The limit of multiple correlation coefficient R 1.23 are:
0 to 1
The multiple correlation coefficient \(R_{1.23}\) is the simple correlation between \(X_{1}\) and its best linear predictor \(\hat X_{1}\) based on \(X_{2}, X_{3}\). Because the predicted values are scaled to move in the same direction as \(X_{1}\), this correlation is never negative.
Equivalently, \(R^{2}\) is a proportion of variance explained, so \(0\le R^{2}\le 1\) and therefore \(0\le R\le 1\). The range \(-1\) to \(1\) belongs to the simple correlation \(r\), not \(R\). Hence the limits are 0 to 1.
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Important Questions from Correlation Analysis
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Reason (R): The term with negative correlation has the effect of reducing the computed value of total portfolio risk, given other terms that are positive.
In the light of the above statements, choose the most appropriate answer from the options given below:
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