linguistic:paraphrasing
As squared correlation coefficient

In linear least squares multiple regression with an estimated intercept term, R equals the square of the Pearson correlation coefficient between the observed y {\displaystyle y} and modeled (predicted) f {\displaystyle f} data values of the dependent variable.

In a linear least squares regression with a single explanator but without an intercept term, this is also equal to the squared Pearson correlation coefficient of the dependent variable y {\displaystyle y} and explanatory variable x. {\displaystyle x.}

It should not be confused with the correlation coefficient between two explanatory variables, defined as

where the covariance between two coefficient estimates, as well as their standard deviations, are obtained from the covariance matrix of the coefficient estimates, (X T X) − 1 {\displaystyle (X^{T}X)^{-1}}.

Under more general modeling conditions, where the predicted values might be generated from a model different from linear least squares regression, an R value can be calculated as the square of the correlation coefficient between the original y {\displaystyle y} and modeled f {\displaystyle f} data values. In this case, the value is not directly a measure of how good the modeled values are, but rather a measure of how good a predictor might be constructed from the modeled values (by creating a revised predictor of the form α + βƒ). According to Everitt, this usage is specifically the definition of the term "coefficient of determination": the square of the correlation between two (general) variables.