A random sample of two variables,x and y,produced the following observations: Compute the correlation coefficient for these sample data.
A)-0.9707
B)-0.2141
C)0.5133
D)0.8612

Question

A random sample of two variables,x and y,produced the following observations:  Compute the correlation coefficient for these sample data.
A)-0.9707 
B)-0.2141 
C)0.5133 
D)0.8612

Quizplus · Accepted Answer

To find the correlation coefficient, we need to use the formula:
r = (nΣxy - ΣxΣy) / sqrt([nΣx²-(Σx)²][nΣy²-(Σy)²])
Using the given data, we get:
n = 11
Σx = 72
Σy = 85
Σxy = 593
Σx² = 956
Σy² = 1165
Plugging these values into the formula, we get:
r = (11*593 - 72*85) / sqrt([11*956-(72)²][11*1165-(85)²])
r = -0.9707
Therefore, the best choice is A because it is the only option that matches this value.

A Random Sample of Two Variables,x and Y,produced the Following