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Correlation Indicates the relationship between two dependent variables (x and y)

Correlation Indicates the relationship between two dependent variables (x and y) Symbol: r (Pearson correlation coefficient) -1< r < 1. Positive Correlation As value of variable X increases, value of variable Y increases. Strong Positive Corr. r = .80.

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Correlation Indicates the relationship between two dependent variables (x and y)

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  1. Correlation Indicates the relationship between two dependent variables (x and y) Symbol: r(Pearson correlation coefficient) -1< r < 1

  2. Positive Correlation As value of variable X increases, value of variable Y increases

  3. Strong Positive Corr. r = .80

  4. Strong positive correlation: - low variability of the data - one variable acts as a good predictor of the second variable.

  5. Weaker Positive Corr. r = .50

  6. Weaker correlations: - More variability in the data - Less predictability

  7. Negative correlation As value of variable X increases, value of variable Y decreases.

  8. Strong negative Corr. r = -.80

  9. Grades Social Activities

  10. No Correlation r = 0 Statistics Ability # of bananas eaten

  11. Variables measured on different scales e.g. Height and weight Correlation formula converts the scores into z-score to make them comparable

  12. Limit of correlation is that it identifies a relationship, but is NOT identifying cause

  13. Multiply each value of X by its corresponding Y. Add the products. Multiply sum by n

  14. Add all the X values. Add all the Y values. Multiply the two sums.

  15. Variation of the formula for SS for X

  16. Variation of the formula for SS of Y

  17. Quiz One Quiz Four (X) (Y) 28 30.5 28 29.5 30 39 29 36.5 21 30.5

  18. Quiz One Quiz Four (X) (Y) 28 30.5 28 29.5 30 39 29 36.5 21 30.5  X = 136  Y = 166

  19. Quiz One Quiz Four (X) X2 (Y) 28 784 30.5 28 784 29.5 30 900 39 29 841 36.5 21 441 30.5  X2 = 3750

  20. Quiz One Quiz Four (X) (Y) Y2 28 30.5 930.25 28 29.5 870.25 30 39 1521 29 36.5 1332.25 21 30.5 930.25   Y2 = 5584

  21. Quiz One Quiz Four (X) (Y) (X)(Y) 28 30.5 854 28 29.5 826 30 39 1170 29 36.5 1058.5 21 30.5 640.5  XY = 4549

  22.  X = 136  Y = 166  X2 = 3750  Y2 = 5584  XY = 4549 n = 5

  23. Critical Value: df = n -- 2 r crit. = .878

  24. df Critical r 3 .878 5 .754 10 .576 20 .423 50 .273 100 .195

  25. How much variability of X and Y is jointly shared?

  26. How much of the variability of X can be accounted for by variability in Y?

  27. r2 = the strength or the amount of shared variability

  28. r r2 .9 .81 or 81% .8 .64 or 64% .7 .49 or 49%

  29. df Critical r 3 .878 5 .754 10 .576 20 .423 50 .273 100 .195

  30. # of absences test grade 8 35 0 48 3 43 2 41 5 39 6 36  X = 24 Y = 242

  31. # of absences test grade 8 64 35 1225 0 0 48 2304 3 9 43 1849 2 4 41 1681 5 25 39 1521 6 36 36 1296 X2= 138 Y2 = 9876

  32. # of absences test grade 8 35 280 0 48 0 3 43 129 2 41 82 5 39 195 6 36 216 xy = 902

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