How to find confidence intervals for the slope of a least-squares regression line - AP Statistics
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Question
You estimate a regression model with 
and 
, where 
is the beta coefficient and 
is the standard error. Construct 95% confidence intervals for 
.
You estimate a regression model with
Answer
To construct 95% confidence intervals for 
, we simply take the coefficient and add/subtract 
. This is because 
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 
.
To construct 95% confidence intervals for
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