote for a women plotted against the year of the survey.

3. Scatterplot (cont.) Hurricane katrina killed more than 1100 people and caused over 100 billion dollars damages. High wind speed is associated with low atmospheric pressure. A scatterplot of Max Wind Speed (in mph) vs. Central Pressure (in mb) for 163 hurricanes that have hit the United States since 1851.

4. Direction: positive or negative?

5. Form: linear or not?

6. Scatter: small or large?

7. Outliers

8. Roles of variables X: explanatory (predictor, independent) variable Y: response (outcome, dependent) variable Example: are people who smoke more likely to get lung cancer? (Fisher testified in court that lung cancer is one of the causes of smoking.) –X: smoke –Y: lung cancer

9. How to quantify the strength of association?

10. Correlation Units should not matter Let’s convert the two variables to z-scores –Make them on the same scale –Z x –Z y

12. Correlation coefficient Units should not matter Let’s convert the two variables to z-scores –Make them on the same scale –Z x –Z y

13. Cautions A high correlation does NOT mean one variable causes another. Measures the strength of the linear association between two quantitative variables –Linear association –Quantitative variables Outliers –Outliers can distort the correlation dramatically –The relationship between IQ and shoe size among comedians shows a correlation of 0.50. Shoe size is associated with IQ?

14. Cautions (cont.) Outliers can distort the correlation dramatically A scatterplot of IQ vs. Shoe size.

15. Cautions (cont.) Uncorrelated does NOT imply no association. Here the correlation is -0.05.

16. Cautions (cont.) High correlation does not imply linear relationship. Here the correlation is 0.979, but the relationship is actually bent.

17. Properties of r Sign of r gives the direction of the association -1<= r <= 1 X and Y are uncorrelated  r = 0 Correlation treats x and y symmetrically, i.e., r(x,y)=r(y,x) No units Does not change by shifting or rescaling Uncorrelated does NOT imply no association. Sensitive to outliers

18. Correlation table Report the correlations of many variables together

19. association does not imply causation population# of storks # of chimney

20. Lurking variable A hidden variable that stands behind a relationship and determines it by simultaneously affecting the other two variables. Damage # of firefighters Size of fire