Simple linear regression: Difference between revisions

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: <math> s_\widehat{\beta} = \sqrt{ \frac{\frac{1}{n - 2}\sum_{i=1}^n \widehat{\varepsilon}_i^{\,2}} {\sum_{i=1}^n (x_i -\bar{x})^2} }</math>
 
is the unbiased ''standard error'' estimator of the estimator <math>\widehat{\beta}</math>.
 
This {{mvar|t}}-value has a [[Student's t-distribution|Student's {{mvar|t}}]]-distribution with {{math|''n'' − 2}} degrees of freedom. Using it we can construct a confidence interval for {{mvar|β}}: