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

2. AP Statistics, Section 3.2, Part 1
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. AP Statistics, Section 3.2, Part 1
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. AP Statistics, Section 3.2, Part 1
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. AP Statistics, Section 3.2, Part 1
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