Exploring Relationships Between Numerical Variables

1. Exploring Relationships Between Numerical Variables Correlation

2. Try this … • Sketch two scatterplots that have the same form and direction, but different strengths. • Pick a sport of your choice and identify two variables that should have a positive association. Explain your reasoning.

3. Association & Correlation If there is a linear association between two numerical variables, we can measure the strength and direction of the data by looking at its ____________. • If the association is negative, then r 0. • If the association is positive, then r 0. correlation (r) < >

4. } } Direction POSITIVE NEGATIVE

5. Strength 0 0 r = -0.04 r = 0.54 r = -0.31 r = 0.82 +1 -1 r = -0.97 r = 0.89 -1 < r < 1

6. Reversed Variables The value of r will not change if the explanatory & response variables are reversed. r = -0.91 r = -0.91

7. TI-84 • Turn on the Diagnostic feature • Enter data into L1 & L2 • Apply lists to a linear form

8. Applet • go to the following website: http://bcs.whfreeman.com/sris/#730892__752214__ • choose Correlation and Regression • enter the Explanatory & Response variables Click ‘OK’ r value

9. Correlation & Causation • Even if there is a strong correlation between two numerical variables, is it a good idea to conclude that changes in one variable will cause changes in the other variable? No – causation can only be determined in an EXPERIMENTAL study

10. Sum it Up correlation (r) The ___________ is a measure of the strength and direction of a linear association between two numerical variables. Some important characteristics of the correlation include: • <r< • If the association is negative, then r 0. If the association is positive, then r 0. • If there is very little scatter from the linear form, the r is close to or . If there is lots of scatter from a linear form, then r is close to . -1 1 < > -1 1 0 Practice: (change number of points to 100): http://statweb.calpoly.edu/chance/applets/guesscorrelation/GuessCorrelation.html