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

Published byLester Williams Modified over 8 years ago

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Presentation on theme: "Correlation Assumptions: You can plot a scatter graph You know what positive, negative and no correlation look like on a scatter graph."— Presentation transcript:

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 xx 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. x x x x x x x xx 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 xx x x x x x x x x x x x x x x x x x x x x x x ① ② ③④ Correlation Positive (most in 1 st & 3 rd ) Negative (most in 2 nd & 4 th ) None Assuming you believe a linear relationship exists, we can calculate a measure of how strong it is.

5 Product Moment Correlation Coefficient (PMCC) Quadrant 1 st 2 nd 3 rd 4 th ① ② ③④ x x x x x x x xx x x x x

6 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st 2 nd 3 rd 4 th ① ② ③④ x

7 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + 2 nd 3 rd 4 th ① ② ③④ x

8 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + 2 nd 3 rd 4 th ① ② ③④ x

9 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd 3 rd 4 th ① ② ③④ x

10 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd 3 rd 4 th ① ② ③④ x Complete the table…

11 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - 3 rd 4 th ① ② ③④ x

12 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + 3 rd 4 th ① ② ③④ x

13 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd 4 th ① ② ③④ x

14 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd 4 th ① ② ③④ x

15 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd - 4 th ① ② ③④ x

16 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd -- 4 th ① ② ③④ x

17 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd --+ 4 th ① ② ③④ x

18 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd --+ 4 th ① ② ③④ x

19 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd --+ 4 th + ① ② ③④ x

20 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd --+ 4 th +- ① ② ③④ x

21 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd --+ 4 th +-- ① ② ③④ x

22 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd --+ 4 th +-- ① ② ③④ x

23 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd --+ 4 th +-- x If we sum the values… For this example, since most points are in 1 st & 3 rd quadrants, the total will be positive (hence positive correlation) A negative correlation would be overall negative No correlation would give a sum close to zero What would be the effect on the sum in the example above if we used a data set ten times bigger?

24 Product Moment Correlation Coefficient (PMCC) x x x x x x x xx x x x Quadrant 1 st + + + 2 nd - + - 3 rd --+ 4 th +-- x If we sum the values… For this example, since most points are in 1 st & 3 rd quadrants, the total will be positive (hence positive correlation) A negative correlation would be overall negative No correlation would give a sum close to zero What would be the effect on the sum if we changed the units, e.g. used cm instead of metres for a measurement?

25 Product Moment Correlation Coefficient (PMCC) If we sum the values… For this example, since most points are in 1 st & 3 rd quadrants, the total will be positive (hence positive correlation) 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 NB. Don’t use PMCC if a different type of correlation exists, For example if points follow a clear curve

27 An easier version of the formula NB You are given all these formulas in the exam

28 Example Find PMCC 1528.8 1726.0 2018.5 2228.0 2524.5 2829.5 3048.2 3141.8

29 Find PMCC 1528.8 1726.0 2018.5 2228.0 2524.5 2829.5 3048.2 3141.8

30 Find PMCC 1528.8 1726.0 2018.5 2228.0 2524.5 2829.5 3048.2 3141.8

31 Example Find PMCC 1528.8225 1726.0 2018.5 2228.0 2524.5 2829.5 3048.2 3141.8

32 Example Find PMCC 1528.8225829.44 1726.0 2018.5 2228.0 2524.5 2829.5 3048.2 3141.8

33 Example Find PMCC 1528.8225829.44432 1726.0 2018.5 2228.0 2524.5 2829.5 3048.2 3141.8 Complete the table and calculate the totals

34 Example Find PMCC 1528.8225829.44432 1726.0 289676.00442 2018.5 400342.25370 2228.0 484784.00616 2524.5 625600.25613 2829.5 784870.25826 3048.2 9002323.241446 3141.8 9611747.241296

35 Example Find PMCC 1528.8225829.44432 1726.0 289676.00442 2018.5 400342.25370 2228.0 484784.00616 2524.5 625600.25612.5 2829.5 784870.25826 3048.2 9002323.241446 3141.8 9611747.241295.8

36 Example Find PMCC 3141.8 9611747.241295.8 1528.8225829.44432

37 Example Find PMCC

38 Example Find PMCC 1528.8 1726.0 2018.5 2228.0 2524.5 2829.5 3048.2 3141.8

39 Example 1528.8 1726.0 2018.5 2228.0 2524.5 2829.5 3048.2 3141.8

40 Example Find PMCC 1528.8 1726.0 2018.5 2228.0 2524.5 2829.5 3048.2 3141.8

41 Example Find PMCC 1528.8 1726.0 2018.5 2228.0 2524.5 2829.5 3048.2 3141.8

42 Example of Q that can’t be done using the data function

43 490.2 4 s.f. 0.906 3 s.f.

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