This document discusses methods for determining the relationship between two variables, including linear regression and median regression. Linear regression finds the line of best fit by minimizing the distance between the data points and the line. Median regression is a more robust method that divides the data into groups, finds the median values, and draws a line between them. The document also describes how correlation can be measured numerically from -1 to 1 or qualitatively as strong, moderate, weak, or no correlation to indicate the degree of relationship between the variables.

1. CORRELATION & MEDIAN REGRESSION LINE General Mathematics

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?

14. Linear Modelling

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

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

17. 60 19.5-6.1 = 13.4 Gradient =

18. The “y-intercept” 19.5 y = mx + b “ y” = Number of sickies (N) “ x” = Age in years (A) N = -0.2233A + 19.5

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.

20. Step 1: Divide all the points into three equal groups from left to right

21. Step 2: In each block find the median from left to right

22. Step 3: Find the median from top to bottom

23. Step 4: Draw a line joining first and third median pts

24. Step 5: Draw a line parallel to this through the middle median point

25. Step 6: Move the solid line ⅓ of the way towards the dotted line

26. Step 6: Move the solid line ⅓ of the way towards the dotted line

27. Step 6: Move the solid line ⅓ of the way towards the dotted line

28. Step 6: Move the solid line ⅓ of the way towards the dotted line

29. Step 6: Move the solid line ⅓ of the way towards the dotted line

30. Step 6: Move the solid line ⅓ of the way towards the dotted line

31. Step 6: Move the solid line ⅓ of the way towards the dotted line

32. Step 6: Move the solid line ⅓ of the way towards the dotted line

33. Step 6: Move the solid line ⅓ of the way towards the dotted line

34. Step 6: Move the solid line ⅓ of the way towards the dotted line

35. By removing all our construction lines we can see our median regression line clearly and can work out the equation.

36. By removing all our construction lines we can see our median regression line clearly and can work out the equation.

37. Correlation

38. These points show some strong relationship between the person’s age and the number of sickies they take (Correlation)

39. These points show a correlation that is not so strong:

40. These points show a correlation that is relatively weak:

41. These points show no correlation at all:

42. Correlation Coefficients

43. The degree of correlation can be assigned a number from – 1 to 1

44. These points are perfectly correlated, so they possess a correlation coefficient of +1 (positive because of positive slope)

45. Let us see what happens as the correlation gradually fades away: Correlation = +1

46. Let us see what happens as the correlation gradually fades away: Correlation = +0.98

47. Let us see what happens as the correlation gradually fades away: Correlation = +0.90

48. Let us see what happens as the correlation gradually fades away: Correlation = +0.36

49. Let us see what happens as the correlation gradually fades away: Correlation = 0

50. Let us see what happens as the correlation gradually fades away: Correlation = -0.41

51. Let us see what happens as the correlation gradually fades away: Correlation = -0.90

52. Let us see what happens as the correlation gradually fades away: Correlation = -0.97

53. Let us see what happens has the correlation gradually fades away: Correlation = -1 Correlation is negative because of negative slope

54. We can also assign words to describe the degree of correlation

55. Strong positive correlation

56. Moderate positive correlation

57. Weak positive correlation

58. No correlation

59. Weak negative correlation

60. Moderate negative correlation

61. Strong negative correlation

62. The End