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.
Similar Questions
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Important Questions from Correlation Analysis
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): If the securities with less than perfect negative correlation between their price movements are combined, portfolio risk can be reduced significantly.
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:
X, Y and Z are three uncorrelated variables having variances \(\sigma_x^2, \sigma_y^2 \:and\:\sigma_z^2\) respectively, then the correlation between X + Y and Y + Z is:
If X ∼ N (0, 1) and Y = X2 then the correlation coefficient r (X, Y) is
Calculate the correlation coefficient between the following values :
x: 3, 5, 1, 7, 5
y: 4, 3, 0, 8, 2
Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z = X + Y and r be the correlation coefficient between X and Y. If the variance of Z equals 0, then the value of r is _______ (round off to 2 decimal places).
