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

Study concepts, example questions & explanations for AP Statistics

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Example Questions

Example Question #12 : Confidence Intervals

You estimate a regression model with \(\displaystyle \beta = 3.4\) and \(\displaystyle SE = .024\), where \(\displaystyle \beta\) is the beta coefficient and \(\displaystyle SE\) is the standard error.  Construct 95% confidence intervals for \(\displaystyle \beta\).

Possible Answers:

\(\displaystyle \left [ 3.4,3.45 \right ]\)

\(\displaystyle \left [ 3.1,3.45 \right ]\)

\(\displaystyle \left [ 3.35,3.45 \right ]\)

Correct answer:

\(\displaystyle \left [ 3.35,3.45 \right ]\)

Explanation:

To construct 95% confidence intervals for \(\displaystyle \beta\), we simply take the coefficient and add/subtract \(\displaystyle 1.96\times the\ standard\ error\ of\ \beta\). This is because \(\displaystyle \beta\) 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 \(\displaystyle \beta\).

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