CORRELATION & MEDIAN REGRESSION LINE General Mathematics
In order to answer this we need to collect some data Is there a mathematical relationship between a person’s age and the n...
 
 
 
 
 
 
 
 
 
 
 
Linear Modelling
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 hav...
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 hav...
60 19.5-6.1 = 13.4 Gradient =
The “y-intercept” 19.5 y = mx + b “ y” = Number of sickies (N) “ x” = Age in years (A) N = -0.2233A + 19.5
A statistically more accurate way is to find a  median regression line This is a more fancy way of finding the line of bes...
Step 1:   Divide all the points into three equal groups from left to right
Step 2:  In each block find the median from left to right
Step 3:  Find the median from top to bottom
Step 4:  Draw a line joining first and third median pts
Step 5:  Draw a line parallel to this through the middle median point
Step 6:  Move the solid line  ⅓  of the way towards  the dotted line
Step 6:  Move the solid line  ⅓  of the way towards  the dotted line
Step 6:  Move the solid line  ⅓  of the way towards  the dotted line
Step 6:  Move the solid line  ⅓  of the way towards  the dotted line
Step 6:  Move the solid line  ⅓  of the way towards  the dotted line
Step 6:  Move the solid line  ⅓  of the way towards  the dotted line
Step 6:  Move the solid line  ⅓  of the way towards  the dotted line
Step 6:  Move the solid line  ⅓  of the way towards  the dotted line
Step 6:  Move the solid line  ⅓  of the way towards  the dotted line
Step 6:  Move the solid line  ⅓  of the way towards  the dotted line
By removing all our construction lines we can see our median regression line clearly and can work out the equation.
By removing all our construction lines we can see our median regression line clearly and can work out the equation.
Correlation
These points show some strong relationship between the person’s age and the number of sickies they take (Correlation)
These points show a correlation that is not so strong:
These points show a correlation that is relatively weak:
These points show no correlation at all:
Correlation Coefficients
The degree of correlation can be assigned a number from  – 1 to 1
These points are perfectly correlated, so they possess a correlation coefficient of +1 (positive because of positive slope)
Let us see what happens as the correlation gradually fades away: Correlation = +1
Let us see what happens as the correlation gradually fades away: Correlation = +0.98
Let us see what happens as the correlation gradually fades away: Correlation = +0.90
Let us see what happens as the correlation gradually fades away: Correlation = +0.36
Let us see what happens as the correlation gradually fades away: Correlation = 0
Let us see what happens as the correlation gradually fades away: Correlation = -0.41
Let us see what happens as the correlation gradually fades away: Correlation = -0.90
Let us see what happens as the correlation gradually fades away: Correlation = -0.97
Let us see what happens has the correlation gradually fades away: Correlation = -1 Correlation is negative because of nega...
We can also assign words to describe the degree of correlation
Strong   positive  correlation
Moderate positive  correlation
Weak positive  correlation
No correlation
Weak negative  correlation
Moderate negative  correlation
Strong negative  correlation
The End
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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

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