1 / 22

Understanding Correlation: Key Concepts and Assignments in Math 1680

This assignment focuses on understanding correlation between two variables, aiding in predicting values based on their relationship. Students are required to read Chapters 8 and 9 while reviewing Chapter 7 on algebra concepts. They will solve exercises from different sets and prepare for Quiz #5 on normal distribution. The correlation coefficient, measuring linear association, will be explored, alongside the importance of scatter diagrams and the effects of outliers on data analysis. Submission is due on February 28th, leading up to Test 1 projected for March 2nd.

jafari
Télécharger la présentation

Understanding Correlation: Key Concepts and Assignments in Math 1680

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related