After confirming that the fitted model meets the assumptions necessary for linear regression, the next step of a regression analysis is usually to evaluate how well the model is performing in terms of fit and accuracy. R-Squared is one such measure.

**R-squared** is the classic evaluation metric in linear regression, or more precisely if there are multiple predictors, adjusted R-squared. This statistic measures the proportion of variability accounted for through the terms included in the model out of the total variability inherent in the response variable

SSE: Residual Sum of Squares

SST: Total Sum of Squares

Values closer to 1 indicate that the chosen predictors are capturing the majority of variability inherent in the data, meaning the residual sum of squares (SSE) is a small fraction of the total sum of squares (SST). Values close to 0 imply that the model is doing little better than just predicting the overall mean for each observation, meaning most of the variability picked up in the model is from noise.

**Adjusted R-squared** adds a penalty for additional terms included in the model, as regular R-squared will always increase with more terms, even if they are not adding any significance. Adjusted R^{2} is found by :