Confidence Interval and Prediction Interval

Confidence Interval (CI)

describes the uncertainty in $\bar Y$ as an estimate of $\mu$, where $\bar Y$ is the sample mean and $\mu$ the population(true) mean

• 95% CI means that the true mean value will be inside this interval with 95% probability

• Suppose repeated samples of Y_i are taken of the same size and at the same fixed values of X as were used to determine the fitted line above. Then of all the 95% CIs constructed for the mean value of Y for a given value of X, $X_0$ say, 95% of these intervals will contain the true value of this mean value of Y at $X_0$
  

Prediction Interval (PI)

describes the uncertainty in $\bar x$ as an estimate of the next measurement value.

95% PI means that next measurement value will be in the interval with 95% probability


reference

• http//webche.ent.ohiou.edu/che408/Confidence%20Intervals_notes.ppt
• Applied regression analysis - Darper, norman Richard. page 29 ..