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# Correlation

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Correlation NSW Genral Mathematics Course

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### Correlation

1. 1. CORRELATION & MEDIAN REGRESSION LINE General Mathematics
2. 2. In order to answer this we need to collect some data Is there a mathematical relationship between a person’s age and the number of sickies they take?
3. 14. Linear Modelling
4. 15. To draw a line of best fit we have (as a rule of thumb), roughly as many points on one side of the straight line as we have on the other side
5. 16. To draw a line of best fit we have (as a rule of thumb), roughly as many points on one side of the straight line as we have on the other side
6. 17. 60 19.5-6.1 = 13.4 Gradient =
7. 18. The “y-intercept” 19.5 y = mx + b “ y” = Number of sickies (N) “ x” = Age in years (A) N = -0.2233A + 19.5
8. 19. A statistically more accurate way is to find a median regression line This is a more fancy way of finding the line of best fit, eliminating the possibility of getting variations from one person to another, ie. there is only one true line of best fit.
9. 20. Step 1: Divide all the points into three equal groups from left to right
10. 21. Step 2: In each block find the median from left to right
11. 22. Step 3: Find the median from top to bottom
12. 23. Step 4: Draw a line joining first and third median pts
13. 24. Step 5: Draw a line parallel to this through the middle median point
14. 25. Step 6: Move the solid line ⅓ of the way towards the dotted line
15. 26. Step 6: Move the solid line ⅓ of the way towards the dotted line
16. 27. Step 6: Move the solid line ⅓ of the way towards the dotted line
17. 28. Step 6: Move the solid line ⅓ of the way towards the dotted line
18. 29. Step 6: Move the solid line ⅓ of the way towards the dotted line
19. 30. Step 6: Move the solid line ⅓ of the way towards the dotted line
20. 31. Step 6: Move the solid line ⅓ of the way towards the dotted line
21. 32. Step 6: Move the solid line ⅓ of the way towards the dotted line
22. 33. Step 6: Move the solid line ⅓ of the way towards the dotted line
23. 34. Step 6: Move the solid line ⅓ of the way towards the dotted line
24. 35. By removing all our construction lines we can see our median regression line clearly and can work out the equation.
25. 36. By removing all our construction lines we can see our median regression line clearly and can work out the equation.
26. 37. Correlation
27. 38. These points show some strong relationship between the person’s age and the number of sickies they take (Correlation)
28. 39. These points show a correlation that is not so strong:
29. 40. These points show a correlation that is relatively weak:
30. 41. These points show no correlation at all:
31. 42. Correlation Coefficients
32. 43. The degree of correlation can be assigned a number from – 1 to 1
33. 44. These points are perfectly correlated, so they possess a correlation coefficient of +1 (positive because of positive slope)
34. 45. Let us see what happens as the correlation gradually fades away: Correlation = +1
35. 46. Let us see what happens as the correlation gradually fades away: Correlation = +0.98
36. 47. Let us see what happens as the correlation gradually fades away: Correlation = +0.90
37. 48. Let us see what happens as the correlation gradually fades away: Correlation = +0.36
38. 49. Let us see what happens as the correlation gradually fades away: Correlation = 0
39. 50. Let us see what happens as the correlation gradually fades away: Correlation = -0.41
40. 51. Let us see what happens as the correlation gradually fades away: Correlation = -0.90
41. 52. Let us see what happens as the correlation gradually fades away: Correlation = -0.97
42. 53. Let us see what happens has the correlation gradually fades away: Correlation = -1 Correlation is negative because of negative slope
43. 54. We can also assign words to describe the degree of correlation
44. 55. Strong positive correlation
45. 56. Moderate positive correlation
46. 57. Weak positive correlation
47. 58. No correlation
48. 59. Weak negative correlation
49. 60. Moderate negative correlation
50. 61. Strong negative correlation
51. 62. The End