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Introduction to Correlation (Dr. Monticino)

Introduction to Correlation (Dr. Monticino). 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

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Introduction to Correlation (Dr. Monticino)

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  1. Introductionto 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. 28th ) • 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

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

  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 • r = .31

  20. Outliers • r = .72

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

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

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