Prediction Interval and Confidence Interval

Prediction Interval (PI)

a prediction interval reflects the uncertainty around a single value.

Confidence Interval (CI)

a confidence interval reflects the uncertainty around the mean prediction values.

PI v.s CI

Fig.1 Prediction interval v.s Confidence interval

Fig.2 95% confidence interval (grey), 95% prediction interval (red)

How to obtain the Confidence Interval

1. Get a bootstrap sample from the existing dataset.
2. Fit a regression model to the bootstrap sample, and record the estimated coefficients.
3. Repeat steps 1-2, say, 1,000 times.
4. You now have 1,000 bootstrap values for each coefficient; Fin the appropriate percentiles for each one.

Note that there is a formula approach to obtain the confidence interval instead of the bootstrapping approach.