1. Exploring Relationships Between Numerical Variables Correlation

2. Try this … 1.Sketch two scatterplots that have the same form and direction, but different strengths. 2.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 r = 0.54 r = 0.82 r = 0.89 r = -0.04 r = -0.31 r = -0.97 -1 < r < 1 0 +1 0

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

7. TI-84 ①Turn on the Diagnostic feature ①Enter data into L 1 & L 2 ②Apply 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 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. Practice: (change number of points to 100): http://statweb.calpoly.edu/chance/applets/guesscorrelation/GuessCorrelation.html correlation (r) 1 < > 0 1