Section 3.2

1. Section 3.2 AP Statistics October 1st, 2010 Mr. Calise

2. Correlation • Is there a “correlation” between a baseball team’s “earned run average” and the number of wins? • Is the association strong or weak? • Is the association positively associated or negatively associated? AP Statistics, Section 3.2, Part 1

3. Calculating Correlation • The calculation of correlation is based on mean and standard deviation. • Remember that both mean and standard deviation are not resistant measures. AP Statistics, Section 3.2, Part 1

4. Calculating Correlation The formula for calculating z-values. Both z-values are negative. Their product is positive. • What does the contents of the parenthesis look like? • What happens when the values are both from the lower half of the population? From the upper half? Both z-values are positive. Their product is positive. AP Statistics, Section 3.2, Part 1

5. Calculating Correlation • What happens when one value is from the lower half of the population but other value is from the upper half? One z-value is positive and the other is negative. Their product is negative. AP Statistics, Section 3.2, Part 1

6. Using the TI-83 to calculate r • You must have “DiagnosticOn” from the “Catalog” AP Statistics, Section 3.2, Part 1

7. Using the TI-83 to calculate r • Run LinReg(ax+b) with the explantory variable as the first list, and the response variable as the second list AP Statistics, Section 3.2, Part 1

8. Using the TI-83 to calculate r • The results are the slope and vertical intercept of the regression equation (more on that later) and values of r and r2. (More on r2 later.) AP Statistics, Section 3.2, Part 1

9. Facts about correlation • Both variables need to be quantitative • Because the data values are standardized, it does not matter what units the variables are in • The value of r is unitless. AP Statistics, Section 3.2, Part 1

10. Facts about correlation • The value of r will always be between -1 and 1. • Values closer to -1 reflect strong negative linear association. • Values closer to +1 reflect strong positive linear association. • Values close to 0 reflect no linear association. • Correlation does not measure the strength of non-linear relationships AP Statistics, Section 3.2, Part 1

11. Interpreting r • If the -1<r<-.75, the association is called “strong negative” • If the -.75<r<-.25, the association is called “moderate negative” • If the -.25<r<0, the association is called “weak negative” • And r=0, no correlation! AP Statistics, Section 3.2, Part 1

12. Interpreting r • If the 0<r<.25, the association is called “weak positive” • If the .25<r<.75, the association is called “moderate positive” • If the .75<r<1, the association is called “strong positive” AP Statistics, Section 3.2, Part 1

13. Facts about correlation • Correlation is blind to the relationship between explanatory and response variables. • Even though you may get a r value close to -1 or 1, you may not say that explanatory variable causes the response variable.We will talk about this in detail in the second semester. AP Statistics, Section 3.2, Part 1

14. AP Statistics, Section 3.2, Part 1

15. Assignment • Exercises 3.19, 3.20, 3.27, 3.31, 3.36, 3.37, The Practice of Statistics. AP Statistics, Section 3.2, Part 1