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Correlation

Correlation. Assumptions: You can plot a scatter graph You know what positive, negative and no correlation look like on a scatter graph. Correlation describes the strength of the relationship between two variables. Paired data is often known as bivariate data.

cathleen-hall
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Correlation

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  1. Correlation Assumptions: You can plot a scatter graph You know what positive, negative and no correlation look like on a scatter graph

  2. Correlation describes the strength of the relationship between two variables. Paired data is often known as bivariate data. • In S1 we will look at ways of measuring the degree of linear association • First establish whether a linear correlation exists using a scatter diagram. x x x x x x x x x x x x x x x x x x x x x x x x x x x x

  3. Correlation describes the strength of the relationship between two variables. Paired data is often known as bivariate data. • In S1 we will look at ways of measuring the degree of linear association • First establish whether a linear correlation exists using a scatter diagram. We could plot a new point - the mean of the values and the values, i.e. x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x

  4. x x x x x x x x x x x x x x x x x x x x x x x x x x x x By redrawing axes through we can look at the scatter of points in quadrants ① ② Correlation Positive (most in 1st & 3rd) Negative (most in 2nd & 4th) None ③ ④ x x x Assuming you believe a linear relationship exists, we can calculate a measure of how strong it is.

  5. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  6. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  7. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  8. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  9. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  10. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x Complete the table… x x x x x x x x x x x x

  11. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  12. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  13. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  14. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  15. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  16. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  17. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  18. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  19. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  20. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  21. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  22. Product Moment Correlation Coefficient (PMCC) ① ② ③ ④ • We could calculate a measure based on each point’s distance from the mean, e.g. we could find x x x x x x x x x x x x x

  23. Product Moment Correlation Coefficient (PMCC) x x x x x x x x x x x x • If we sum the values… • For this example, since most points are in 1st & 3rd quadrants, the total will be positive (hence positive correlation) What would be the effect on the sum in the example above if we used a data set ten times bigger? x • A negative correlation would be overall negative • No correlation would give a sum close to zero

  24. Product Moment Correlation Coefficient (PMCC) x x x x x x x x x x x x • If we sum the values… • For this example, since most points are in 1st & 3rd quadrants, the total will be positive (hence positive correlation) What would be the effect on the sum if we changed the units, e.g. used cm instead of metres for a measurement? x • A negative correlation would be overall negative • No correlation would give a sum close to zero

  25. Product Moment Correlation Coefficient (PMCC) • If we sum the values… • For this example, since most points are in 1st & 3rd quadrants, the total will be positive (hence positive correlation) We for the PMCC • A negative correlation would be overall negative • No correlation would give a sum close to zero To eliminate these problems we use the following formula. This will always give a value between -1 and 1

  26. To eliminate these problems we use the following formula. This will always give a value between -1 and 1 : a perfect negative linear correlation : a perfect positive linearcorrelation : no linear correlation NB. Don’t use PMCC is a different type of correlation exists, For example if points follow a clear curve

  27. An easier version of the formula • The following are easier to use in calculations NB You are given all these formulas in the exam

  28. Example • Find PMCC

  29. Example • Find PMCC

  30. Example • Find PMCC

  31. Example Complete the table and calculate the totals • Find PMCC

  32. Example • Find PMCC

  33. Example • Find PMCC

  34. Example • Find PMCC Now calculate to 3 s.f.

  35. Example • Calculators – pro’s & cons • The Casio calculators can work out PMCC but the exam often asks you to find parts of the equation before finding (testing you are not simply using one) • Also there will be about 6 marks for PMCC – you will lose all 6 if you mistype one data value in the time pressure of the exam. • But, check your answer using a calculator. • Find PMCC to 3 s.f.

  36. Example • Find PMCC

  37. Example Enter data in the and columns

  38. Example Enter data in the and columns • Find PMCC

  39. Example Enter data in the and columns • Find PMCC to 3 s.f.

  40. Example of Q that can’t be done using the data function a) Find b) Find

  41. Example of Q that can’t be done using the data function a) Find 490.2 4 s.f. 0.906 3 s.f. b) Find

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