Please consider the following values for the variables X and Y. Treat each row as a pair of scores for the variables X and Y (with the first row providing the labels "X" and "Y").
X | Y |
2 | 4 |
4 | 3 |
6 | 5 |
7 | 7 |
11 | 6 |
Please calculate Pearson's correlation coefficient (r) for these data and report your answer below. When reporting your answer, please provide three decimal places (if relevant).
Solution:
x | y | x2 | y2 | x⋅y |
2 | 4 | 4 | 16 | 8 |
4 | 3 | 16 | 9 | 12 |
6 | 5 | 36 | 25 | 30 |
7 | 7 | 49 | 49 | 49 |
11 | 6 | 121 | 36 | 66 |
x=30 | y=25 | x2=226 | y2=135 | xy=165 |
r = n ( xy )- (x ) (y) / n [ ( x2 ) - ( x )2 ] [ n (y2 ) - ( y )2
r = 5 (165) - (30 * 25 )/ [ 5 * 226 - ( 30 ) 2 [ 5 * 135 - ( 25 ) 2 ]
r = 825 - 750 / 1130 - 900 675 -625
r = 75 / 23050
r = 75 / 15.1658 * 7.0711
r = 75 / 107.2381
r = 0.699
Please consider the following values for the variables X and Y. Treat each row as a...
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