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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A. If means of both the variables are equal
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C. If there is linear relationship between two variables
D. If data are obtained in interval or ratio scale for both the variables
E. If direction of relationship between two variables is known
Choose the most appropriate answer from the options given below :
