Section 6.2: Regression, Prediction, and Causation

1. Section 6.2:Regression, Prediction, and Causation

2. Correlation and Regression • Correlation and regression are closely connected; however correlation does not require you to choose an explanatory variable and regression does. • Both correlation and regression are strongly affected by outliers… • What do you think Hawaii is known for that is definitely an outlier compared to the other 49 states?

3. Rainfall … Correlation: If Hawaii is included, r = 0.195; if Hawaii is not included, r = 0.408. Regression: If Hawaii is included, the LSRL is the solid line; if Hawaii is not included, the LSRL is the dotted line.

4. Correlation and Regression • The usefulness of the regression line for prediction depends on the strength of the correlation between the variables. • The square of the correlation is the right measure to use… • r squared will be a number between 0 and 1. The higher the number, higher the amount it accounts for all the variation along the line (you want a high number)…example 0.972 = 97.2% successful in explaining the regression line.

5. Causation • A strong relationship between 2 variables does not always mean that changes in one variable cause changes in the other. • The relationship between two variables is often influenced by other variables lurking in the background. • The best evidence for causation comes from randomized comparative experiments. • The observed relationship between 2 variables may be due to direct causation, common response, or confounding. • An observed relationship can be used for prediction without worrying about causation as long as the patterns found in the past data continue to hold true.

6. Causation • There is a strong relationship between cigarette smoking and death rate from lung cancer. Does smoking cigarettes cause lung cancer? • There is a strong association between the availability of handguns in a nation and that nation’s homicide rate from guns. Does easy access to hand guns cause more murders? • Which one do you think is a better case for direct causation?

7. Causation • Does watching television extend your lifespan? • Countries which are rich enough to have televisions are probably also fortunate enough to have better nutrition, clean water, better health care, etc. than poorer nations. • This was called a “nonsense correlation”. The correlation is real, but the conclusion is nonsense.

8. Causation • Common Response: a lurking variable influences both x and y creates a high correlation even though there is no direct connection between x and y. Ex., obesity in children: a explanatory variable can be TV viewing time, but lurking variables may be inheritance from parents, overeating, or lack of physical activity,

9. Causation • Confounding: a child may be overweight not because of their poor eating habits but because their parents provide poor choices (their parents have bad eating habits themselves).

10. Evidence for Causation • If an experiment is not possible, you must meet the following criteria to prove causation: • The association between the variables is strong. • The association between the variables is consistent.

11. Evidence for Causation (cont’d) • If an experiment is not possible, you must meet the following criteria to prove causation • Higher doses are associated with stronger responses. • The alleged cause precedes the effect in time. • The alleged cause is plausible.

12. Homework • Page 384..391 #6.34-6.37, 6.42