1. Introduction to Correlation (Dr. Monticino)

2. Assignment Sheet Math 1680  Read Chapters 8 and 9  Review Chapter 7 – algebra review on lines  Assignment #6 (Due Monday Feb. 28 th )  Chapter 8 Exercise Set A: 1, 5, 6 Exercise Set B: ALL Exercise Set C: 1, 3, 4 Exercise Set D: 1  Quiz #5 – Normal Distribution (Chapter 5)  Test 1 is still projected for March 2, assuming we get through chapter 10 by then…

3. Correlation  The idea in examining the correlation of two variables is to see if information about the value of one variable helps in predicting the value of the other variable  To say that two variables are correlated does not necessarily imply that one causes a response in the other.  Correlation measures association. Association is not the same as causation

4. Scatter Diagram

6. Correlation Coefficient  The correlation coefficient is a measure of linear association between two variables  r is always between -1 and 1. A positive r indicates that as one variable increases, so does the other. A negative r indicates that as one variable increases, the other decreases

7. Correlation Coefficient  The correlation coefficient is unitless  It is not affected by  Interchanging the two variables  Adding the same number to all the values of one variable  Multiplying all the values of one variable by the same positive number

8. Correlation Coefficient r = AVERAGE((x in standard units)  (y in standard units))

9. Example  Find the correlation coefficient for following data set

10. Example  Step 1: Put x and y values into standard units  Need to find respective averages and standard deviations Av(X) = 60.7 SD of X = 30.4 Av(Y) = 43.4 SD of Y = 18.1

11. Example  Step 1: Put x and y values into standard units

12. Example  Step 2: Find (x standard units)  (y standard units)

13. Example  Step 3: Find average of (x standard units)  (y standard units) values

14. SD Line  Standard deviation line is THE line which the correlation coefficient is measuring dispersion around  SD line passes through the point (x-average,y-average)  Slope of SD line is  (SD of y)/(SD of x) if + correlation  -(SD of y)/(SD of x) if - correlation

15. Example  Draw SD line for following data set Av(X) = 60.7 SD of X = 30.4 Av(Y) = 43.4 SD of Y = 18.1

16. Example Point on SD line (60.7, 43.4) Slope of SD line 18.1/30.4 =.595 Equation of SD line

17. Correlation Coefficient Definition  Visually, the definition of correlation is reasonable Average Lines

18. More on Correlation  Correlation can be confounded by outliers and non-linear associations  When possible, look at the scatter diagram to check for outliers and non- linear association  Do not be too quick to delete outliers  Do not force a linear association when there is not one

19. Outliers n r =.31

20. Outliers n r =.72

21. Non-Linear Association n r =.22 (Dr. Monticino)

22. Discussion Problems  Questions or Comments?  Chapter 8  Review Exercises: 1,2, 3, 5, 7, 8, 9, 11