Scatter diagrams, strong and weak correlation, positive and negative correlation, lines of best fit, extrapolation and interpolation. Aimed at UK level 2 students on Access and GCSE Maths courses.

1. Correlation part 1 Relationship between variables...

4. “ Children brought up in homes with more household appliances tend to perform better in school. Therefore, household appliances improve intelligence.”

5. “ Teens involved in violent crimes tend to play violent video games. Therefore, playing violent video games causes teenagers to get involved in criminal behaviour.” http://btr.michaelkwan.com/2009/01/10/correlation-does-not-imply-causation/

6. Correlation does not imply causation...

7. ...but the existence of a correlation can flag something worth investigating...

8. Taller people might be heavier than shorter people, but you will have to allow for body shape

9. Taller people might be heavier than shorter people, but you will have to allow for body shape Scatter diagrams can show you the relationship between variables...

10. Scatter diagram Another chart – X Y plot in MS Excel

11. The student data set handout...

12. Forearm and handspan

15. Serge Rachmaninov could play a left hand chord of C E-Flat G C G

17. Describing the pattern Words and ellipses

20. Strong Positive Correlation No correlation, little relationship Moderate Negative Correlation

22. Line of best fit Only for medium to strong correlations...

25. 1. Follows trend of points

26. 1. Follows trend of points 2. Roughly equal numbers of points above and below line

27. 1. Follows trend of points 2. Roughly equal numbers of points above and below line 3. Does not (necessarily) pass through any given point

28. 1. Follows trend of points 2. Roughly equal numbers of points above and below line 3. Does not (necessarily) pass through any given point 4. Nothing special about outer points or axes origin!

31. Too shallow

32. Too Steep

33. Lines of best fit will pivot around the point which represents the mean of the X and the mean of the Y variables.

34. Using LOBF to make predictions Drawing lines on the graph

35. Y X

36. Y X

37. Y X

38. Y X Predicting a value of the X variable from the Y value

39. Y X

40. Y X

41. Y X Predicting a value of the Y variable from the X value

43. Interpolation and extrapolation Safe data processing

44. Y X The LOBF has been drawn beyond the range of the data

45. Y X

46. Y X Could be a small part of a curve – and the curve could go either way...

47. Y X

48. Y X Interpolation - Predictions within the range of the data points safe...

49. Y X

50. Y X

51. Y X

52. Y X

53. Y X Extrapolation - Predictions outside the range of the data points unsafe... very large errors possible