How to find confidence intervals for the slope of a least-squares regression line

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AP Statistics › How to find confidence intervals for the slope of a least-squares regression line

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You estimate a regression model with $\beta = 3.4$ and , where $\beta$ is the beta coefficient and is the standard error. Construct 95% confidence intervals for $\beta$ .

$\left [ 3.35,3.45 \right ]$

$\left [ 3.4,3.45 \right ]$

$\left [ 3.1,3.45 \right ]$

Explanation

To construct 95% confidence intervals for $\beta$ , we simply take the coefficient and add/subtract $1.96\times the\ standard\ error\ of\ \beta$ . This is because $\beta$ is assumed to follow a symmetrical distribution (the normal), and 95% of the values in the sampling distribution are contained within 1.96 standard errors of $\beta$ .

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