Correlation and Regression

Two-variable data

Correlation coefficient

r = \frac{1}{n - 1} \sum (\frac{x_{i} - \bar{x}}{s_{x}}) (\frac{y_{i} - \bar{y}}{s_{y}})

Least-squares line

\hat{y} = a + b x

b = r(s_y/s_x), a = ȳ − b·x̄

Residual

residual = y - \hat{y}

actual minus predicted

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