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: <math> \hat{b} = \frac {\sum_{i=1}^{N} {(x_{i}y_{i})} - N \bar{x} \bar{y}} {\sum_{i=1}^{N} (x_{i})^2 - N \bar{x}^2} = r \frac {s_y}{s_x} </math>
Here, r is the correlation coefficient of X and Y, s<sub>x</sub> is the sample [[standard deviation]] of X and s<sub>y</sub> is the sample standard deviation of Y.
== Inference ==
Under the assumption that the error term is normally distributed, the estimate of the slope coefficient has a [[normal distribution]] with mean equal to '''b''' and standard error given by:
: <math> s_ \hat{b} = \sqrt { \frac {\sum_{i=1}^N \hat{\varepsilon_i}^2 /(N-2)} {\sum_{i=1}^N (x_i - \bar{x})^2} }.</math>
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