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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>
A confidence interval for ''b'' can be created using a t-distribution with N-2 degrees of freedom:
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