1 / 21

Chapter 6

Chapter 6. Describing Relationships: Correlation. Relationships. Positive relationship Pairs of scores vary in the same direction. When one goes up, the other goes up; when one goes down the other goes down. As temperature goes up, water consumption goes up.

daryl-lara
Télécharger la présentation

Chapter 6

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. Chapter 6 Describing Relationships: Correlation

  2. Relationships Positive relationship • Pairs of scores vary in the same direction. • When one goes up, the other goes up; when one goes down the other goes down. • As temperature goes up, water consumption goes up. • As perceived status of a car goes up, the price goes up. Chapter 6

  3. Relationships Negative relationship • Pairs of scores vary in the opposite direction. • When one goes up, the other goes down; when one goes down the other goes up. • When the temperature goes down, gas usage for heating goes up. • As the altitude goes up, the percentage of oxygen in the air goes down. Chapter 6

  4. Relationships No Relationship Pairs of scores vary independently of each other. The number of students in the Commons has no relationship to the size of cargo barges on the Mississippi. The amount of time studying Statistics has no relationship to the on-time arrival percentage for Southwest Airlines. Chapter 6

  5. Scatter plots Chapter 6

  6. Scatter plots Chapter 6

  7. Relationships • Strong or Weak relationship? • The more closely the dot cluster approximates a straight line, the stronger (the more regular) the relationship will be. Chapter 6

  8. Correlation coefficient (r) A correlation coefficient is a number between -1 and 1 that describes the relationship between variables. Named for Karl Pearson The sign of r indicates the type of linear relationship, whether positive or negative. The numerical value of r, without regard to sign, indicates the strength of the linear relationship. Chapter 6

  9. Estimating correlations Correlation Example Generator Chapter 6

  10. Caution!! The strength of a correlation does NOT signify causality. Page 137 !!! Chapter 6

  11. Now….the fun!!! Calculating a correlation. Use the computational formula on page 143. Chapter 6

  12. Correlation calculation steps • Assign a value to n. • Sum all scores for x and y. • Multiply each pair (x*y) and sum the products. • Square each x and find the sum of the squares. • Square each y and find the sum of the squares. • Calculate the intermediate values for: • Sum of products • Sum of squares for x • Sum of squares for y • Plug in intermediate values to solve for r Chapter 6

  13. Correlation Calculation r = SPxy √ SSxSSy Chapter 6

  14. Correlation calculation formula • Sum of products SPxy= Σ XY - (Σ X)(Σ Y) n • Sum of squares for X SSx = Σ(X)2 – (ΣX)2 n • Sum of squares for Y SSy= Σ(Y)2 – (ΣY)2 n Chapter 6

  15. Practice Calculate the value of r, using the computational formula for the data on page 143. Chapter 6 Answer on page 487

  16. Practice Calculate the value of r, using the computational formula for the following data. Chapter 6 Answer on page 487

  17. Practice Calculations Chapter 6 Answer on page 487

  18. Correlation calculation SPxy= Σ XY - (Σ X)(Σ Y) = 32 – (12)(14) = 32-168 = 32-28 = 4 n 6 6 SSx = Σ(X)2 – (ΣX)2= 28 – (144) = 28-24 = 4 n 6 SSy= Σ(Y)2 – (ΣY)2= 42 – (196) = 42-32.67 = 9.33 n 6 r = SPxy = 4 = 4 = 4 √SSxSSy √ (4)(9.33) √ 37.32 6.11 = .65 Chapter 6

  19. Gather the following data from at least 10 people in the class and calculate the correlation coefficient. The number of miles you live from the campus and the average number of hours you work each week. Chapter 6

  20. Outliers The best strategy is to report the correlation that includes and exclude the outliers. Chapter 6

  21. Correlation Matrix Chapter 6

More Related