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A generalization of linear regression allowing for nonlinear relationships via a "link function" and for the variance of the response to depend on the predicted value. (Not to be confused with "general linear model" which extends the ordinary linear model to general covariance structure and multivariate response.)
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How different will that be between the R-squared of linear regression y~x and square of cor(...
Generally, both of them can represent the linear relationship between x and y scale to [0,1].
Are they 99% very similar?