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12.1 Determine the Pearson product-moment correlation coefficient for the following data. x 1 11 9 7...

12.1 Determine the Pearson product-moment correlation coefficient for the following data.

x

1 11 9 7 5 3 2

y

9 4 6 5 7 7 8


(Do not round the intermediate values. Round your answer to 3 decimal places.)


Correlation coefficient, r = enter the Correlation coefficient rounded to 3 decimal places

Solutions

Expert Solution

Solution:

x y x2 y2 x⋅y
1 9 1 81 9
11 4 121 16 44
9 6 81 36 54
7 5 49 25 35
5 7 25 49 35
3 7 9 49 21
2 8 4 64 16
x=38 y=46 x2=290 y2=320 xy=214

r = n ( xy )- (x ) (y) / n [ ( x2 ) - ( x )2 ] [ n (y2 ) - ( y )2

r = 7 (214) - (38 * 46) / [7 *290 - ( 38 ) 2   [ 7 * 320 - ( 46 ) 2 ]

r = 1498 - 1748 / 2030 - 1444  2240 - 2116

r = 250 /  586124

r = 250 / 269.5626

r = 2656 / 2910.80

r = - 0.9274

.The Correlation coefficient = - 0.927


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