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...

2. We are covering...
● Idea of correlation
● Plotting scatter diagrams
● Describing the pattern of points
● Drawing line of best fit and using the LOBF to
make predictions
● Finding the difference between interpolation
and extrapolation

3. Activity 1: Read the following
slides...
● Look for holes in the arguments
● Can you state what the fallacies might be?
● Are they valid and false?
● Or just invalid?

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

13. Scatter diagram of forearm length and handspan width
51
49
47
Forearm (cm)
45
43
41
39
37
35
16 17 18 19 20 21 22 23 24 25
Handspan (cm)

14. Scatter diagram of forearm length and handspan width
51
49
47
Forearm (cm)
45
43
41
39
37
35
16 17 18 19 20 21 22 23 24 25
Handspan (cm)

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

16. Activity 2: plot scatter diagram
● Plot your own scatter diagram of the hand span
and forearm data
● What scale are you going to use?
● Where will you start and finish the axes?
● Compare your scatter diagram with someone
else. Does the pattern of crosses look about the
same?

17. Describing the pattern
Words and ellipses

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

21. Homework Q1
● Plot a scatter diagram of Handspan vs Shoe
Size from this data set
● Describe the pattern using the vocabulary
developed on the last slide
● Do you think that the relationship between shoe
size and hand span might be stronger than the
relationship between hand span and fore arm
length? What basis have you for your opinion?

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

39. Y
X

40. Y
X

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

42. Activity 3: Draw LOBF
● Take your plot of the forearm and handspan length and
draw a line of best fit on the graph
● Compare your LOBF with someone else. Is yours
shallow or steep or somewhere in the middle?
● Use your graph to predict the forearm length of
someone with a hand span of 20.5 cm
● Use your graph to predict the hand span of someone
whose forearm is 48cm long
● How do the results compare with others? Which
prediction varies more?

43. Interpolation and extrapolation
Safe data processing

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

45. Y
X

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

47. Y
X

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

49. Y
X

50. Y
X

51. Y
X

52. Y
X

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

54. Homework Q2
● Draw a LOBF on your shoe size and hand span
scatter diagram
● Use your LOBF to predict the hand span of
someone with a shoe size of 7½
● Use the LOBF to predict the shoe size of
someone with a hand span of 24.5 cm
● Which prediction is the most reliable. Write a
sentence to two explaining your answer