Question

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).

Answer 1

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