1 / 15

Chapter 7

Chapter 7. Correlation. Suppose we found the age and weight of a sample of 10 adults. Create a scatterplot of the data below. Is there any relationship between the age and weight of these adults?. Suppose we found the height and weight of a sample of 10 adults.

imelda-byers
Download Presentation

Chapter 7

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 7 Correlation

  2. Suppose we found the age and weight of a sample of 10 adults. Create a scatterplot of the data below. Is there any relationship between the age and weight of these adults?

  3. Suppose we found the height and weight of a sample of 10 adults. Create a scatterplot of the data below. Is there any relationship between the height and weight of these adults? Is it positive or negative? Weak or strong?

  4. The closer the points in a scatterplot are to a straight line - the stronger the relationship. The farther away from a straight line – the weaker the relationship

  5. Identify as having a positive association, a negative association, or no association. + • Heights of mothers & heights of their adult daughters - • Age of a car in years and its current value + • Weight of a person and calories consumed • Height of a person and the person’s birth month NO • Number of hours spent in safety training and the number of accidents that occur -

  6. Correlation Coefficient (r)- • A quantitative assessment of the strength & direction of the linear relationship between bivariate, quantitative data • Pearson’s sample correlation is used most • parameter - r (rho) • statistic - r

  7. Calculate r. Interpret r in context. There is a strong, positive, linear relationship between speed limit and average number of accidents per week.

  8. Strong correlation No Correlation Moderate Correlation Weak correlation Properties of r(correlation coefficient) • legitimate values of r is [-1,1]

  9. value of r does not depend on the unit of measurement for either variable x (in mm) 12 15 21 32 26 19 24 y 4 7 10 14 9 8 12 Find r. Change to cm & find r. The correlations are the same.

  10. value of r does not depend on which of the two variables is labeled x x 12 15 21 32 26 19 24 y 4 7 10 14 9 8 12 Switch x & y & find r. The correlations are the same.

  11. value of r is non-resistant x 12 15 21 32 26 19 24 y 4 7 10 14 9 8 22 Find r. Outliers affect the correlation coefficient

  12. value of r is a measure of the extent to which x & y are linearly related Find the correlation for these points: x -3 -1 1 3 5 7 9 Y 40 20 8 4 8 20 40 Sketch the scatterplot r = 0, but has a definite relationship!

  13. Association vs. Causation • In a famous example of a correlation study, the following results were obtained. • Number of Methodist Ministers Cuban Rum Imported to Boston • Year in New England (in barrels) • ---------------------------------------------------------------------------------------------------------------- • 1860 63 8376 • 1865 48 6406 • 1870 53 7005 • 1875 64 8486 • 1880 72 9595 • 1885 80 10,643 • 1890 85 11,265 • 1895 76 10,071 • 1900 80 10,547 • 1905 83 11,008 • 1910 105 13,885 • 1915 140 18,559 • 1920 175 23,024 • 1925 183 24,185 • 1930 192 25,434 • 1935 221 29,238 • 1940 262 34,705 • The correlation coefficient for this relationship is r = .999986.

  14. r = .9999 So does an increase in ministers cause an increase in consumption of rum?

  15. Correlation does not imply causation Correlation does not imply causation Correlation does not imply causation

More Related