Math — Least-Squares Regression

\hat{y} = \beta_0 + \beta_1 x

\beta_1 = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}

r = \frac{\sum (x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum(x_i-\bar{x})^2 \sum(y_i-\bar{y})^2}}

R^2 = 1 - \frac{SS_{res}}{SS_{tot}}