1. 1 Minimum Area Confidence Set (MACS) Criterion for Confidence bands in Simple Linear Regression W. Liu, University of Southampton, UK A.J. Hayter, University of Denver, USA

2. 2 Outline Confidence bands Confidence set of a confidence band MACS criterion Best 3-segment band Best 2-segment band Comparison of best 3-segment band and hyperbola band Discussion

3. 3 Confidence bands

4. 4 Hyperbola band over (a, A)

5. 5 3-segment band

6. 6 2-segment band

7. 7 Confidence set of a band

8. 8

9. 9 Confidence set of the 3-segment band

10. 10

11. 11 Confidence set of the 2-segment band

12. 12

13. 13 MACS criterion

14. 14 Best 3-segment band

15. 15 Best 2-segment band

16. 16

17. 17

18. 18 Comparison of the best 3-segment band and hyperbola band

19. 19 Discussion MACS criterion is related to the D- optimality in design of experiments The average width criterion is the other criterion Future research

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