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R-Squared

What is R-Squared?

The R-Squared $(R^2)$ of a regression is an indicator of how well the model explains variation in data. We have observations $\{y_i\}$ with mean $\mu_y$ and the predictions of our model $\{\hat{y_i}\}$.

$$R^2 = \frac{explained\; sum \;of\; squares\; (ESS)}{total\; sum\; of \;squares\; (TSS)}$$

$$R-Squared\; Near\; One\;$$

A graph demonstrating R-Squared near one.

$$R-Squared\; Near\; Zero\;$$

A graph demonstrating R-Squared near zero.