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## 11-5 CONFIDENCE INTERVALS

### 11-5.1 Confidence Intervals on the Slope and Intercept

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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, _{i}, in the regression model are normally and independently distributed,

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 β_{1} in simple linear regression is