Correlation Indicates the relationship between two dependent variables

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

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

Weaker Positive Corr. r =. 50

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

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

Strong negative Corr. r = -. 80

Grades Social Activities

No Correlation r=0 Statistics Ability # of bananas eaten

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

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

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

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

Variation of the formula for SS for X

Variation of the formula for SS of Y

Quiz One Quiz Four (X) (Y) 28 30. 5 28 29. 5 30 39 29 36. 5 21 30. 5

Quiz One Quiz Four (X) (Y) 28 30. 5 28 29. 5 30 39 29 36. 5 21 30. 5 X = 136 Y = 166

Quiz One Quiz Four (X) X 2 28 784 30. 5 28 784 29. 5 30 900 39 29 841 36. 5 21 441 30. 5 X 2 = 3750 (Y)

Quiz One Quiz Four (X) (Y) Y 2 28 30. 5 930. 25 28 29. 5 870. 25 30 39 1521 29 36. 5 1332. 25 21 30. 5 930. 25 Y 2 = 5584

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

X = 136 Y = 166 X 2 = 3750 Y 2 = 5584 XY = 4549 n=5

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

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

How much variability of X and Y is jointly shared?

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

r 2 = the strength or the amount of shared variability

r r 2 . 9 . 81 or 81% . 8 . 64 or 64% . 7 . 49 or 49%

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

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

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

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