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Question: enter image description here

My problem:

All possible formulae of Multiple and Partial Correlation Coefficient I know :- enter image description here

But I am not sure, which one to use to know about the situation or condition mentioned in the question.

Please help.

Thank you.

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  • 2
    $\begingroup$ In light of your several most recent questions, perhaps you should stop trying to use algebraic formulas and focus instead on learning what these coefficients mean. In this instance, can you articulate what it means for a partial correlation coefficient to be $-1$? To be $1$? $\endgroup$ – whuber Nov 28 '18 at 22:22
  • $\begingroup$ A Multiple correlation coefficient has its range between [0,1] and a Partial correlation coefficient has its range between [-1,1]..Now firstly as the given question has multiplication of a partial and a multiple correlation and a multiple correlation can never be negative, thus such a situation might result only if the partial correlation is -1.. $\endgroup$ – user163580 Nov 28 '18 at 22:55
  • $\begingroup$ Partial correlation_12.345...p is basically the correlation between X1 and X2 excluding influence of variables X3, X4,..,Xp..So if partial correlation is -1, it means there is a negative association between X1 and X2 i.e one decreases with increment of the other..I guess so, as far as my knowledge.. $\endgroup$ – user163580 Nov 28 '18 at 22:55
  • $\begingroup$ Also that the multiple correlation coefficient should be 1.That means X1 is bestly interpreted by the variables X2, X3,..., Xp $\endgroup$ – user163580 Nov 28 '18 at 23:09

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