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11-5   CONFIDENCE INTERVALS

11-5.1   Confidence Intervals on the Slope and Intercept

In addition to point estimates of the slope and intercept, it is possible to obtain confidence interval estimates of these parameters. The width of these confidence intervals is a measure of the overall quality of the regression line. If the error terms, imagesi, in the regression model are normally and independently distributed,

Images

are both distributed as t random variables with n – 2 degrees of freedom. This leads to the following definition of 100(1 – α)% confidence intervals on the slope and intercept.

Confidence Intervals on Parameters

Under the assumption that the observations are normally and independently distributed, a 100(1 – α)% confidence interval on the slope β1 in simple linear regression is


  

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