Confidence regions and bands

Rgure 7.12. F-distribution for 10 and 10 degrees of freedom, showing 95% confidence limit. 

To calculate the 1 - a confidence region, the following relationship can be nsed for the linear case  

This yields an elliptical contour. In more general terms, the 1 — a confidence region is determined by 

As described in Section 7.5.1, the 1 -a confidence interval for the dependent variable y(xo) is determined according to 

If this calculation is performed for several different points (x), a point-wise confidence band is retrieved. It is also possible to determine the 1 - a confidence interval for the value predicted, which is obtained when considering all intervals simultaneously, i.e. 

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