Table 3.1.
Computational details for the four examples shown in Figure 3.3
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Recall that each example starts out with the same values of Xi and Yi:
      Xi = {1, 2, 3, 4, 5, 6}  and  Yi = {2, 4, 6, 8, 10, 12}
They differ only with respect to how these values are paired up with one another. Hence, the following values will remain the same from one example to another

N = 6
xXi = 21
xXi2 = 91
 xYi = 42
xYi2 = 364
SSX = 17.5 SSY = 70.0

The only thing that changes is the co-variation, as measured in its rawest form by the sum of the XiYi cross-products (shown in the red cell), and then by SCXY, the sum of co-deviates. Recall that the computational formulas for the relevant SS and SC measures are


and that the formula for the correlation coefficient is
r = SCXY
sqrt[SSX x SSY]

Xi
Yi
  Xi2
Yi2
  XiYi

























SSX = 17.5    SSY = 70.0
sqrt[SSX x SSY] = 35.0
SCXY = 

r = /35 =
Example I (r = +1.0, r2 = 1.0)
Example II (r = +0.66, r2 = 0.44)
Example III (r = —1.0, r2 = 1.0)
Example IV (r = —0.66, r2 = 0.44)
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