Question

how much variance has been explained by a correlation of 9​

Answer 1

A correlation of 9 signifies that the correlation explains (9)2=0.81 or 81 percent of the variation.

• The linear relationship among any two variables is expressed by the correlation indicated by "r." When attempting to evaluate a linear relationship, it is assumed that one of them is acting as an independent variable and the other as a dependent variable, which is commonly designated by X and Y, respectively.
• While r signifies the percentage of values of Y explained by X, r2 denotes the percentage of values of Y explained by X.
• As a result, (9)2 = 0.81 would be the proportion of Y variation explained by X. In this scenario, 0.81 can alternatively be interpreted as X explaining 81 percent of the variation in Y.
• However, the absolute value of the covariance.

          p=$\frac{cov(X,Y)}\sqrt{var(X)var(Y)}$

        where p correlation is the proportion of variance explained by correlation, and p² is the fraction of variance explained by correlation.