We are now ready to give a definition of R squared. On the contrary, the less the predictions of the linear regression model areĪccurate, the highest the variance of the residuals is. Then the residuals are always equal to zero and their sample variance is also Intuitively, when the predictions of the linear regression model are perfect, Variability of the outputs that we are not able to explain Is a measure of the variability of the residuals, that is, of the part of the Unless stated otherwise, we are going to maintain the assumption that Variance of the residuals when the sample mean of the Variability that we are trying to explain with the regression Is a measure of the variability of the outputs, that is, of the Regression: Sample variance of the outputs (for example, an OLS estimate), we compute the residuals of the We choose a definition that is easy to understand, and then we make some brief In which the linear regression includes a constant among its regressors. Usually, these definitions are equivalent in the special, but important case Several slightly different definitions can be found in the More details about the degrees-of-freedom adjustmentīefore defining the R squared of a linear regression, we warn our readers that
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